Nonlinear dynamics for proper ferroelastic transitions for which the landau condition is violated

On the basis of a lattice model the domain structure for ferroelastic transformations is examined. The model accounts for both strongly nonlinear and competing interactions which allow for, in some situations, the propagation of nonlinear excitations. The model can be mostly applied to proper ferroelastic transformations of which In-Tl, Ti-Ni, etc.… are good prototypes. The phonon dispersion of the transverse acoustic waves obtained in the linearized case is discussed and the results show first a phonon softening at nonzero wave-number and next an upwards convexity of the phonon branch near the long-wavelength limit. This can be seen as pre-transitional effects. In a fully nonlinear case we consider vanishing dilatation transformations and the continuum approximation is applied to the one-dimensional version. Then, we investigate nonlinear excitations; three main classes of solution are found: i) quasi-harmonic solutions corresponding to periodically modulated structures in space which is a precursor effect of the elastic transformation, ii) an array of solitons made of periodic arrangements of parent-elastic domains and iii) a moving strain soliton. All the significant results are numerically illustrated by means of the microscopic model. Finally, the similarity to martensitic transformations and some extensions of the model are outlined.     

3D Organic–Inorganic Perovskite Ferroelastic Materials with Two Ferroelastic Phases: [Et3P(CH2)2F][Mn(dca)3] and [Et3P(CH2)2Cl][Mn(dca)3]

Organic–inorganic hybrid perovskite-type multiferroics have attracted considerable research interest owing to their fundamental scientific significance and promising technological applications in sensors and multiple-state memories. The recent achievements with divalent metal dicyanamide compounds revealed such malleable frameworks as a unique platform for developing novel functional materials. Herein, two 3D organic–inorganic hybrid perovskites [Et₃P(CH₂)₂F][Mn(dca)₃] ( 1 ) and [Et₃P(CH₂)₂Cl][Mn(dca)₃] ( 2 ) (dca=dicyanamide, N(CN)₂⁻) are presented. Accompanying the sequential phase transitions, they display a broad range of intriguing physical properties, including above room temperature ferroelastic behavior, switchable dielectricity, and low-temperature antiferromagnetic ordering (T_c=2.4 K for both 1 and 2 ). It is also worth noting that the spontaneous strain value of 1 is far beyond that of 2 in the first ferroelastic phase, as a result of the precise halogen substitution. From the point view of molecular design, this work should inspire further exploration of multifunctional molecular materials with desirable properties.     

Crystallographic and microstructural aspects of the superconductor YBa2Cu3O7-y —an overview

Crystal structures and structural inhomogeneities observed in YBa₂Cu₃O_7-y are reviewed. It is brought out that a proper understanding of the nature of the structural inhomogeneities is essential for exploiting the technological potential of this material. The need for an adequate characterization of specimens used for experiments is emphasized. Practical implications of the ferroelastic nature of the material are discussed.     

Stress-Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex

Domain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry-breaking phase transitions in the mononuclear Mn³⁺ compound [Mn(3,5-diBr-sal₂(323))]BPh₄, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress-induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc-P1 transition     

非均匀铁弹畴变对离面极化压电陶瓷应力强度因子的影响研究

基于文献中报道的试验结果，本文考虑非均匀的畴变过程区，它包含一个位于中心的饱和区和环绕饱和区的渐变区．为了描述外加应力引起的部分铁弹畴变，本文采用一个显式的基于最小能量原理的非均匀畴变准则．考虑离面极化的压电陶瓷，假设其初始极化矢量平行于离面方向．畴变后的电畴位于面内，具体方位由最大释放功来确定．基于非均匀畴变准则，本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布．并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响．结果表明：(1) 静止裂纹尖端处的畴变减小了材料的起裂强度；(2) 准静态稳态裂纹附近的畴变增加了材料的断裂强度．且理论预测的R曲线渐近值与试验结果定量吻合．     

On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an X-ray diffraction study

The effective thickness of ferroelastic twin-walls (W-walls) in Pb₃(PO₄)₂ at room temperature (≈ 0.7 T _c ) was determined by X-ray diffraction. The diffraction profiles were analysed using a wall profile e=eotanh x/w where W is the effective wall thickness including the effects of wall bending and surface relaxations. The experimental value W is around 10 unit cells which is larger than expected from standard renormalization arguments. The limitations of such experimental studies are discussed.     

