Hai-fu Fan

Image processing in high-resolution electron microscopy using the direct method. II. Image deconvolution

A new method is proposed to estimate the defocus (Δf) from a single electron micrograph (EM). The method has been tested by simulations using theoretical EMs calculated under different defocus conditions. The preliminary method is successful except when the EM is taken near the optimum defocus. This can be improved by making use of the information from the electron diffraction pattern. The method will be effective for radiation-sensitive materials.

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.

Image Processing in High-Resolution Electron Microscopy using the Direct Method. I. Phase Extension

A procedure to combine the information from an electron micrograph (EM) and the corresponding electron diffraction (ED) pattern is proposed. Here the ED data will be used to obtain a set of amplitudes of the structure factors, while the EM will be used to obtain a set of starting phases assuming the weakphase-object approximation. A direct method is then used to extend the phase information from a resolution of about 2 to 1 A. The efficiency of the procedure has been verified by the test calculation on the model structure of copper perchlorophthalocyanine.

OASIS: a computer program for breaking phase ambiguity in one-wavelength anomalous scattering or single isomorphous substitution (replacement) data

The phase problem is reduced to a sign problem once the anomalous-scatterer or the replacing-heavy-atom sites are located. OASIS adopts the CCP4 format [Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763]. It applies a direct-method procedure to break the phase ambiguity intrinsic to one-wavelength anomalous scattering (OAS) or single isomorphous replacement (SIR) data.

Direct Methods in Superspace. I. Preliminary Theory and Test on the Determination of Incommensurate Modulated Structures

The validity of the Sayre equation [Sayre (1952). Acta Cryst. 5, 60-65] for (3+n)-dimensiona l periodic structures is examined. A practical procedure is proposed for the determination of incommensurate modulated structures; this is an extension of the direct method previously proposed for solving superstructures [Fan Hai-fu, He Lao, Qian Jin-zi & Liu Shixiang (1978). Acta Phys. Sin. 27, 554-558]. With the newly proposed method, the phase problem for the main as well as the satellite reflections can be solved directly without making particular assumptions about the modulation. A .known incommensurate modulated structure, y-Na2CO3, was used in the test. Satisfactory results were obtained.

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.

SAD phasing by combination of direct methods with the Solve/Resolve procedure

In the initial stage of SAD phasing, the essential point is to break the intrinsic phase ambiguity. The presence of two kinds of phase information enables the discrimination of phase doublets from SAD data prior to density modification. One is from the heavy atoms (anomalous scatterers), while the other is from the direct-methods phase relationships. The former can be expressed by the Sim distribution, while the latter can be expressed by the Cochran distribution. Typically, only the Sim distribution has been used to yield initial phases for subsequent density modification. However, it has been demonstrated that using direct-methods phases based on the product of the Sim and Cochran distributions can lead to improved initial phases. In this paper, the direct-methods phasing procedure OASIS has been improved and combined with the SOLVE/RESOLVE procedure. Experimental SAD data from three known proteins with expected Bijvoet ratios / in the range 1.4-7.0% were used as test cases. In all cases, the phases obtained using the program RESOLVE beginning with initial phases based on experimental phases plus Sim and direct-methods information were more accurate than those based on experimental plus Sim phase information alone.

Combining Direct Methods with Isomorphous Replacement or Anomalous Scattering Data. III. The Incorporation of Partial Structure Information

o-~ = The probability formulas given in Parts I and II of this series have been improved by incorporating the information contained in Sims distribution. Possible applications to the discrimination of the phase ambiguities arising from the single isomorphous replacement technique, the one-wavelength anomalous scattering (OAS) technique or pseudo centrosymmetry in small structures are discussed. With a set of experimental protein OAS data, the efficiency of the improved formula has been shown to be better than that of the older one.

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.