EBSD patterns simulating multilayer twins based on dynamical theory of electron diffraction.

Electron backscatter diffraction (EBSD) can be employed to determine crystal structures but has not been used alone to identify defects at the atom scale due to the lack of understanding of the EBSD patterns generated by various structure defects. In the present work, the EBSD patterns of FCC-Fe with 9-layer, 6-layer and 3-layer twin structures are simulated, respectively, using the revised real space (RRS) method and compared with the counterpart of perfect crystals. Our results show that when the electron beam is incident along a direction parallel to the twin plane, the pattern appears symmetrical with respect to the corresponding Kikuchi band of the twin plane, and the diffraction details within the Kikuchi band also exhibit symmetry with respect to the middle line of the Kikuchi band. Moreover, the overall clarity of the patterns decreases, and the pattern becomes more blurred with increasing the distance from the Kikuchi band corresponding to the twin plane. By contrast, the incident electron beam along the direction perpendicular to the twin plane results in diffraction superposition of the matrix region and the shear region, which shows twofold rotational symmetry with respect to the Kikuchi pole corresponding to the normal to the twin plane. In addition, some extra Kikuchi bands appear in the EBSD patterns due to the long-period structures of the multilayer twins. As the number of multilayer twins decreases, the number of extra Kikuchi bands decreases and the area of the blurring pattern increases. The correlation between twin structures and EBSD patterns provides theoretical insights for identifying twin structures by the EBSD technique.

EBSD patterns simulation of dislocation structures based on electron diffraction dynamic theory.

Electron backscatter diffraction (EBSD) technology is a powerful tool for materials characterization including crystal orientation mapping, phase identification, and strain analysis. However, it is still challenging for using EBSD to identify crystallographic defects due to the insufficient understanding of the diffraction patterns of different defect structures. In the present work, EBSD patterns of FCC-Fe with 1/2 < 110 > edge dislocation dipole and 1/6 < 11̅2 > screw dislocation quadrupole structures are simulated by the revised real space (RRS) method. Our results showed that the presence of dislocations deteriorates the overall quality of the diffraction pattern and have different effects on different Kikuchi bands and Kikuchi poles. The edges of the Kikuchi band corresponding to the edge dislocation glide plane are sharp and the diffraction details within the band are clear. The sharpness of the edges of the Kikuchi band corresponding to the crystal plane normal to the dislocation Burgers vector is reduced, but the intra-band diffraction details are clear. Other Kikuchi bands show obvious anisotropic blurring. The diffraction details of the Kikuchi pole corresponding to the screw dislocation Burgers vector are clear, the edges of the Kikuchi bands across this pole are sharp, and the diffraction details within the bands are clear in the segments close to this pole and blurred in the segments far away from it. Other Kikuchi bands and Kikuchi poles are blurred. Our results indicate that the EBSD pattern can be simulated based on the electron diffraction dynamic theory and the correlation between dislocation structure and EBSD pattern is revealed, which provides theoretical guidance for the resolution of dislocation structures by the EBSD technique.

All-Scale Hierarchical Structure Contributing to Ultralow Thermal Conductivity of Zintl Phase CaAg0.2Zn0.4Sb.

TiNiSi-type Zintl phase CaAgSb can transform into LiGaGe-type Zintl phase CaAg x Zn(1- x )/2Sb when some of the Ag atoms are substituted by Zn atoms, leading to an ultralow thermal conductivity of ≈0.4 W m-1 K-1 in the whole measured temperature range of CaAg0.2Zn0.4Sb. The microstructure is then investigated by spherical aberration-corrected electron microscopy on an atomic scale, which reveals an all-scale hierarchical structure that can scatter the phonons in a wide frequency range. There exist a large quantity of CaAgSb nanometer precipitates as well as quite a lot of edge dislocations close to these nanometer precipitates, thus releasing the stress caused by the mismatch between the precipitates and the parent phase. Many twin boundaries also exist around the CaAgSb precipitates. High-density point defects contain the randomly dispersed Ag vacancies and Zn atoms substituted for the Ag atoms. All these widely distributed multidimensional defects contribute to the decrease of lattice thermal conductivity in a wide temperature range.

A fast reciprocal space method for image simulation.

In this paper, we introduce a fast reciprocal space method for image simulation. It is well known that the scattering matrix (SM) P with NxN elements consists of N different structure factors and N different excitation errors. However, most structure factors of the SM P are extremely small so that they can be neglected. Therefore, the size of the SM P is reduced drastically. On the other hand, the structure factors have two-dimensional space group symmetries, so that by reducing the symmetry related structure factors to symmetrically independent structure factors, the size of the SM P can be reduced further. The calculation speed based on the simplified SM P will be several hundred times faster than that by other conventional methods. In this paper, we describe the method for how to reduce the SM P in detail and give an example of implementation.