Renormalization phenomena in Ba-diluted ferroelastic lead phosphate, (Pb1-x Ba x )3(PO4)2

Abstract

In the improper ferroelastic palmierite-type lead phosphate order parameter coupling with a defect induced conjugate field leads to the renormalization of the two different critical temperatures of three order parameter components {Q ₃} and {Q ₁ Q ₂}. The influence of the lead dilution by barium on the ferroelastic domain pattern, the critical temperature of the ferroelastic transformation R m–C2/c and the development of the intermediate regime in (Pb_1–x Ba _x )₃(PO₄)₂ is studied using optical birefringence measurements, Raman and infrared spectroscopy. At the ferroelastic transition temperature T _c the orientational contribution of the three-states Potts model becomes critical. T _c is reduced from 453 K (x = 0) to zero K at x? 0.12. Modifications of the shape of zigzag needle domains as well as the angle between the monoclinic binary axis and the W walls along [031] with temperature and increasing Ba-content are reported. Above the ferroelastic transition point the component Q ₃, which corresponds to the displacive part in the Gibbs free energy, leads to dynamic short-range monoclinic deformation in the trigonal matrix. The temperature where Q ₃ shows critical behaviour is renormalized to 720 K (x = 0.12) as compared with 563 K in pure lead phosphate. For x>0.13 no monoclinic precursor clusters were found.     

Ferroelastic detwinning of the high-temperature superconductor YBa2Cu3O7-δ

Crystals of YBa₂Cu₃O_7-δ (YBC) were prepared using a flux technique. The as-grown crystals were typically on the order of 200 μm × 200 μm × 50 μm, where the 50 μm dimension is in the c-direction. Ferroelastic behavior was observed by applying a uniaxial stress along the [100]_tet-direction using a specially-designed fixture which was mounted to a programmable hot/cold stage of a polarizing reflected-light microscope. Domain wall motion was observed for temperatures greater than 200°C, and complete poling was accomplished at stresses on the order of 50–100 MPa at temperatures of 350–400°C. An ionic diffusion-activated mechanism is suggested.     

Elastic studies of phase transitions

We report some results on acoustic studies of phase transitions in which the order parameter is coupled to the elastic wave strain, when direct behaviour observation is not possible. First by Brillouin scattering it was possible to observe the softening of C₅₅ of ammonium oxalate hemihydrate and it was concluded that the order parameter is not the deformation. In the case of members of A₂MX₄ family a softening of C₆₆ related to a shear wave near the lock-in transition was observed for [N(CH₃)₄]₂ZnCl₄, as previously found for C ₅₅ of K₂SeO₄. Such a behaviour did not occur for (NH₄)₂BeF₄ in which a strong hysteresis effect appeared.     

Proton Dynamics in Letovicite, (NH4)3H(SO4)2: A H and N NMR Spectroscopic Study

The improper ferroelastic phase letovicite (NH₄)₃H(SO₄)₂ has been studied by ¹H MAS NMR as well as by static ¹⁴N NMR experiments in the temperature range of 296–425 K. The ¹H MAS NMR resonance from ammonium protons can be well distinguished from that of acidic protons. A third resonance appears just below the phase transition temperature which is due to the acidic protons in the paraelastic phase. The lowering of the second moment M₂ for the ammonium protons takes place in the same temperature range as the formation of domain boundaries, while the signals of the acidic protons suffer a line narrowing in the area of T_c. The static ¹⁴N NMR spectra confirm the temperature of the motional changes of the ammonium tetrahedra. Two-dimensional ¹H NOESY spectra indicate a chemical exchange between ammonium protons and the acidic protons of the paraphase.