Dislocation Forces on an Edge Dislocation Near Crack Tip in Ferroelectric Materials

BaZnGeO4 undergoes many phase transitions from I to V phase. The highest temperature phase I has a BaAl2O4 type structure with a hexagonal lattice. Recent X-ray diffraction study showed that the incommensurate (IC) lattice modulation appears along the c axis in the III and IV phases with a period of about 4c, and a commensurate (C) phase with a modulated period of 4c exists between the III and IV phases in the narrow temperature region (—58°C to —47°C on cooling), called the III' phase. The modulations in the IC phases are considered displacive type, but the detailed structures have not been studied. It is also not clear whether the modulation changes into periodic arrays of discommensurations (DC’s) near the III-III' and IV-V phase transition temperature as found in the ferroelectric materials such as Rb2ZnCl4.At room temperature (III phase) satellite reflections were seen around the fundamental reflections in a diffraction pattern (Fig.1) and they aligned along a certain direction deviated from the c* direction, which indicates that the modulation wave vector q tilts from the c* axis. The tilt angle is about 2 degree at room temperature and depends on temperature.

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Investigation of ferroelectrics using conventional and in situ electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170669 ◽

1994 ◽

Vol 52 ◽

pp. 586-587

Author(s):

V. Saikumar ◽

H. M. Chan ◽

M. P. Harmer

Keyword(s):

Nonvolatile Memory ◽

Ferroelectric Materials ◽

Gate Insulator ◽

Sensors And Actuators ◽

In Situ Electron Microscopy ◽

Ferroelectric Domains ◽

Domain Boundaries ◽

Domain Interactions ◽

Memory Applications

In recent years, there has been a growing interest in the application of ferroelectric thin films for nonvolatile memory applications and as a gate insulator in DRAM structures. In addition, bulk ferroelectric materials are also widely used as components in electronic circuits and find numerous applications in sensors and actuators. To a large extent, the performance of ferroelectric materials are governed by the ferroelectric domains (with dimensions in the micron to sub-micron range) and the switching of domains in the presence of an applied field. Conventional TEM studies of ferroelectric domains structures, in conjunction with in-situ studies of the domain interactions can aid in explaining the behavior of ferroelectric materials, while providing some answers to the mechanisms and processes that influence the performance of ferroelectric materials. A few examples from bulk and thin film ferroelectric materials studied using the TEM are discussed below.Figure 1 shows micrographs of ferroelectric domains obtained from undoped and Fe-doped BaTiO3 single crystals. The domain boundaries have been identified as 90° domains with the boundaries parallel to <011>.

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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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Simulation and Contrast Analysis of tem Images of Cracks

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100181658 ◽

1990 ◽

Vol 48 (1) ◽

pp. 578-579

Author(s):

D. Goyal ◽

A. H. King

Keyword(s):

Displacement Vector ◽

Crack Tip ◽

Perfect Crystal ◽

Operating Conditions ◽

Displacement Fields ◽

Fringe Contrast ◽

Orthogonal Geometry ◽

Moire Fringe ◽

Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

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