Katsumi Hamano

Critical Phenomena and Anomalous Thermal Hysteresis Accompanying the Normal-Incommensurate-Commensurate Phase Transitions in Rb2ZnCl4

Measurements were made of the dielectric constant along the ferroelectric axis e a , the spontaneous polarization P s and the heat capacity c p of Rb 2 ZnCl 4 crystals in the temperature range from -150^° C to 150°C. The normal-incommensurate transition point determined as the peak position of c p lies at 30.1°C, which is about 6°C lower than the temperature for the maximum of e a . It was found that e a and P s show a characteristic thermal hysteresis over a wide temperature range including the incommensurate-commensurate trarasition point (-80^° C ). The thermal hysteresis occurs even when heating and cooling runs are cycled within the incommensurate phase. The observed thermal hysteresis is understood if we assume that defects such as impurities act as obtacles to diffusion of discommensurations and prevent the crystal from reaching thermal equilibrium.

X-Ray Study on the Thermal Hysteresis of the Modulation Wavevector in (Rb1-xKx)2ZnCl4

The modulation wavevector \(k_{z}{=}(\frac{1}{3}{-}\delta)c^{*}\) exhibits remarkable thermal hysteresis over a wide temperature range including the incommensurate-commensurate transition point in the mixed crystal system (Rb 1- x K x ) 2 ZnCl 4 with x =0, 0.005, 0.02, 0.28, 0.92, 0.997 and 1. This hysteresis seems to correspond to the thermal hysteresis observed in the dielectric constant and to support the proposal by Hamano et al . that the pinning of the modulation wave by defects causes the hysteresis. In the Rb rich case ( x ≦0.02), the parameter δ has a tendency to be fixed to the value realized at the normal-incommensurate transition point. In the K rich case ( x =0.997), it decreases monotonically with decreasing temperature, with a plateau in a middle range of the incommensurate phase. In the middle range of x , δ is pinned to a constant value down to low temperature.

Effect of impurities on the incommensurate-commensurate phase transitions in Rb2ZnCl4, K2ZnCl4 and Rb2ZnBr4

Abstract The thermal hysteresis accompanying the incommensurate-commensurate phase transitions in Rb2ZnCl4, K2ZnCl4 and Rb2ZnBr4 is assumed to be caused by pinning of the incommensurate wave by defects in the crystal. The results obtained for (Rb1-xKx)2ZnCl4 mixed crystal system are also well explained in terms of such pinning effect of defects.

Transient Dielectric Behavior during the Commensurate-to-Incommensurate Phase Transition in Rb2ZnCl4

The kinetic process of the commensurate-to-incommensurate phase transition in Rb 2 ZnCl 4 has been studied by tracing the time variations of the polarization and dielectric constant during the transition induced by removing the applied high dc electric field from the sample. The polarization shows an abrupt dropat the instant of field removal and then decays monotonically. The dielectric constant first increases, reaches a maximum and then decreases toward the thermal equilibrium value. The relaxation process slows down as T c is approached from above. A qualitative explanation of the observed transient characteristics is presented on the basis of a nucleation model. It is suggested that at an early stage of the transition the nucleated discommensurations are spaced more widely than in the final thermal equilibrium state.

Spontaneous Polarization Measurement in NaNo2

Spontaneous polarization of NaNO 2 was determined by reversing P s with a relatively low d c field of from 60 V/cm to 12 kV/cm and measuring the polarization reversal charge with an electrometer and a recorder. A clear jump in P s of 5.8 µC/cm 2 was observed at the Curie point T c . The dielectric constant e 22 in the ferroelectric phase obeys the Curie-Weiss law very well over a wide temperature range and P s is proportional to (1- T / T 0 ) 0.20±0.02 over 25°C below T c , where T 0 is the ferroelectric Curie-Weiss temperature. Below room temperature P s does not vary appreciably. The saturation polarization is estimated to be 11.9 µC/cm 2 . The electronic contribution to P s is discussed on the basis of a point-dipole approximation. It is probable that about one third of the total spontaneous polarization is contributed from the electronic polarization. The experimental technique is described in detail.

Piezoelectric Property of SbSl Single Crystal

The piezoelectric modulus d 33 , electromechanical coupling factor k 33 and elastic compliance coefficients s 33 D , s 33 E of SbSI have been determined by measuring the resonant and anti-resonant frequencies on single crystals of 3 mm in length and 0.7×0.7 mm 2 in cross section. The d 33 has been found to show the highest value of 10 -4 cgsesu near the Curie point. The k 33 shows an extremely high value of 90% just below the Curie point and nearly constant value of about 75∼85% in the range of temperature below 0°C.

Effect of purification on dielectric properties near the commensurate-incommensurate transition point of Rb2ZnCl4

Abstract Purification of Rb2ZnCl4 by recrystallization and zone melting is described in detail and the results of chemical analysis are given. Single crystals were grown from an aqueous solution which had been purified by repeated recrystallization. The thermal hysteresis of the dielectric constant in the purified crystal was reduced to 0.2 K from 2.8 K in the unpurified crystal. The switching time of the field-induced commensurate-incommensurate transition was shortened significantly in the vicinity of Tc . These indicate the weakening of pinning in the purified crystal. The low relaxation frequency of domain wall motion in the commensurate phase starts to rise abruptly when the transition to the incommensurate phase begins. This is understood to reflect a process in which the isolated domain walls are incorporated into the discommensuration lattice of the incommensurate phase. The mathematical analysis of the ordinary recrystallization process and the reverse process is given in Appendix.

Elastic Anomalies of Rb2ZnCl4 around the Normal-Incommensurate Phase Transition Point

Ultrasonic velocities and attenuations of Rb 2 ZnCl 4 were measured as functions of temperature. The observed anomalies of the velocities are discussed in relation to the incommensurate soft mode.

Thermal Hysteresis Accompanying the Incommensurate-Commensurate Phase Transitions in Rb2ZnBr4 and Rb2ZnCl4

The dielectric constants of Rb 2 ZnBr 4 and Rb 2 ZnCl 4 exhibit remarkable thermal hysteresis over wide temperature ranges including their incommensurate-commensurate transition points. The most characteristic feature of this thermal hysteresis is that it occurs even when a cooling run is turned to a heating run in the incommensurate phases, i.e., the thermal hysteresis occurs even when the crystal has no experience of phase transition. This phenomenon was studied in detail in this work. If the turning temperature T turn is in the range where the incommensurate wave number is independent of temperature (the range of constant δ), the thermal hysteresis does not occur, while if T turn is in the range of varying incommensurate wave number (the range of varying δ), the thermal hysteresis appears. This fact seems to support our idea that the thermal hysteresis of the dielectric constant is caused by pinning of the incommensurate wave.

X-Ray Study on the Thermal Hysteresis of the Incommensurate Wave Number in Rb2ZnCl4

The incommensurate wave number \(k_{z}=(\frac{1}{3}-\delta)c^{*}\) in Rb 2 ZnCl 4 has been investigated by X-ray scattering. Over a wide temperature range including the incommensurate-commensurate transition point the parameter δ and the width of the satellite reflection show thermal hystereses which seem to correspond to the thermal hysteresis of the dielectric constant observed by Hamano et al.