Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls

A simple model of the evolution of ferroelectric microstructure in single crystals is developed by using variational methods to minimize a functional based on free energy and dissipation. The thermodynamic variables in this formulation correspond to the positions of a set of domain walls within a single ferroelectric crystal. The total dissipation rate is taken to be a function of the velocities of the individual domain walls. With only two-degrees of freedom, a model of this type has sufficient richness to reproduce many of the observed features found in the single crystal response of a tetragonal ferroelectric. This includes the dielectric hysteresis, butterfly hysteresis, and the variation of the hysteresis loops under uniaxial compressive stress. Additional degrees of freedom can be used to capture multi-axiality. The model also highlights the marked differences in response that should occur when a single crystal is subjected to different boundary conditions.

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The direct determination of magnetic domain wall profiles using a split detector STEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100109471 ◽

1978 ◽

Vol 36 (1) ◽

pp. 466-467

Author(s):

J.N. Chapman ◽

P.E. Batson ◽

E.M. Waddell ◽

R.P. Ferrier

Keyword(s):

Electron Microscope ◽

Domain Wall ◽

Transmission Electron Microscope ◽

Domain Walls ◽

Photographic Plate ◽

Magnetic Domain ◽

Direct Determination ◽

Quantitative Information ◽

Scanning Transmission Electron Microscope ◽

Transmission Electron

By far the most commonly used mode of Lorentz microscopy in the examination of ferromagnetic thin films is the Fresnel or defocus mode. Use of this mode in the conventional transmission electron microscope (CTEM) is straightforward and immediately reveals the existence of all domain walls present. However, if such quantitative information as the domain wall profile is required, the technique suffers from several disadvantages. These include the inability to directly observe fine image detail on the viewing screen because of the stringent illumination coherence requirements, the difficulty of accurately translating part of a photographic plate into quantitative electron intensity data, and, perhaps most severe, the difficulty of interpreting this data. One solution to the first-named problem is to use a CTEM equipped with a field emission gun (FEG) (Inoue, Harada and Yamamoto 1977) whilst a second is to use the equivalent mode of image formation in a scanning transmission electron microscope (STEM) (Chapman, Batson, Waddell, Ferrier and Craven 1977), a technique which largely overcomes the second-named problem as well.

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Lorentz microscopy study of magnetic domain walls in Fe-Cr-Co alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100109458 ◽

1978 ◽

Vol 36 (1) ◽

pp. 462-463

Author(s):

Yalcin Belli

Keyword(s):

Domain Walls ◽

Magnetic Domain ◽

Microscopy Study ◽

Ferromagnetic Phase ◽

Stable Phase ◽

Magnetic Domains ◽

Lorentz Microscopy ◽

Magnetic Hardening ◽

Electron Microscopes ◽

Co Alloys

Fe-Cr-Co alloys have great technological potential to replace Alnico alloys as hard magnets. The relationship between the microstructures and the magnetic properties has been recently established for some of these alloys. The magnetic hardening has been attributed to the decomposition of the high temperature stable phase (α) into an elongated Fe-rich ferromagnetic phase (α1) and a weakly magnetic or non-magnetic Cr-rich phase (α2). The relationships between magnetic domains and domain walls and these different phases are yet to be understood. The TEM has been used to ascertain the mechanism of magnetic hardening for the first time in these alloys. The present paper describes the magnetic domain structure and the magnetization reversal processes in some of these multiphase materials. Microstructures to change properties resulting from, (i) isothermal aging, (ii) thermomagnetic treatment (TMT) and (iii) TMT + stepaging have been chosen for this investigation. The Jem-7A and Philips EM-301 transmission electron microscopes operating at 100 kV have been used for the Lorentz microscopy study of the magnetic domains and their interactions with the finely dispersed precipitate phases.

