Ferroelastic Crystals Research Articles

Determination of quadrupolar spin coupling for spin 7/2 using two pulse sequences

The response of a spin 7/2 system subject to a first-order quadrupolar interaction and excited by two in-phase pulses separated by time delay τ is calculated ignoring high frequency terms. The results obtained are valid for any ratio of the quadrupolar coupling to the amplitude of an RF pulse. It is shown here that single- and multiple-quantum coherences developed during the first pulse can be detected at the end of the second pulse. Other pulse sequences with various phase cycling are also discussed. The results are applied to 51V nuclei in a single ferroelastic crystal of BiVO4.

First order transitions by conduction calorimetry: Application to deuterated potassium dihydrogen phosphate ferroelastic crystal under uniaxial pressure

The specific heat c and the heat power W exchanged by a Deuterated Potassium Dihydrogen Phosphate ferroelectric-ferroelastic crystal have been measured simultaneously for both decreasing and increasing temperature at a low constant rate (0.06 K/h) between 175 and 240 K. The measurements were carried out under controlled uniaxial stresses of 0.3 and 4.5±0.1 bar applied to face (110). At Tt=207.9 K, a first order transition is produced with anomalous specific heat behavior in the interval where the transition heat appears. This anomalous behavior is explained in terms of the temperature variation of the heat power during the transition. During cooling, the transition occurs with coexistence of phases, while during heating it seems that metastable states are reached. Excluding data affected by the transition heat, the specific heat behavior agrees with the predictions of a 2-4-6 Landau potential in the range of 4–15 K below Tt while logarithmic behavior is obtained in the range from Tt to 1 K below Tt. Data obtained under 0.3 and 4.5 bar uniaxial stresses exhibit the same behavior.

Elastooptic light diffraction on the domain structure of Pb3(PO4)2 ferroelastic crystals

The results of the investigation of elastooptic light diffraction on ferroelastic domains in Pb3(PO4)2 crystals are submitted in this paper. The description of the orientation of the optical indicatrices in various domains at the ferroelastic phase transition with a change of symmetry is made. The temperature and angular dependencies of the diffraction efficiency are obtained. It is found that most probably the change of the diffraction angle wih temperature is connected to the change of the orientation of W'-–domain walls.

Deflection of light by phase boundaries in antiferroelectric liquid crystals

Light deflection phenomena in an antiferroelectric chiral smectic liquid crystal MHPOBC were investigated. At electric field induced phase transitions between antiferroelectric (AF) state to ferroelectric (F) one, characteristic deflected lights were observed; dependence of the angle of deflection on temperatures and on angles of incidence were quite different from those of diffraction lights due to a periodical change of refractive index caused by helical structure of chiral liquid crystals. On the basis of numerical analysis for domain walls of ferroelastic crystals, it is concluded that the light deflection is due to refraction and reflection phenomena at the phase boundaries between AF and F states coexisting at the field induced phase transition.

Monoclinic Spin Hamiltonian Analysis of EPR Spectra of Mn2+ in BiVO4 Single Crystals

AbstractX‐band EPR spectra of Mn2+ in ferroelastic BiVO4 single crystals at room temperature taken in three orthogonal planes are analyzed using a twestage least‐squares fitting procedure. The absence of site splitting from the spectra shows unequivocally that Mn2+ lies on a site with two‐fold rotation symmetry, whose two fold axis is parallel to the monoclinic crystal axis. The low symmetry effects arising from the monoclinic site symmetry are evidenced by the observed coincidence of the extrema for transitions between different Zeeman levels along the monoclinic axis, and by the 180° rotational symmetry in the monoclinic plane and a small noncoincidence of the turning points in this plane. In the first stage, the spectra are fitted using the monoclinic form of the electronic Zeeman and fine structure terms (of second and fourth degree) appropriate for the crystallographically determined orientation of the monoclinic axis. In the second stage, fitting of the nuclear hyperfine tensor (A) and the nuclear quadrupole tensor (P) is carried out with fixed values of the electronic Zeeman tensor (g) and fine structure terms, i.e. the tensor (D) and the fourth‐degree terms, as obtained in the first stage. The principal axes of g, D, A, and P are found to be non‐coincident in the monoclinic plane, as would be generally expected for a monoclinic site.

Mesoscopic structures in ferroelastic crystals: needle twins and right-angled domains

The shape and orientation of twin walls are calculated within the limits of elasticity theory. Single twin walls are oriented along lattice planes which are determined by the condition that the variation in the spontaneous strain through the twin walls does not generate secondary strain fields. The twin walls have a finite thickness which is described by the Landau - Ginzburg theory. Two twin walls can bend towards each other and form a wedge-shaped junction. The trajectories of the twin walls in the plane perpendicular to the junction are needle shaped so that domains enclosed by the twin walls are commonly called `needle domains'. It is shown that the actual shape of the trajectory varies widely between straight lines (i.e. planar walls near the junction) to parabolic or exponential (i.e. curved twin walls near the junction which make the needle tip appear blunt). The essential physical parameters which determine the shape of the trajectory are, firstly, the energies to bend a wall segment, secondly, the energy required to rotate a planar wall segment in an elastically anisotropic medium and, thirdly, the Peierls energy which is required to move a walls segment laterally. Various characteristic trajectories are discussed including those of junctions between orthogonal walls.

