F.H. Li

Maximum entropy image deconvolution in high resolution electron microscopy

The principle of image deconvolution in HREM by means of maximum entropy (ME) is introduced. The ME image deconvolution was performed in terms of a single image taken at an arbitrary defocus condition or in terms of the combination of an image with the corresponding electron diffraction pattern. The weighted ME method is introduced for crystals thicker than a weak phase object. The test results on simulated images of chlorinated-copper phthalocyanine for various defocus values are shown. The method is also efficient for crystals consisting of atoms with great differences in atomic weight and for very noisy images.

Crystal structure determination of K2O·7Nb2O5 by combining high-resolution electron microscopy and electron diffraction

Abstract With an image deconvolution procedure based on the principle of maximum entropy, positions of metallic atoms in crystal of K 2 O·7Nb 2 O 5 have been determined from a single high-resolution electron microscope image and from the combination of the image and the electron diffraction pattern. The function of image decovolution is to transform an image taken under an arbitrary defocus condition into the structure image. The structure images restored from two original images taken under much different defocus conditions show almost the same contrast. In the restored structure images, niobium and potassium atoms appear as black dots with larger and smaller contrast, respectively. The positions of oxygen atoms have been determined by the phase-extension technique developed in X-ray crystallography. Moduli of structure factors up to H = 1 A p-1 were obtained from the electron diffraction pattern, while phases within H ⩽ (1.9 A) p-1 were derived from Fourier transform of the electron microscope image after deconvolution. The Sayre equation was used to extend the phase from (1.9 A) p-1 to 1 A p-1 and to retrieve the phases of those reflections within (1.9 A) p-1 , which were rejected in image deconvolution owing to unreliable values of the contrast transfer function. Fourier synthesis was used to improve the quality of the image after phase extension. The final structure image reveals clearly all atoms in the unit cell.

ZnS nanowires and their coaxial lateral nanowire heterostructures with BN

ZnS nanowires and their coaxial lateral BN nanowire heterostructures with a length of hundreds of micrometers and an average diameter of similar to 300 nm were fabricated via one-step chemical vapor deposition method. Wurtzite ZnS nanowires were coated by a shell of fluffylike hexagonal BN sheets distributed randomly. Thermogravimetric analysis indicates that the heterostructures have a much better oxidation resistance compared with ZnS nanowires. Their similar optical property suggests that the ZnS/BN heterostructures would have potential applications in thermally and chemically rigorous environments. (c) 2007 American Institute of Physics.

A method of electron diffraction intensity correction in combination with high-resolution electron microscopy

A robust algorithm and computer program have been developed for the parameterization of elastic and absorptive electron atomic scattering factors. The algorithm is based on a combined modified simulated-annealing and least-squares method, and the computer program works well for fitting both elastic and absorptive atomic scattering factors with five Gaussians. As an application of this program, the elastic electron atomic scattering factors have been parameterized for all neutral atoms and for s up to 6 Angstrom(-1). Error analysis shows that the present results are considerably more accurate than the previous analytical fits in terms of the mean square value of the deviation between the numerical and fitted scattering factors. Parameterization for absorptive atomic scattering factors has been made for 17 important materials with the zinc blende structure over the temperature range 1 to 1000 K, where appropriate, and for temperature ranges for which accurate Debye-Waller factors are available. For other materials, the parameterization of the absorptive electron atomic scattering factors can be made using the program by supplying the atomic number of the element, the Debye-Waller factor and the acceleration voltage. For ions or when more accurate numerical results for neutral atoms are available, the program can read in the numerical values of the elastic scattering factors and return the parameters for both the elastic and absorptive scattering factors. The computer routines developed have been tested both on computer workstations and desktop PC computers, and will be made freely available via electronic mail or on floppy disk upon request.