Quantitative comparison between real space and Bloch wave methods in image simulation.

Both Bloch wave (BW) and real space multislice (RS-MS) methods are based on the Schrödinger equation. The BW method is considered to be the most accurate and popular simulation method used in various simulations, and it has solved many crystallographic problems. In this paper, we verified that the aforementioned two methods are similar to each other with minor difference. First, the RS-MS method is implemented in the real space, while the BW method is carried out in the reciprocal space. Furthermore, by quantitatively calculating exit wavefunctions of four crystals, i.e., Cu, MgAl2O4, Mg44Rh7 and KNbO3, we found that the RS-MS method offers certain advantages over the BW method. Firstly, the RS-MS method takes all the structure factors into account to calculate crystal potentials, so accuracy loss caused from the crystal potential is effectively avoided. Secondly, the dimension of the scattering matrix for the RS-MS method is proportional to the area of the 2 dimensional (2D) unit cell which is perpendicular to the incident beam direction, whereas that for the BW method is proportional to the square of the area of the 2D unit cell. To reduce computation time, reduction of dimension of the scattering matrix for the BW method has to be performed, thus accuracy loss is inevitable even if compensated by the Bethe potential method. For crystals with a small 2D unit cell, both simulation methods work well. When the area of the 2D unit cell is larger than square of 2.0nm, for example KNbO3, the size of the scattering matrix of the BW method is too large to be carried out by simulation and one should use the RS-MS method instead. This paper presents a tutorial comparison of the different methods.

Accurate determination of lattice parameters based on Niggli reduced cell theory by using digitized electron diffraction micrograph.

In this paper, we used Niggli reduced cell theory to determine lattice constants of a micro/nano crystal by using electron diffraction patterns. The Niggli reduced cell method enhanced the accuracy of lattice constant measurement obviously, because the lengths and the angles of lattice vectors of a primitive cell can be measured directly on the electron micrographs instead of a double tilt holder. With the aid of digitized algorithm and least square optimization by using three digitized micrographs, a valid reciprocal Niggli reduced cell number can be obtained. Thus a reciprocal and real Bravais lattices are acquired. The results of three examples, i.e., Mg4Zn7, an unknown phase (Precipitate phase in nickel-base superalloy) and Ba4Ti13O30 showed that the maximum errors are 1.6% for lengths and are 0.3% for angles.

An accurate multislice method for low-energy transmission electron microscopy.

The conventional multislice method (CMS), originally proposed by Cowley and Moodie (1957), is an important algorithm for image and electron diffraction calculations in transmission electron microscopy. Nevertheless, this method is based on the so-called high-energy approximation, which neglects the second differential term ∂(2)φ(r)/∂z(2) to greatly simplify the calculation without severe loss of accuracy. In the current study, we show that for low-energy transmission electron microscopy (LE-TEM) (<100 kV), the high-energy approximation error becomes large and the accurate multislice method, proposed by Chen and Van Dyck (1997), can be used as an alternative method to obtain more accurate calculations. The accurate multislice method, called the revised real space method (RRS) in this paper, can be realized by treating the propagation and scattering as an entirety in real space. A detailed comparison of the numerical results of the RRS and CMS at different accelerating voltages, Debye-Waller factors, and beam tilts is performed. Results show that for image and diffraction simulations in LE-TEM, CMS is no longer sufficiently accurate and the RRS procedure can be used as an alternative method with reasonable computing time.

Symmetry-adapted spherical harmonics method for high-resolution 3D single-particle reconstructions.

Three-dimensional (3D) reconstruction is the last and an essential step toward high-resolution structural determination in single-particle cryo-electron microscopy (cryoEM). We have implemented a new algorithm for reconstructing 3D structures of macromolecular complexes with icosahedral symmetry from cryoEM images. Icosahedral symmetry-adapted functions (ISAFs) are used to interpolate structural factors in the reciprocal space to generate a 3D reconstruction in spherical coordinates. In our implementation, we introduced a recursive method for deriving higher order ISAFs from three lower order seed functions. We demonstrate improvements of our new method in both the noise suppression and the effective resolution in 3D reconstruction over the commonly used Fourier-Bessel synthesis method introduced by Crowther et al. three decades ago. Our 3D reconstruction method can be extended to macromolecular complexes with other symmetry types and is thus likely to impact future high-resolution cryoEM single-particle reconstruction efforts in general.