Quasicrystals approximants

We have reconstructed the 3D structure of a complex quasicrystal approximant v-AlCrFe (P6 m, a = 40.687 and c = 12.546 A) (Zou et al, 2004). Due to the huge unit cell, it was necessary to combine crystallographic data from 13 projections to resolve the atoms. Electron microscopy images containing both amplitude and phase information were combined with amplitudes from electron diffraction patterns. 124 of the 129 unique atoms (1176 in the unit cell) were found in the remarkably clean calculated potential maps. This investigation demonstrates that inorganic crystals of any complexity can be solved by electron crystallography. 

Since then this method has been used to solve numerous other complex crystal structures [6-13]. Because solving a stmcture from a single projection requires a short (3 to 5 A) crystal axis, the method was later extended to combine the information from several orientations which allows also to uncover stmctures with pronounced overlap of the atom columns in projection. This technique was applied in 1990 to solve the 3D stmcture of the mineral staurolithe HFe2Al9Si404 [14, 15] and more recently to determine the stmcture of the huge quasicrystal approximant v-AlCrFe [16] which contains 129 atoms per as5mimetric unit. How CIP works to solve a crystal stmcture from projected data is shown in figure 10 (for further details see [17]). 

Here the principles of constructing a 3D structure model from several HREM images of projections of inorganic crystals will be presented. Some of the principles may also be applied to non-periodic objects. A complex quasicrystal approximant v-AlCrFe is used as an example (Zou et al., 2003). Procedures for ab initio structure determination by 3D reconstruction are described in detail. The software CRISP, ELD. Triple and 3D-Map are used for 3D reconstruction. The 3D reconstruction method was demonstrated on the silicate mineral (Wenk et al. 1992). It was also applied to solve the 3D structures of a series mesoporous materials (Keneda etal. 2002). 

Al-Cr-Fe alloys are of interest as new lightweight alloys for structural apphcations, in particular, for the production of protective coatings formed by alumina scales from alloys of compositions that he in the Al-rich comer of the system. Al-Cr-Fe quasicrystal approximants are also potential candidates for new applications because of their specific properties. Alternatively, the addition of chromium to Fc3Al- and FeAl-based alloys produces excellent candidates for moderate and high temperature apphcations. [2005Pal] showed that... 

Toward Quasicrystals and Their Approximants 3.1 Polar Intermetallics Containing the Triels... 

By using slightly different words, approximants are translationally normal crystal compounds generally with large unit cells that contain condensed, highly symmetric building blocks such as dodecahedra and icosahedra and have compositions close to those of related quasicrystals. 

Crystal approximants. Several crystalline phases contain more or less closely packed atomic assemblies (polyhedra, clusters) which have been considered fundamental constituents of several quasicrystals, metal glasses and liquids. Such crystalline phases (crystal approximants), as reported in the previous paragraph, are often observed in the same (or similar) systems, as those corresponding to the formation of quasicrystals and under similar preparation conditions. Crystalline phases closely related to the quasicrystals (containing similar building blocks) have generally complex structures as approximants to the ico-quasicrystals we may, for instance, mention the Frank-Kasper phases (previously described in 3.9.3.1). 

Abstract. We compute the velocity correlation function of electronic states close to the Fermi energy, in approximants of quasicrystals. As we show the long time value of this correlation function is small. This means a small Fermi velocity, in agreement with previous band structure studies. Furthermore the correlation function is negative on a large time interval which means a phenomenon of backscattering. As shown in previous studies the backscattering can explain unusual conduction properties, observed in these alloys, such as for example the increase of conductivity with disorder. 

Nobumichi Tamura (left) obtained his Ph.D. in 1993 at the Institut National Polytechnique de Grenoble (INPG) for his work on the structure of quasicrystals and crystalline approximant phases. In 1998 he moved to Oak Ridge National Laboratory to contribute to the development of a new synchrotron-based X-ray microfocus technique capable of resolving strain and texture in thin films with submicrometer spatial resolution. He applied this technique in the field of microelectronics. He is currently staff scientist at the Lawrence Berkeley National Laboratory, where he leads the X-ray microdiffraction project at the Advanced Light Source. His research interest is presently focused on the study of mechanical properties of thin films at mesoscopic scale using synchrotron radiation. 

Quasicrystals represent the third type of aperiodic materials. Quasiperiodicity may occur in one, two, or three dimensions of physical space and is associated with special irrational numbers such as the golden mean r = (1 -h /5)/2, and = 2 -F V3. The most remarkable feature of quasicrystals is the appearance of noncrystal-lographic point group symmetries in their diffraction patterns, such as 8/mmm, lO/mmm, l2/mmm, and 2lm35. The golden mean is related to fivefold symmetry via the relation r = 2 cos( r/5) r can be considered as the most irrational number, since it is the irrational number that has the worst approximation by a truncated continued fraction,... 

The Fibonacci sequence can be used to explain the idea of a periodic rational approximant. If the sequence. .. LSLLSLSLS... represents a quasicrystal, then the... 

K Kimura, A Hori, H Yamashita, H Ino. CrystaUine structures as an approximant of quasicrystals and distortion of B12 icosahedron in boron-rich solids. Phase Transitions 44 173, 1993. 

Aud] Audier, M., Durand-Charre, M., Laclau, E., Klein, H., Phase EquiUbria in the Al-Cr System , J. Alloys Compd., 220, 225-230 (1995) (Crys. Stracture, Experimental,, 17) [1995Li] Li, X.Z., Dong, C., Dubois, J.M., Structural Study of Crystalline Approximants of the Al-Cu-Fe-Cr Decagonal Quasicrystal , J. Appl. Crystallogr., 28(2), 96-104 (1995) (Crys. Stracture, Experimental, 16)... 

Dem] Demange, V., Ghanbaja, J., Machizaud, F., Dubois, J.M., About -y-Brass Phases in die Al-Cr-Fe System and flieir Relationships to Quasicrystals and Approximants , Philos. Mag., 85(12), 1261-1272 (2005) (Crys. Structure, Experimental, 36)... 

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