Calculation of structure images of crystalline defects

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.

7-beam lattice images of (110) oriented Ge

1978 ◽  
Vol 36 (1) ◽  
pp. 290-291
Author(s):  
J.R. Parsons ◽  
C.W. Hoelke
Keyword(s):  
Image Features ◽  
Objective Lens ◽  
Lattice Plane ◽  
Lattice Image ◽  
Crystalline Defects ◽  
Transmission Electron ◽  
Lattice Images ◽  
Electron Microscopes ◽  
Structural Aspects ◽  
Beam Lattice

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.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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

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.

Many-beam lattice images calculated at 100 kV and 1000 kV

1980 ◽  
Vol 36 (6) ◽  
pp. 1033-1041 ◽  
Author(s):  
M. Tanaka ◽  
B. Jouffrey
Keyword(s):  
Lattice Images ◽  
Beam Lattice

n-Beam lattice images. II. Methods of calculation

1972 ◽  
Vol 28 (6) ◽  
pp. 536-548 ◽  
Author(s):  
D. F. Lynch ◽  
M. A. O'Keefe
Keyword(s):  
Methods Of Calculation ◽  
Lattice Images ◽  
Beam Lattice

Many-Beam Lattice Images from Thicker Crystals

1978 ◽  
Vol 36 (3) ◽  
pp. 130-139
Author(s):  
S. Iijima
Keyword(s):  
Electron Microscopy ◽  
Materials Science ◽  
Complex Oxides ◽  
Crystal Defects ◽  
Planar Defects ◽  
Transmission Electron ◽  
Lattice Images ◽  
The Many ◽  
Atom Configuration ◽  
Beam Lattice

Nearly a decade ago, the usefulness of lattice images for studying crystal defects was reported by Allpress et al. (1969). They analyzed abnormally spaced lattice fringes of crystals of the complex oxides and derived successfully the nature of planar defects occurring on a unit cell scale. Since then the method for studying atom configuration in crystals using high resolution transmission electron microscopy (HRTEM) has been investigated extensively. The studies have involved theoretical calculation of the many-beam lattice images of perfect crystals and applications of the method to solve problems in materials science.

Study of Diffuse Scattering by Means of High Resolution Structure Images

1976 ◽  
Vol 34 ◽  
pp. 476-477
Author(s):  
Sumio Iijima ◽  
G. R. Anstis
Keyword(s):  
High Resolution ◽  
Neutron Diffraction ◽  
Diffuse Scattering ◽  
Reciprocal Space ◽  
The Other ◽  
X Ray ◽  
Actual Model ◽  
High Resolution Structure ◽  
Made In ◽  
Resolution Structure

Disorders in crystals with relatively simple structures which gave diffuse scattering have been extensively studied by X-ray or neutron diffraction methods. All these investigations were based on traditional diffraction methods and observations were made in reciprocal space (note observable diffraction intensities can be considered only in terms of interatomic vectors) and therefore the results obtained there leaves considerable ambiguity, particularly when we try to derive an actual model of the disordered crystals. A solution of this problem will be given only by knowing all atom positions in an assembly of atoms and for this case the observable diffracted intensity is given bywhere (xi,yi) and (xj,yj) represent position vectors of the i th and j th atoms with scattering factors fi and fj from an arbitrary origin. On the other hand, a crystal containing imperfections can be defined by

scholarly journals Synchrotron x-ray thermal diffuse scattering probes for phonons in Si/SiGe/Si trilayer nanomembranes

MRS Advances ◽  
2016 ◽  
Vol 1 (48) ◽  
pp. 3263-3268
Author(s):  
Kyle M. McElhinny ◽  
Gokul Gopalakrishnan ◽  
Donald E. Savage ◽  
David A. Czaplewski ◽  
Max G. Lagally ◽  
...  
Keyword(s):  
Diffuse Scattering ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Elastic Anisotropy ◽  
Sige Layer ◽  
Reciprocal Space ◽  
Thermal Diffuse Scattering ◽  
X Ray ◽  
Recent Developments ◽  
Thermal Diffuse

ABSTRACTNanostructures offer the opportunity to control the vibrational properties of via the scattering of phonons due to boundaries and mass disorder as well as through changes in the phonon dispersion due to spatial confinement. Advances in understanding these effects have the potential to lead to thermoelectrics with an improved figure of merit by lowering the thermal conductivity and to provide insight into electron-phonon scattering rates in nanoelectronics. Characterizing the phonon population in nanomaterials has been challenging because of their small volume and because optical techniques probe only a small fraction of reciprocal space. Recent developments in x-ray scattering now allow the phonon population to be evaluated across all of reciprocal space in samples with volumes as small as several cubic micrometers. We apply this approach, synchrotron x-ray thermal diffuse scattering (TDS), to probe the population of phonons within a Si/SiGe/Si trilayer nanomembrane. The distributions of scattered intensity from Si/SiGe/Si trilayer nanomembranes and Si nanomembranes with uniform composition are qualitatively similar, with features arising from the elastic anisotropy of the diamond structure. The TDS signal for the Si/SiGe/Si nanomembrane, however, has higher intensity than the Si membrane of the same total thickness by approximately 3.75%. Possible origins of the enhancement in scattering from SiGe in comparison with Si include the larger atomic scattering factor of Ge atoms within the SiGe layer or reduced phonon frequencies due to alloying.

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