Generating a 64 × 64 beam lattice by geometric phase modulation from arbitrary incident polarizations

The direct imaging of a crystal lattice has intrigued electron microscopists for many years. What is of interest, of course, is the way in which defects perturb their atomic regularity. There are problems, however, when one wishes to relate aperiodic image features to structural aspects of crystalline defects. If the defect is inclined to the foil plane and if, as is the case with present 100 kV transmission electron microscopes, the objective lens is not perfect, then terminating fringes and fringe bending seen in the image cannot be related in a simple way to lattice plane geometry in the specimen (1).The purpose of the present work was to devise an experimental test which could be used to confirm, or not, the existence of a one-to-one correspondence between lattice image and specimen structure over the desired range of specimen spacings. Through a study of computed images the following test emerged.

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Calculation of structure images of crystalline defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108556 ◽

1978 ◽

Vol 36 (1) ◽

pp. 282-283

Author(s):

M.A. O'Keefe ◽

Sumio Iijima

Keyword(s):

Diffuse Scattering ◽

Computing Time ◽

Continuous Distribution ◽

Sampling Interval ◽

Reciprocal Space ◽

Objective Lens ◽

Lattice Images ◽

Slice Method ◽

Space Cell ◽

Beam Lattice

We have extended the multi-slice method of computating many-beam lattice images of perfect crystals to calculations for imperfect crystals using the artificial superlattice approach. Electron waves scattered from faulted regions of crystals are distributed continuously in reciprocal space, and all these waves interact dynamically with each other to give diffuse scattering patterns.In the computation, this continuous distribution can be sampled only at a finite number of regularly spaced points in reciprocal space, and thus finer sampling gives an improved approximation. The larger cell also allows us to defocus the objective lens further before adjacent defect images overlap, producing spurious computational Fourier images. However, smaller cells allow us to sample the direct space cell more finely; since the two-dimensional arrays in our program are limited to 128X128 and the sampling interval shoud be less than 1/2Å (and preferably only 1/4Å), superlattice sizes are limited to 40 to 60Å. Apart from finding a compromis superlattice cell size, computing time must be conserved.

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Point and planar defects in the iron sulfide compounds Fe1-xS

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010011221x ◽

1984 ◽

Vol 42 ◽

pp. 434-435

Author(s):

Thao A. Nguyen

Keyword(s):

Low Temperatures ◽

Direct Evidence ◽

Iron Sulfide ◽

Planar Defects ◽

Selective Area ◽

Vacancy Ordering ◽

Different Types ◽

Lattice Images ◽

The Subject ◽

Beam Lattice

It is well known that the large deviations from stoichiometry in iron sulfide compounds, Fe1-xS (0≤x≤0.125), are accommodated by iron vacancies which order and form superstructures at low temperatures. Although the ordering of the iron vacancies has been well established, the modes of vacancy ordering, hence superstructures, as a function of composition and temperature are still the subject of much controversy. This investigation gives direct evidence from many-beam lattice images of Fe1-xS that the 4C superstructure transforms into the 3C superstructure (Fig. 1) rather than the MC phase as previously suggested. Also observed are an intrinsic stacking fault in the sulfur sublattice and two different types of vacancy-ordering antiphase boundaries. Evidence from selective area optical diffractograms suggests that these planar defects complicate the diffraction pattern greatly.

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The observation of solutions in Ni3Nb

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104765 ◽

1988 ◽

Vol 46 ◽

pp. 540-541

Author(s):

Z.M. Wang ◽

J.P. Zhang

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Phase Modulation ◽

High Resolution Electron Microscopy ◽

Antiphase Domain ◽

Boundary Area ◽

Matrix Type ◽

Resolution Electron ◽

Domain Boundaries ◽

Kontorova Model

High resolution electron microscopy reveals that antiphase domain boundaries in β-Ni3Nb have a hexagonal unit cell with lattice parameters ah=aβ and ch=bβ, where aβ and bβ are of the orthogonal β matrix. (See Figure 1.) Some of these boundaries can creep “upstairs” leaving an incoherent area, as shown in region P. When the stepped boundaries meet each other, they do not lose their own character. Our consideration in this work is to estimate the influnce of the natural misfit δ{(ab-aβ)/aβ≠0}. Defining the displacement field at the boundary as a phase modulation Φ(x), following the Frenkel-Kontorova model [2], we consider the boundary area to be made up of a two unit chain, the upper portion of which can move and the lower portion of the β matrix type, assumed to be fixed. (See the schematic pattern in Figure 2(a)).

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THE MOLECULAR GEOMETRIC PHASE AND LIGHT-INDUCED CONICAL INTERSECTIONS

Proceedings of the 72nd International Symposium on Molecular Spectroscopy ◽

10.15278/isms.2017.tg06 ◽

2017 ◽

Author(s):

Emil Zak

Keyword(s):

Geometric Phase ◽

Conical Intersections

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