Surveys recent theories on the transition between commensurate (C) and incommensurate (I) phases, and on properties of the I phase. The devil's staircase concept for the I phase is described. Differences between theories in two and three dimensions are discussed, together with those on chaotic structures.

https://iopscience.iop.org/article/10.1088/0034-4885/45/6/001/pdf

Commensurate phases, incommensurate phases and the devil's staircase

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

Inorganic perovskite ferroelectrics are widely used in nonvolatile memory elements, capacitors, and sensors because of their excellent ferroelectric and other properties. Organic ferroelectrics are desirable for their mechanical flexibility, low weight, environmentally friendly processing, and low processing temperatures. Although almost a century has passed since the first ferroelectric, Rochelle salt, was discovered, examples of highly desirable organic perovskite ferroelectrics are lacking. We found a family of metal-free organic perovskite ferroelectrics with the characteristic three-dimensional structure, among which MDABCO ( N -methyl- N9 -diazabicyclo[2.2.2]octonium)–ammonium triiodide has a spontaneous polarization of 22 microcoulombs per square centimeter [close to that of barium titanate (BTO)], a high phase transition temperature of 448 kelvins (above that of BTO), and eight possible polarization directions. These attributes make it attractive for use in flexible devices, soft robotics, biomedical devices, and other applications.

http://science.sciencemag.org/content/sci/361/6398/151.full.pdf

Metal-free three-dimensional perovskite ferroelectrics

Superionic conductors are compounds that exhibit exceptionally high values of ionic conductivity within the solid state. Indeed, their conductivities often reach values of the order of 1 Ω−1 cm−1, which are comparable to those observed in the molten state. Following Faraday's first observation of high ionic conductivity within the solids β-PbF2 and Ag2S in 1836, a fundamental understanding of the nature of the superionic state has provided one of the major challenges in the field of condensed matter science. However, experimental and theoretical approaches to their study are often made difficult by the extensive dynamic structural disorder which characterizes superionic conduction and the inapplicability of many of the commonly used approximations in solid state physics. Nevertheless, a clearer picture of the nature of the superionic state at the ionic level has emerged within the past few decades. Many different techniques have contributed to these advances, but the most significant insights have been provided by neutron scattering experiments and molecular dynamics simulations. This review will summarize the state of current knowledge concerning the crystal structures and conduction processes of superionic conductors, beginning with a comparison of the behaviour of two of the most widely studied binary compounds, AgI and β-PbF2. Each can be considered a parent of two larger families of highly conducting compounds which are related by either chemical or structural means. These include perovskite-structured oxides and Li+ containing spinel-structured compounds, which have important commercial applications in fuel cells and lightweight batteries, respectively. In parallel with these discussions, the relative importance of factors such as bonding character and the properties of the mobile and immobile ions (charge, size, polarizability, etc) in promoting the extensive lattice disorder which characterizes superionic behaviour will be assessed and the possibilities for predicting a priori which compounds will display high ionic conductivity discussed.

/pdf/superionics-crystal-structures-and-conduction-processes-1q9bpg4zfv.pdf

Superionics: crystal structures and conduction processes

Induced multiferroics, where ferroelectricity arises through the magnetic order, have attracted significant interest, despite maximum Curie temperatures of only 40 K. The discovery of multiferroic coupling up to 230 K in CuO therefore represents a major advance towards high-TC multiferroics. Materials that combine coupled electric and magnetic dipole order are termed ‘magnetoelectric multiferroics’1,2,3,4. In the past few years, a new class of such materials, ‘induced-multiferroics’, has been discovered5,6, wherein non-collinear spiral magnetic order breaks inversion symmetry, thus inducing ferroelectricity7,8,9. Spiral magnetic order often arises from the existence of competing magnetic interactions that reduce the ordering temperature of a more conventional collinear phase10. Hence, spiral-phase-induced ferroelectricity tends to exist only at temperatures lower than ∼40 K. Here, we propose that copper(II) oxides (containing Cu2+ ions) having large magnetic superexchange interactions11 can be good candidates for induced-multiferroics with high Curie temperature (TC). In fact, we demonstrate ferroelectricity with TC=230 K in cupric oxide, CuO (tenorite), which is known as a starting material for the synthesis of high-Tc (critical temperature) superconductors. Our result provides an important contribution to the search for high-temperature magnetoelectric multiferroics.