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Temperature Dependence of Magnetic Domains and Wall Structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009573x ◽

1972 ◽

Vol 30 ◽

pp. 496-497

Author(s):

Sonoko Tsukahara ◽

Tadami Taoka ◽

Hisao Nishizawa

Keyword(s):

Temperature Dependence ◽

Domain Walls ◽

Magnetic Domain ◽

Iron Film ◽

Objective Lens ◽

Lorentz Microscopy ◽

Domain Structures ◽

Wall Structures ◽

Crystal Films ◽

Metallurgical Structure

The high voltage Lorentz microscopy was successfully used to observe changes with temperature; of domain structures and metallurgical structures in an iron film set on the hot stage combined with a goniometer. The microscope used was the JEM-1000 EM which was operated with the objective lens current cut off to eliminate the magnetic field in the specimen position. Single crystal films with an (001) plane were prepared by the epitaxial growth of evaporated iron on a cleaved (001) plane of a rocksalt substrate. They had a uniform thickness from 1000 to 7000 Å.The figure shows the temperature dependence of magnetic domain structure with its corresponding deflection pattern and metallurgical structure observed in a 4500 Å iron film. In general, with increase of temperature, the straight domain walls decrease in their width (at 400°C), curve in an iregular shape (600°C) and then vanish (790°C). The ripple structures with cross-tie walls are observed below the Curie temperature.

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Imaging of ferroelectric domain walls by electron holography

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121636 ◽

1992 ◽

Vol 50 (1) ◽

pp. 246-247

Author(s):

Xiao Zhang

Keyword(s):

Magnetic Field ◽

High Resolution ◽

Domain Walls ◽

Ferroelectric Domain ◽

Object Wave ◽

Electron Holography ◽

High Resolution Imaging ◽

Quantitative Measurements ◽

Resolution Imaging ◽

Electron Microscopes

Electron holography has recently been available to modern electron microscopy labs with the development of field emission electron microscopes. The unique advantage of recording both amplitude and phase of the object wave makes electron holography a effective tool to study electron optical phase objects. The visibility of the phase shifts of the object wave makes it possible to directly image the distributions of an electric or a magnetic field at high resolution. This work presents preliminary results of first high resolution imaging of ferroelectric domain walls by electron holography in BaTiO3 and quantitative measurements of electrostatic field distribution across domain walls.

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The need of electron microscopy in the study of domains and domain walls in ferroelectrics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170487 ◽

1994 ◽

Vol 52 ◽

pp. 550-551

Author(s):

Wenwu Cao

Keyword(s):

Domain Wall ◽

Domain Walls ◽

High Mobility ◽

Continuum Theory ◽

Polarization Vector ◽

Ferroelectric Materials ◽

Dielectric Constants ◽

Nonlocal Coupling ◽

Cubic Symmetry ◽

Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

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A new method for the observation of Type II magnetic contrast

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100176952 ◽

1990 ◽

Vol 48 (4) ◽

pp. 764-765

Author(s):

R.P. Ferrier ◽

S. McVitie

Keyword(s):

Domain Walls ◽

Incident Beam ◽

Objective Lens ◽

Type Ii ◽

Backscattering Coefficient ◽

Magnetic Contrast ◽

Standard Geometry ◽

Backscattered Electron ◽

Imaging Performance ◽

Good Probe

Type II magnetic contrast was first observed by Philibert and Tixier and relies on the change in the effective backscattering coefficient due to interaction of the scattered electrons within the specimen and the local magnetic induction (for a review see Tsuno). Depending on the tilt of the specimen and the position of the backscattered electron detector(s), contrast due to the presence of either or both domains and domain walls can be obtained; in the case of the latter, the standard geometry is for the specimen to be normal to the incident beam and the detectors are positioned above it and close to the optic axis. This is the geometry adopted in our studies, which used a JEOL 2000FX with a special split objective lens polepiece; this permitted the specimen to be in magnetic field-free space, the separate lens gaps above and below allowing good probe forming capabilities combined with excellent Lorentz imaging performance. A schematic diagram is shown in Fig. 1.

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