Precession electron diffraction: observed and calculated intensities.

Theory and algorithms have been developed for performing kinematical and dynamical two-beam and multibeam dynamical simulations of precession electron diffraction patterns. Intensities in experimental precession patterns have been quantified and are shown to be less dynamical.

Structure determination of the hexagonal quasicrystal approximant micro'-(Al,Si)4Cr by the strong reflections approach.

A number of different crystalline phases have been found in Al-rich Al-Cr-Si alloys by transmission electron microscopy (TEM). Among these, the new hexagonal phase micro'-(Al,Si)(4)Cr (a=2.01 and c=1.24 nm) often found coexisting with the hexagonal micro-(Al,Si)(4)Cr (a=1.998 and c=2.4673 nm, isostructural with micro-Al(4)Mn) and also with the hexagonal lambda-(Al,Si)(4)Cr (a=2.839 and c=1.239 nm, isostructural with lambda-Al(4)Mn). It is evident from their electron diffraction patterns that the structures of these three phases are related. The strong reflections in all three are distributed in a similar way. They all exhibit a pseudo-icosahedral symmetry. The structure factor amplitudes and phases for the strong reflections of the micro' phase could therefore be adopted from those of the lambda phase, according to the strong reflections approach. A structure model of the micro' phase is thus deduced from the known lambda-Al(4)Mn. micro' consists of chains of 3+3 or 4+2 interpenetrated icosahedra along the 100 directions. Similar to the lambda phase, there are two flat layers (F) and four puckered layers (P) in each unit cell of micro', stacked along the c-axis in a sequence of PFP(PFP)' where the (PFP)' block is related to the PFP block by a 6(3) screw.

Structure model for the tau(mu) phase in Al-Cr-Si alloys deduced from the lambda phase by the strong-reflections approach.

There are very obvious common features in the electron diffraction patterns of the lambda and tau(mu) phases in the Al-Cr-Si system. The positions of the strong reflections and their intensity distributions are similar for the two structures. The relation of the reciprocal lattices of the lambda and tau(mu) phases is studied. By applying the strong-reflections approach, the structure factors of tau(mu) are deduced from the corresponding structure factors of the known lambda phase. Rules for selecting reflections for the strong-reflections approach are described. Similar to that of lambda, the structure of tau(mu) contains six layers stacked along the c axis in each unit cell. There are 752 atoms in each unit cell, 53 of them are unique. The corresponding composition of the tau(mu) model is Al(3.82 - x)CrSi(x). Simulated electron diffraction patterns from the structure model are in good agreement with the experimental ones. The arrangement of interpenetrated icosahedral clusters in the tau(mu) phase is discussed.