Quantitative determination of the thickness of ferroelectric domain walls using weak beam transmission electron microscopy

Foeth, M; Stadelmann, PA; Buffat, PA

doi:10.1016/s0304-3991(98)00060-6

Cited by 12 publications

(9 citation statements)

References 13 publications

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“…For example, we studied the effect of the gradient energy coefficients on the phase stability diagram using a range of gradient energy coefficients G 11 / G 110 =0.2–0.6. For this range, the calculated domain wall width and domain wall energy for 90° domains in PT lies within the theoretically and experimentally observed domain wall width and domain wall energy 21,27–29 of 5–21 Å and 0.035–0.050 J/m 2 , respectively. We found that the gradient energy coefficient affects only the stability range of the mixture of the orthorhombic and tetragonal a phase, i.e., with the decrease in gradient energy coefficients the stability region of the mixture of orthorhombic and tetragonal a domains shrinks.…”

Section: Resultssupporting

confidence: 83%

A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

Choudhury

Chen

2005

Journal of the American Ceramic Society

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A phase diagram of temperature versus strain was constructed for a (001)‐oriented PbZr1−xTixO3 epitaxial single crystal thin film near the bulk morphotropic boundary composition (x=0.47) on an (001)‐oriented cubic substrate. The phase‐field approach is employed. It is shown that a mixture of distorted rhombohedral, orthorhombic, and tetragonal phases exists under small values of strain, i.e., close to the in‐plane clamped boundary condition. This result contradicts thermodynamic calculations assuming a single‐domain state that predicted a single distorted rhombohedral phase under similar strains. Furthermore, it is demonstrated that under a large tensile strain current phase‐field simulations showed a tetragonal phase with a1/a2 twin structures as the stable state whereas thermodynamic calculations predicted an orthorhombic phase.

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Section: Resultssupporting

confidence: 83%

A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

Choudhury

Chen

2005

Journal of the American Ceramic Society

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“…The thickness of the domain wall L is thus defined as t^ or any multiple of it. A reasonable choice for the domain wall thickness, which is in agreement with previous experiments [9], is the value L = 4fj. With these considerations, we are led to make the assumption that the continuous variation of the geometrical phase across the domain wall has to be described by a function that has the same asymptotic behaviour as P\\.…”

Section: Methodssupporting

confidence: 67%

“…Vj (r) is given by (9) where the m is the rest mass of the electron, Q. is the volume of the unit cell and r n is the position of the atom n in the unit cell. M n = 8n 2 <u 2 > n is the Debye-Waller factor with <u 2 > n being the mean square vibrational amplitude of atom «./ rt ' r ' is the atomic scattering amplitude in the first-order Born approximation.…”

Section: Methodsmentioning

confidence: 99%

A comparison of HREM and weak beam transmission electron microscopy for the quantitative measurement of the thickness of ferroelectric domain walls

Foeth

Sfera

Stadelmann

et al. 1999

Journal of Electron Microscopy

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In this paper we present two methods for the quantitative measurement of the thickness of ferroelectric domain walls, one using high-resolution electron microscopy (HREM) and the other weak beam transmission electron microscopy (WBTEM). These techniques can be used to determine the thickness of domain walls at room temperature as well as close to the ferroelectric to paraelectric phase transition. The first method allows a direct visualization of the lattice distortion across the domain wall, by measuring the continuous deviation of a set of planes with respect to the undistorted lattice. The second method consists in a quantitative analysis of the thickness fringes that appear on weak beam images of inclined domain walls. By fitting simulated fringe profiles to experimental ones, we can extract the thickness of the domain walls in a quantitative way. These two complementary techniques lead to a complete characterization of the thickness of ferroelectric domain walls over a wide range of specimen thicknesses at different magnifications. As an example we apply these methods to ferroelectric domain walls in PbTiO 3 . The domain wall thickness at room temperature is found to be 1.5 ± 0.3 nm using HREM (in very thin samples =10 nm) and 2.1 ± 0.7 nm using WBTEM (in samples thicker than 30 nm).Keywords high-resolution electron microscopy, weak beam imaging, ferroelectric domain walls, PbTiC^, image simulation, quantitative electron microscopy

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“…approximately 4 nm in ferroelectrics [31,32], this would leave unperturbed lattice regions (excluding dislocations) of only about 6 nm essentially within the domain. In this respect the domain wall represents a transition region across which the elastic distortion of the material varies smoothly.…”

Section: Discussionmentioning

confidence: 99%

Microstructure and Electrical Properties of Mn-Ni-In Spinels

Metzmacher

Groen

Reaaney

2000

phys. stat. sol. (a)

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Microstructural investigations of negative temperature coefficient (NTC) ceramics in the Mn±Ni±In±O system have been performed using X-ray diffraction (XRD), scanning (SEM) and transmission electron microscopy (TEM). The electrical properties have been characterized by measurements of resistance, activation energy and aging. The replacement of Mn by In in Mn 2.9± ±x Ni x In 0.1 O 4 (x 0:50À0:66) leads to higher resistivities and thermal constants, both decreasing with increasing Ni content, and minimum aging of 0.1% for x 0:58. Microstructural changes deduced from the a/c ratio and caused by aging are observable for Mn 2.32 Ni 0.58 In 0.1 O 4 which is nearest to the tetragonal/cubic phase boundary. It is concluded that the Mn 3 concentration on octahedral sites increases due to aging. The domain configuration changes with increasing Ni content: samples with low Ni content reveal domain laths ($100 nm width) with internal twinning (<10 nm), samples near to the boundary exhibit finer scaled (5±10 nm), weakly curved domains without twinning and for high Ni contents a slightly increased domain width of 5±15 nm is observed. With the exception of x 0:58, all aged samples show the same microstructure as the corresponding non-aged ones, whereas aged Mn 2.32 Ni 0.58 In 0.1 O 4 is more comparable with Mn 2.40 Ni 0.50 In 0.1 O 4 . Consequently, the choice of composition with respect to the phase boundary is decisive for the electrical and microstructural behaviour.

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Quantitative determination of the thickness of ferroelectric domain walls using weak beam transmission electron microscopy

Cited by 12 publications

References 13 publications

A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

A comparison of HREM and weak beam transmission electron microscopy for the quantitative measurement of the thickness of ferroelectric domain walls

Microstructure and Electrical Properties of Mn-Ni-In Spinels

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Quantitative determination of the thickness of ferroelectric domain walls using weak beam transmission electron microscopy

Cited by 12 publications

References 13 publications

A Phase Diagram for Epitaxial PbZr1−xTixO3 Thin Films at the Bulk Morphotropic Boundary Composition

A Phase Diagram for Epitaxial PbZr1−xTixO3 Thin Films at the Bulk Morphotropic Boundary Composition

A comparison of HREM and weak beam transmission electron microscopy for the quantitative measurement of the thickness of ferroelectric domain walls

Microstructure and Electrical Properties of Mn-Ni-In Spinels

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A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition