Energy-filtered Convergent-beam Electron Diffraction Research Articles

Determination of structure factors, lattice strains and accelerating voltage by energy-filtered convergent beam electron diffraction

Transmission electron microscopes with integrated imaging energy filters make it possible to acquire two-dimensional energy-filtered convergent beam electron diffraction patterns. Zero-loss filtered diffraction patterns can be compared quantitatively with computer simulations and by this the underlying crystallographic parameters can be determined. High-index reflections are used to measure lattice strain with high accuracy and also to determine the accelerating voltage. Low-index reflections are used to measure structure factors. For structure factor determination, we have modified the refinement method of Zuo and Spence [Ultramicroscopy 35 (1991) 185] to include a global optimization algorithm which is a variant of the simulated annealing procedure.

Measurement of Debye-Waller factors of silicon as a function of temperature using energy-filtered CBED rocking-curve technique

The advantages of quantitative Convergent Beam Electron Diffraction (CBED) method for x-ray structure factor determination have been reviewed by Spence. The CBED method requires accurate values of Debye-Waller (D-W) factors for the estimation of the coefficients of crystal potential of the higher order beams, Vg, the calculation of the absorption potential, V′gusing the Einstein model for phonons, and finally the conversion of the fitted values of the coefficients of crystal potential, V″, to x-ray structure factors. Debye-Waller factors are conventionally determined by neutron or x-ray diffraction methods. Because of the difficulties in conducting high temperature neutron and x-ray diffraction experiments, D-W factors are rarely measured at temperatures above room temperature. Debye-Waller factors at high temperatures can be determined by Convergent Beam Electron diffraction (CBED) method using Transmission Electron Microscopy (TEM) employed with a hot stage attachment. Recently Holmestad et al. have attempted to measure the D-W factors by matching the energy-filtered Higher Order Laue Zone (HOLZ) line intensities near liquid nitrogen temperature.

Experimental determination of low order structure factors in the intermetallic compound TiAl

Rocking curves from several low order reflections in TiAl were recorded in digitized form using energy-filtered convergent beam electron diffraction in a transmission electron microscope. The low order reflections studied were 001, 002, 200, 111, 110, 220, 202, 113, and 311. These experimental rocking curves were simulated using computations based on the dynamic theory of electron diffraction. From these simulations, values of the X-ray structure factors for these reflections were deduced, and then used to determine charge difference maps for varioius plane sections in TiAl. These charge difference maps were compared with theoretical predictions, and it was found that there is a considerable degree of agreement between theory and experiment.

On the experimental determination of low-order structure factors in TiAl by energy-filtered convergent-beam electron diffraction

It has been claimed that the effective Peierls stresses and mobilities of certain dislocations in TiAl are influenced by the anisotropy of bonding charge densities. This claim is based on the angular variation of electron charge density calculated by theory. It is important to verify the results of these calculations experimentally, and the present paper describes a series of such experiments. A description of the bonding charge density distribution in materials can be obtained by utilizing the charge deformation density (Δρ (r)) defined by(1) where V is the volume of the unit cell, Fobs is the experimentally determined low order structure factor and Fcalc is the structure factor calculated using the Hartree-Fock neutral atom model. To determine the experimental low order structure factors, a technique involving a combination of convergent beam electron diffraction (CBED) and electron energy loss spectroscopy (EELS) has been used.

Resolution limits in annular dark field STEM

Recent experiments have provided high-resolution annular dark field atom structure images of zone axis crystalline samples. This paper reviews steps towards assessment of such images using simulation and quantitative experiments. Work reviewed includes a power spectral analysis of thin amorphous carbon film images to determine the spherical aberration coefficient C s and to calibrate the defocus Δ f. Agreement with experiment provides evidence of the validity of a “frozen phonon” algorithm for simulation of energy-filtered convergent beam electron diffraction that is then extended to image simulation. For both silicon and indium phosphide the simulations are in good agreement with the incoherent imaging model. Experiments with indium phosphide also support the validity of the incoherent imaging model for zone-axis crystals. Limits of resolution in ADF-STEM for zone-axis-oriented crystals are therefore given by the contrast transfer function of the incoherent imaging model. For a polepiece with C s=0.7 mm at 100 kV, this corresponds to a resolution limit of 1.8 Å at a contrast level of 5% at Scherzer settings. A somewhat larger aperture at larger defocus settings enhances the contrast spatial frequencies close to the resolution limit while decreasing contrast for spatial frequencies further away.

Energy-filtered convergent-beam electron diffraction in STEM

Abstract Energy-filtered convergent-beam electron diffraction (CBED) patterns were obtained from a 10A˚region of the specimen in a scanning transmission electron microscope (STEM) equipped with a digital image-acquisition system. For crystalline silicon, plasmon scattering causes a blurring of the low-order Bragg beams. Significant plasmon intensity was also observed at high angles with an angular distribution duplicating the zero-loss scattering. The plasmon-loss pattern contained a high-order Laue-zone (HOLZ) ring and Kikuchi bands from elastic, phonon, and plasmon multiple scattering. The HOLZ ring intensity relative to the diffuse background was not significantly different from the zero-loss pattern. Quantitative agreement between experimental silicon (100) CBED patterns and patterns calculated by the frozen-phonon technique was achieved. The silicon room-temperature vibration amplitude was determined to be 0.078±0.002A˚as compared with the value of 0.0764±0.0002A˚reported for X-ray measurement [P.J.E. Aldred and M. Hart, Proc. Roy. Soc. (London) A 332 (1973) 223, 239].

Silicon vibration amplitude determined by energy-filtered CBED

The frozen phonon method was recently developed to include the effects of thermal vibrations in the multislice calculation. In this method, each atom in the simulated specimen is displaced by a random amount which follows a Gaussian distribution with a standard deviation equal to the atomic vibration amplitude. Convergent beam electron diffraction (CBED) patterns calculated by this technique contain Kikuchi bands and a thermal diffuse background which were matched quantitatively to experimental Si (100) CBED patterns for scattering angles up to the first order Laue Zone. In this paper, we report the measurement of the room temperature silicon vibration amplitude from comparison of energy filtered CBED with frozen phonon calculations.The energy filtered Si (100) patterns were obtained with a VG HB501A STEM in microdiffraction mode by fixing a convergent probe (7.5mrad half angle, probe size ≈ 40Å) on the specimen and scanning the post specimen electrons over a small axial collector aperture (1.6mrad).