Peculiarities of thermal switching in sodium niobate crystals

The temperature dependence of orientation of W'-type domain walls in a ferroelastic crystal was determined using a polarizing microscope. Results obtained are discussed in relation to the temperature dependence of lattice unit cell parameters based on the Sapriel theory.

Simultaneous measurement of specific heat and latent heat of ferroelastic crystal under uniaxial stress

The specific heat C of SrTiO3 and DKDP ferroclastic crystals was measured under an applied uniaxial stress with a conduction calorimeter whose fluxmeters were built to obtain linear heat conduction and with enough rigidity to apply a controlled uniaxial stress on the sample. The measurements were carried out decreasing the temperature at a constant rate of 0.06K/h; thus the readings of the e.m.f. given by the fluxmeter, when there is no dissipation in the heaters, allow us to calculate the heat flux dQ/dt exchanged by the sample during a first order phase transition. These simultaneous measurements allow us to discriminate the specific heat data affected by the transition heat during the measurement process. The specific heat of SrTiO3 was measured under a constant stress of 0, 2, 4 and 5 kg/cm2 on the face (110).

Some ferroelastic and ferroelectric systems with coupled softening modes

Abstract Various ferroelastic and ferroelectric systems display several softening optic modes, all of which seem often to be related to the one observed transition. Furthermore, some of the soft modes have the symmetry of the order parameter, others even have a different one. It is shown that pseudo-symmetric structures with some dynamic disorder are predestined to such behaviour. Details are exemplified by earlier and recent experimental results on ferroelastic and ferroelectric crystals.

Magnetic Resonances of 51V, 209Bi, Mn2+, and Fe3+in BiVO4Single Crystals

Abstract Nuclear magnetic resonance (NMR) of 51V and 209Bi, and electron paramagnetic resonance (EPR) of Mn2+ and Fe3+ impurities in ferroelastic BiVO4 single crystals are reviewed. The nuclear quadrupole parameters and principal axes of the two host nuclei, 51V and 209Bi, and the second-or-der zero field splitting tensor of the isoelectronic 3 d5 ions, Mn2+ and Fe3+ , in BiVO4 are determined for the first time. Temperature dependence studies on 51V NMR and Mn2+ EPR confirmed that this crystal undergoes a second order phase transition. The substitutional sites of Mn2+ and Fe3+ in BiVO4 are Bi3+ and V5+, respectively.

Low-frequency elastic properties of the incommensurate ferroelastic

The low-frequency elastic properties of incommensurate ferroelastic crystals [N(${\mathrm{CH}}_{3}$${)}_{4}$${]}_{2}$${\mathrm{CuCl}}_{4}$ are studied in the vicinity of the incommensurate phase transitions using parallel-plate-stress and three-point-bending methods. The temperature dependences of the effective elastic constants (relative Young's modulus) along all principal crystal directions and the shear elastic compliance ${\mathit{S}}_{55}$=1/${\mathit{C}}_{55}$ were obtained. Similarly to the elastic properties at ultrasonic frequencies (10 MHz), the elastic anomalies at low frequencies (5 Hz) near the paraelastic-incommensurate transition (at ${\mathit{T}}_{\mathit{i}}$) are well explained in the framework of the plane-wave approximation. In the transition region from the incommensurate to the commensurate improper ferroelastic phase we apply soliton theory. From the experimental data it follows that the anomalous behavior of ${\mathit{S}}_{55}$ near the phase transition from incommensurate to commensurate improper ferroelastic phase has the same features as the dielectric constant in the vicinity of incommensurate-commensurate improper ferroelectric phase transition, including the Curie-Weiss-type anomaly for ${\mathit{S}}_{55}$(T) near ${\mathit{T}}_{\mathit{c}}$, thermal hysteresis phenomena, and similar changes in the character of the anomaly under applied static stress ${\mathrm{\ensuremath{\sigma}}}_{5}$. The last results are explained within the framework of soliton theory proposed by Holakovsky and Dvorak [J. Phys. C 21, 5449 (1988)]. \textcopyright{} 1996 The American Physical Society.

Pressure dependence of the soft modes in the model ferroelastics Hg2I2

The pressure dependence of the soft modes in the paraphase (boundary of the Brillouin zone, X point) and the ferrophase (center of the Brillouin zone, Γ point) is studied in the model ferroelastic crystals Hg2I2. An anomalous linear pressure dependence of the soft-mode frequency in the paraphase (p<pc) is observed. The results obtained and the nature of the ferroelastic phase transition induced in Hg2I2 crystals by a high hydrostatic pressure are discussed.

