Incommensurate superstructures are interesting problems for high
resolution electron microscopy. If modulations are formed within a plane of
a host lattice parallel to the incident beam direction, their structures can
be known directly from images (1,2,3). In this paper, an incommensurate
superstructure of hexagonal potassium tungsten bronze,
K0.3WO3,
is observed by a 100B high-resolution electron microscope and its structure
model is proposed. The hexagonal tungsten bronze was determined by Magneli
(4) and its structure is shown in Fig. 1. The structure consists of
WO6 octahedra and alkali metal ions. The alkali
metal ions situated in hexagonal tunnels do not lie at the same level of the
WO6 octahedra but at ¼ c above or below them. It
was assumed that the alkali metal ions were distributed in a random fashion.
Fig. 2 shows a structure image of
K0.3WO3,
taken along the [100] direction. The white spots correspond to hexagonal
tunnels in Fig. 1. Fig. 3 shows an electron diffraction pattern taken along
the [010] direction. Some additional weak superstructure spots are observed.
The superstructure spot (indicated by A) is situated at a non-integral
multiple position of the subcell spots along the c*-axis, indicating that
the incommensurate superstructure has a multiplicity of 2.2 x c of the
subcell. The non-integral periodicity can be seen in a high-resolution image
taken along the [010] direction, as shown in Fig. 4. At the thick crystal
regions, some weak dark bands running parallel to the c axis are observed,
in which they have two different widths (2 x c or 2.5 x c) along the c axis.
An average distance between the adjacent dark bands becomes about 2.2 x c,
which is consistent with an optical diffraction pattern (inset in Fig. 4).
One of the possible models for the incommensurate superstructure of the
hexagonal tungsten bronze is proposed in Fig. 5. The superstructure arises
from the local ordering of K ion vacancies located in the tunnels along the
c axis. The vacancies are formed at every fourth or fifth site of K ions. We
call them structures with n = 4 and n = 5. The incommensurate superstructure
results from a mixture of the structure elements with n = 4 and n = 5,
causing the formation of a non-integral periodicity observed presently. It
should be noted in Fig. 4 that the image from a thin region does not show
the superstructure but the image from a thick region does. It seems that
this phenomenon arises from dynamical diffraction effects. This will be
discussed in detail on the basis of the image calculation.
An electron microscopic and optical diffraction analysis of the structure of Limulus telson muscle thick filaments.