Cupric oxide as an induced-multiferroic with high-TC.

The temperature dependence of the X-ray diffraction intensity was precisely measured in order to clarify the nature of the ferroelectric phase transition in NaNO 2 . At the transition point, 163°C, the integrated intensity of the Bragg reflection decreases quite abruptly and distinct satellite peaks appear which are observed in a very narrow temperature range and which become diffuse with increasing temperature. It was concluded that the ferroelectric NaNO 2 crystal transforms through the first order transition to an antiferroelectric phase with a sinusoidal modulation of the moment in which the antiferroelectric order is partially attained. The system again meets with another transition to the paraelectric phase at certain temperature above the first transition point. A thermodynamic calculation on the basis of a molecular field approximation was performed. The successive appearance of three phases, the orders of transitions, the temperature dependence of the order parameter and the anomalous volume expa...

Phase Transition in NaNO2

Temperature dependence of neutron diffraction intensities of PbZrO 3 was measured in the room-temperature antiferroelectric phase. Intensities of strong superlattice reflections with wave vectors q Σ ≡(1/4 1/4 0) and q R ≡(1/2 1/2 1/2) show different temperature dependence each other. Intensities of weak superlattice reflections with q P ≡(1/4 1/4 1/2)= q Σ + q R and products of intensities of reflections with q Σ and q R show the same temperature dependence. The crystal structure previously determined by Fujishita et al. [ref. 4] was reexamined; the structure was found to be described by a sum of modulations associated with lattice vibrational modes Σ 3 , R 25 x and R 25 y . Successive phase transitions concerning these modulations were observed at 233°C and at around 235°C on heating, and at around 235°C and at 228°C on cooling. Because the modulation with q R is associated with mode R 25 , another antiferroelectric structural modulation which exists only in the intermediate antiferroelectric phase is r...

A Study of Structural Phase Transitions in Antiferroelectric PbZrO3 by Neutron Diffraction

The magnetic properties of single crystals of Cr alloys containing a small amount of Fe have been studied mainly by neutron diffraction. The alloys with less than 1.5 at.% Fe have been found to have the same magnetic structure as that of pure Cr. With increasing Fe concentration, which corresponds to an increase of the electron to atom ratio, the Neel temperature decreases, the wave vector of the sinusoidally modulated spin density wave increases, while the magnetic moment remains almost constant. The spin-flip temperature also decreases rapidly. The alloys with concentrations between 2 and 4 at% Fe have a simple antiferromagnetic structure at low temperatures, and the first order transition from the antiferromagnetic state to a sinusoidal spin state has been observed with increasing temperature. When the concentration of Fe exceeds 4 at%, the alloy is a simple antiferromagnet up to the Neel temperature. These results are discussed on the basis of the two band model.

Antiferromagnetism in Dilute Iron Chromium Alloys

Distribution and anharmonic thermal vibration of cations in α-AgI

The precise temperature dependence of x-ray diffraction effects near the transition temperature of ferroelectric NaNO2 crystal has been examined The satellite reflections, 1±σ 5 0, start to appear at Ts, 02°C below the well-known first-order transition point Tt Marked asymmetry of the satellite reflections was sometimes observed when a multi-domain crystal was measured The period of the sinusoidal modulation along the a-axis varies from 103 a0 to 84 a0 with increasing temperature The effect of a d c external field along the b-axis on the x-ray diffraction effect was also examined The experimental evidence indicates the presence of a new phase between Ts and Tt Some thermodynamical calculations for the phase transition of NaNO2 were carried out To explain the intensity asymmetry of the satellite reflections the diffraction effect for a distorted crystal was also calculated

Sadao Hoshino

Papers

Phase Transition in NaNO2

A Study of Structural Phase Transitions in Antiferroelectric PbZrO3 by Neutron Diffraction

Antiferromagnetism in Dilute Iron Chromium Alloys

Distribution and anharmonic thermal vibration of cations in α-AgI

X-Ray Study on the Phase Transition of NaNO2