Mechanical and Dielectric Energy Loss Related to Viscous Motion and Freezing of Domain Walls

Three dielectric loss (D) and/or three mechanical loss (Q -1 ) peaks (P1,P2,P3) and corresponding susceptibilities for ferroelectric KDP and TGS, and ferroelastic LNPP crystal and Cu-Al-Zn-Ni alloy have been investigated in the kHz range. P 1 and P 2 almost overlap for first order phase transitions. P i , a very narrow peak, is attributed to the dynamic domains due to fluctuations near Tc. P2 is recognized to be related to domain walls (DWs). The formulas of Q -1 and D caused by the viscous motion of DWs are derived, being fairly coincident with the experimental data of P2. The viscous coefficient, pinning force constant of DW and the spontaneous shear strain have been calculated for Cu-Al-Zn-Ni. The susceptibility, e' or ΔJ/J, always shows a high plateau below Tc and drops down rapidly nearly consistent with the low temperature side of P3 peak for poly-domain TGS, KDP and Cu-Al-Zn-Ni. P3 is thought to originate from the freezing of DWs of high density due to a collective pinning of randomly distributed defects, similar to the pinned-vortex glass model suggested for high Tc superconductors.

Computer simulation of domain formation in crystals

Abstract The phase transitions and the annealing processes simulated by the molecular-dynamics technique for KSCN and YBCO crystals are presented. The KSCN and YBCO model crystals show co-elastic and ferroelastic phase transitions, respectively. On quenching from disordered phases and subsequent annealing, tweed microstructures are obtained, which evolve to strip phases with well defined domain walls. In KSCN the antiphase boundaries are arbitrarily oriented. A number of dielectric and ferroelastic crystals possess incommensurately modulated phases, which could be seen as a sequence of discommensuration planes. The same simulation technique has been used to study the nucleation of topological defects responsible for creation of discommensurations. It is proved that the elastic domain walls favour nucleation of discommensuration planes.

Experimental device for measuring the influence of a uniaxial stress on specific heat: Application to the strontium titanate ferroelastic crystal

A conduction calorimeter where the sample is pressed between two identical heat fluxmeters, each having 50 chromel–constantan thermocouples, is described. The fluxmeters were built to obtain linear heat conduction and with enough rigidity to apply a controlled uniaxial stress on the sample. The method of measurement, together with the fact that the sensors themselves apply the stress to the sample, allow us to obtain absolute values of the specific heat. The specific heat of strontium titanate ferroelastic crystal is measured without stress and under an applied uniaxial stress on the face (110). The measurements were carried out while cooling the sample at a constant rate of 0.06 K/h. The data obtained at intervals of 0.02 K are compared with those obtained with an unannealed and an annealed sample, respectively.

Study of the domain structure in Mn3B7O13I ferroelectric boracite by optical and electron microscopy

Abstract Fully ferroelectric/fully ferroelastic crystals of Manganese-iodine boracite (Mn3B7O13I) were grown by chemical reactions in the vapour phase. Results of observations of the domain structure in uncoated samples of this composition, both by polarized light microscopy and by scanning electron microscopy are presented.

Prominent ferroelastic domain walls in BiVO4 crystal

The domain structure of ferroelastic BiVO4 crystals was investigated by X-ray diffraction, nuclear magnetic resonance, optical polarizing microscopy, transmission electron microscope, and electron diffraction techniques. From these results, it is found that the BiVO4 crystals have only prominent W walls and no non-prominent W' domain walls. A model of the twin structure is suggested, and all experimental results are explained in terms of this model. However, the prominent W wall obtained from our experimental results should not occur in the ferroelastic species 4/mF2/m previously reported. From the acoustic symmetry character of the elastic behaviour, it has been established that there exist two possible W and W' walls for permissible planar walls that are consistent with all experimental observations. Thus, it can be concluded that the BiVO4 crystals having only the W walls found by our group and W' walls obtained by other groups are consistent with the ferroelastic species 4/mmmF2/m rather than 4/mF2/m.

The study of domain walls in Pb3(PO4)2 ferroelastic crystals

The study of domain walls in Pb₃(PO₄)₂ ferroelastic crystals

Structure and ferroelasticity of the ferroelastic crystal KMnCl3.

In order to investigate the types of domain wall that are formed at the ferroelastic phase transition, we developed the ferroelastic crystal ${\mathrm{KMnCl}}_{3}$. ${\mathrm{KMnCl}}_{3}$ undergoes two ferroelastic phase transitions. In the present study, we investigated the domain structure of ${\mathrm{KMnCl}}_{3}$ and the ferroelasticity by applying a mechanical stress. As an important result for the types of domain wall we have found that only three kinds of domain walls, the ${\mathit{W}}_{\mathit{m}}$, ${\mathit{W}}_{\mathit{b}}$, and ${\mathit{W}}_{\mathit{m}\mathit{b}}$ walls, can exist in pure ferroelastic crystals and they can be represented by a crystallographic plane of fixed indices.

Low and high temperature uniaxial stress devices for the study of ferroelastic crystals

Detailed techniques for the construction of low (4–300 K) and high (300–700 K) temperature uniaxial stress application devices are described, designed for studying stress-induced effects, including ferroelastic (/ferroelectric) detwinning, induced phase transitions, piezo-optical effects in ferroic crystals under in situ optical control of their domain states by means of polarized light microscopy. Examples of the successful application of these systems to YBa2Cu3O7−δ , K3Fe5F15, and Cr3B7O13Cl crystals are presented and discussed.