Incommensurate modulation in minute crystals revealed by combining high-resolution electron microscopy and electron diffraction

Abstract Image processing combining high-resolution electron microscopy and electron diffraction is for the first time applied to the determination of incommensurate modulated structures. An image of a minute crystal of the high- T c superconductor Bi 2 Sr 2 Cacu 2 O x is averaged and then transformed to an image of the average structure by a deconvolution technique based on the principle of maximum entropy. The image resolution is then enhanced to about 1 A by the direct-method phase extension. All the unoverlapped atoms and their modulation are clearly seen in the final image.

Structural features of the incommensurate modulation in the Pb-doped Bi-2223 high-Tc phase revealed by direct-method electron diffraction analysis

Structural modulation waves in the Pb-doped Bi-2223 (Bi2Sr2Ca2Cu3Ox) phase are observed for the first time on the potential distribution function projected along the a axis. The newly developed multidimensional direct methods were used. Unlike the previous techniques, there is no need to assume any modulation model before the modulation waves can be seen directly from the resulting Fourier map. The symmetry of the title compound belongs to the four-dimensional space group P111Bbmb with three-dimensional unit cell parameters a=5.49 AA, b=5.41 AA, c=37.1 AA, alpha = beta = gamma =90 degrees and the modulation wavevector q=0.117b*. Occupational and positional modulations are obvious for most atoms. Disordered oxygen atoms arranged perpendicular to the b axis bridging the Cu(2)-Ca-Cu(1)-Ca-Cu(2) layers were observed.

Nature of interfacial defects and their roles in strain relaxation at highly lattice mismatched 3C-SiC/Si (001) interface

Misfit defects in a 3C-SiC/Si (001) interface were investigated using a 200 kV high-resolution electron microscope with a point resolution of 0.194 nm. The [110] high-resolution electron microscopic images that do not directly reflect the crystal structure were transformed into the structure map through image deconvolution. Based on this analysis, four types of misfit dislocations at the 3C-SiC/Si (001) interface were determined. In turn, the strain relaxation mechanism was clarified through the generation of grow-in perfect misfit dislocations (including 90° Lomer dislocations and 60° shuffle dislocations) and 90° partial dislocations associated with stacking faults.

Atomic configuration in core structure of Lomer dislocation in Si0.76Ge0.24/Si.

The core structure of a Lomer dislocation in SiGe/Si system has been revealed at atomic level. This is attained by applying the image deconvolution technique in combination with dynamical diffraction effect correction to the high-resolution image taken with a 200 kV field-emission gun high-resolution electron microscope. The Lomer dislocation has a Hornstra-like core. The contrast of the image simulated on the basis of derived atomic configuration is in agreement with that of the experimental image.

Image deconvolution for defected crystals in field-emission high-resolution electron microscopy

Abstract It is demonstrated that for images taken with a field-emission high-resolution electron microscope the image deconvolution based on the weak-phase object approximation is available for restoring the crystal defects with the resolution close to the information resolution limit. The image deconvolution is firstly carried out for simulated [1 1 0] images of perfect and defect Si crystal structure models with different thickness. The deconvoluted images reveal the atomic pairs as black dumbbells and show the correct atomic configuration including that at the twin boundary and near the 60° dislocation core for the crystal thickness at least up to 76 A. An experimental [1 1 0] image of SiGe Si has been restored to reveal an extended stacking fault sandwiched between two partial dislocations at the atomic level.

Correction for the dynamical electron diffraction effect in crystal structure analysis

A method is proposed to correct for the dynamical electron diffraction effect in crystal structure analysis. A rough structure model is first obtained by conventional structure-analysis methods neglecting the dynamical diffraction effect. From the rough structure model, multislice calculations are used to estimate the crystal thickness through the observed dynamical diffraction wave amplitudes. With this estimated thickness, the observed diffraction wave amplitudes are calibrated to give a set of fictitious observed kinematic structure-factor magnitudes. Based on such a set of magnitudes, a traditional least-squares procedure is used to refine structural parameters. The reliability of the result is checked by the consistency between the observed dynamical diffraction wave amplitudes and those found from the multislice calculation. The process can be made iterative. Tests were performed with two known structures, Bi-2212 and Pb-doped Bi-2223 high-T(c) superconductors, and satisfactory results were obtained.