UnitCell Tools, a package to determine unit-cell parameters from a single electron diffraction pattern

Electron diffraction techniques in transmission electron microscopy (TEM) have been successfully employed for determining the unit-cell parameters of crystal phases, albeit they exhibit a limited accuracy compared with X-ray or neutron diffraction, and they often involve a tedious measurement procedure. Here, a new package for determining unit-cell parameters from a single electron diffraction pattern has been developed. The essence of the package is to reconstruct a 3D reciprocal primitive cell from a single electron diffraction pattern containing both zero-order Laue zone and high-order Laue zone reflections. Subsequently, the primitive cell can be reduced to the Niggli cell which, in turn, can be converted into the unit cell. Using both simulated and experimental patterns, we detail the working procedure and address some effects of experimental conditions (diffraction distortions, misorientation of the zone axis and the use of high-index zone axis) on the robustness and accuracy of the software developed. The feasibility of unit-cell determination of the TiO2 nanorod using this package is also demonstrated. Should the parallel-beam, nano-beam and convergent-beam modes of the TEM be used flexibly, the software can determine unit-cell parameters of unknown-structure crystallites (typically >50 nm).

Convergent-beam electron-diffraction-pattern symmetry of nanodomains in complex lead-based perovskite crystals

Convergent-beam electron diffraction (CBED) recorded using nanometre-sized probes, in principle, can detect the highest symmetry in a crystal. However, symmetry reduction may occur by overlapping crystal domains along the beam direction. Thus, delineating the relationship between the recorded and the crystal symmetry is important for studying crystals with complex nanodomains. This paper reports a study of the averaged local symmetry of 71°/109° rhombohedral (R), 90° tetragonal (T) and 180° monoclinic (M) nanodomain structures. The averaged symmetry of nanodomain structures is investigated by CBED simulations using the multislice method. The simulation results show that the 71°-R, 109°-R and 90°-T nanodomain structures partially mimic the monoclinic symmetries ofCmandPmthat have been proposed by the adaptive phase model. This study is also compared to the reported experimental CBED patterns recorded from PMN-31%PT.

Unit Cell Determination of New Minerals by Using Electron Diffraction

Many new minerals recently discovered in Kazakhstan had platy (niksergievite), fiber (kazakhstanite) or fine powder (mitryaevaite) structural appearance. In monoclinic minerals with perfect or good (001) cleavage, d100 i d010-spacings in the hk0 zone could be measured on selected area electron-diffraction pattern from monocrystal tilted the way that axis c is parallel to the electron beam direction. This method was used for measuring d-spacings in new minerals such as kazakhstanite, niksergievite as well as in new discovered micas – sokolovaite and orlovite. In minerals with triclinic structure (mitryaevaite) the same method was used to determine d100, d010 as well as γ=1800-γ* (γ* is an angle between reciprocal lattice axes a* and b*). hk0-indices of each ring were defined by comparison of the normal texture (ring type) pattern and selected area pattern. For example, hk0-indices for triclinic cell of mitryaevaite were (010), (100), (-110), (110), (020) etc. When specimen with preferred orientation is tilted under angle φ toward electron beam, an "oblique texture" electron-diffraction pattern is obtained. Arcs of the ellipses on such diffraction pattern are formed by intersection of Ewald sphere with ring nodes. The height of the arc's maximum above the tilt axis is calculated by using the following formula: D=hp+ks+lq, where p, s, q are measured on the diffraction pattern [1-3]. For example, on "oblique texture" electron-diffraction pattern from vanalite with perfect (010) cleavage, arcs are merged with layer lines that intersect the ellipses and D=ks. Allocation of indices on texture electron-diffraction patterns from monoclinic niksergievite, sokolovaite and orlovite with perfect (001) cleavage is more difficult. In these cases, D= hp+lq. Heights of the arcs are situated symmetrical in regards to each lq level. With the help of "oblique texture" diffraction patterns stacking polytypes were indicated for such minerals.