Theory of the Transition in KH2PO4
TL;DR: In this paper, the theory of spontaneous polarization along the axis of the crystal, resulting in a well-known transition, similar to Rochelle salt, with polarization below the Curie point was worked out.
Abstract: Potassium dihydrogen phosphate contains phosphate groups connected by hydrogen bonds. Different possible arrangements of the hydrogens result effectively in different orientations of the (H2PO4)— dipoles. Since these have the lowest energy when pointing along the axis of the crystal, there is a tendency toward spontaneous polarization along this axis, resulting in the well‐known transition, similar to Rochelle salt, with polarization below the Curie point. The theory of this transition is worked out, using statistical methods to count the number of arrangements of hydrogens consistent with each total polarization of the crystal, and deriving the free energy. It is found that the theory predicts a phase change of the first order, with sudden transition from the polarized state at low temperature to the unpolarized state at high temperature, rather than the lambda‐point transition or phase change of the second order which is observed. However, the observed transition is confined to a very narrow temperature range compared to that predicted, for instance, by the Weiss theory, so that it seems as if it might be merely a broadened transition of the first order. It is suggested that the broadening may result from the irregular shifts of transition temperatures of individual domains in the crystal on account of stresses resulting from the large piezoelectric effect and the resulting deformation of the crystal below the transition point. The susceptibility above the Curie point comes out by the theory to be 4.33 times as great as it should according to the Weiss theory, a result which seems to be in general agreement with experiment. The entropy change in the transition is given by the theory as 0.69 unit, somewhat smaller than the observed value of about 0.8 unit. No explanation is suggested for this discrepancy.
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TL;DR: In this paper, the fundamental physics behind the scarcity of ferromagnetic ferroelectric coexistence was explored and the properties of known magnetically ordered ferro-electric materials were examined.
Abstract: Multiferroic magnetoelectrics are materials that are both ferromagnetic and ferroelectric in the same phase. As a result, they have a spontaneous magnetization that can be switched by an applied magnetic field, a spontaneous polarization that can be switched by an applied electric field, and often some coupling between the two. Very few exist in nature or have been synthesized in the laboratory. In this paper, we explore the fundamental physics behind the scarcity of ferromagnetic ferroelectric coexistence. In addition, we examine the properties of some known magnetically ordered ferroelectric materials. We find that, in general, the transition metal d electrons, which are essential for magnetism, reduce the tendency for off-center ferroelectric distortion. Consequently, an additional electronic or structural driving force must be present for ferromagnetism and ferroelectricity to occur simultaneously.
3,146 citations
TL;DR: This research opens up a new class of multiferroics in which the electrical ordering is achieved by means of hydrogen bonding, and the compounds become canted weak ferromagnets below 40 K.
Abstract: Multiferroic behavior in perovskite-related metal−organic frameworks of general formula [(CH3)2NH2]M(HCOO)3, where M = Mn, Fe, Co, and Ni, is reported. All four compounds exhibit paraelectric−antiferroelectric phase transition behavior in the temperature range 160−185 K (Mn: 185 K, Fe: 160 K; Co: 165 K; Ni: 180 K); this is associated with an order−disorder transition involving the hydrogen bonded dimethylammonium cations. On further cooling, the compounds become canted weak ferromagnets below 40 K. This research opens up a new class of multiferroics in which the electrical ordering is achieved by means of hydrogen bonding.
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TL;DR: In this article, the problem of finding the number of ways of drawing arrows on the bonds of a square planar net so that precisely two arrows point into each vertex was studied.
Abstract: At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits two possible positions for the hydrogen atom, subject to certain constraints called the “ice condition.” The statement of the problem in two dimensions is to find the number of ways of drawing arrows on the bonds of a square planar net so that precisely two arrows point into each vertex. If N is the number of molecules and (for large N) W N is the number of arrangements, then S = Nk lnW. Our exact result is W = (4/3)3/2.
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TL;DR: In this article, the experimental studies of displacive phase transitions in solids are summarized, focusing on inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized.
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 ($\ensuremath{\omega}g{10}^{11}$ 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).
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TL;DR: In a qualitative way, the anomalous properties of Rochelle salt can be explained on the basis of four different theories: ($a$) on the dipole theory, ($b$) by assuming polymorphic transitions at the Curie points, ($c) by postulating an anomalous piezoelectric effect, and ($d$) with an interaction theory which assumes that the structure and the fundamental properties of the crystal have no unusual characteristics as mentioned in this paper.
Abstract: In a qualitative way the anomalous properties of Rochelle salt can be explained on the basis of four different theories: ($a$) on the dipole theory, ($b$) by assuming polymorphic transitions at the Curie points, ($c$) by postulating an anomalous piezoelectric effect, and ($d$) with an inter-action theory which assumes that the structure and the fundamental properties of the crystal have no unusual characteristics and which ascribes the observed anomalies to an accidental degeneration of the piezoelectric interaction between the elastic deformation and the electric polarization. The existence of a polymorphic transition at the upper Curie point is demonstrated in a new experiment and it is shown that this transition is a spontaneous elastic deformation. It can be explained on the basis of either one of the four theories. A quantitative analysis of the experimental data, which leads to a new interpretation of the elastic and piezoelectric measurements, shows that the theories ($b$) and ($c$) are not valid for Rochelle salt. The experimental data verify the conclusions of the dipole theory insofar as they lead to the result that Rochelle salt would show an abnormal temperature dependence of the dielectric constant even if the crystal were not piezo-electric or if the piezoelectric deformations could be suppressed. However, it is doubtful whether the clamped crystal has a Curie point. The observed Curie points of the free crystal result from the lattice-dipole coupling as described by the interaction theory.
92 citations