Quasicrystals with 1-D Translational Periodicity and A Ten-Fold Rotation Axis

1985 ◽  
Vol 58 ◽  
Author(s):  
L. Bendersky

ABSTRACTStudies of phase formation in rapidly solidified Al-Mn alloys (composition range 18-22 at% Mn) show that an icosahedral phase is replaced by another noncrystallographic phase, a decagonal phase. The decagonal phase is another example of quasicrystal: It has a noncrystallographic point group (10/m or lO/mmm) together with long-range orientational order and onedimensional translational symmetry. The decagonal phase is an intermediate phase between an icosahedral phase and a crystal both from the symmetry and from the solidification condition points of view.

Author(s):  
K.H. Kuo ◽  
H. Zhang

Decagonal quasicrystal is a two-dimensional one with a periodicity of about 1.2 or 1.6 nm along its tenfold rotation axis. It is known to exist in rapidly solidified Al-rich Al-Mn-Si and Al-Cr-Si alloys, sometimes coexisting with the bcc α-AlMnSi or cubic Al13Cr4Si4 phase. Both these two crystalline phases are known to have many icosahedral units in them. The structural similarity between the decagonal phase and the related bcc α-AlMnSi has been studied extensively lately.However, recently we have found a new base-centered orthorhombic phase with a=1.24, b=3.79, and c=1.23 nm coexisting with the decagonal phase to these alloys. Moreover, evidence of a continuous transformation from the latter to the former has been found by selected area electron diffraction. Fig. la is the tenfold electron diffraction pattern (EDP) of the decagonal quasicrystal with strong spots forming a series of concentric decagons. However, in the region close to the boundary to the crystal, the circle on which the inner 10 strong spots lie becomes an ellipse with its long axis in the arrowed direction (Fig. 1b). The closer to the boundary, the more the distortion of this decagon (Fig. 1c) and finally the EDP changes almost to a 2D crossgrid pattern of a base-centered crystal (a reciprocal unit cell is outlined in Fig. 1d).


Author(s):  
Weimin Bian ◽  
Yimei Zhu

We propose a crystal model that is in excellent agreement with the experimental electron diffraction patterns and high-resolution electron microscopy images of the icosahedral phase in Mn-Al and related systems. Structurally, the model has long-range translational order with a large unit-cell (Im3 space group) containing 10038 atoms, as well as orientational order characterized by symmetry close to the m35 point group which is commonly assigned for quasicrystals.Fig.l(a)-(c) show, respectively, the SAD patterns of the so-called twofold, threefold, and fivefold axes observed in rapid quenched Al-14at%Mn. Simulation of the corresponding SAD patterns (Fig.l(d)-(h)) suggested that they did not result from a single zone-axis diffraction, but from several closely orientated zone axes. For example, Fig.1(f) was generated by the superposition of the [305], [508], and [8 0 13],…. axes (denoted as N-<305>); the rotation angles from the [001] axis to each axis are 30.96°, 32.01°, and 31.61 °, respectively. All are very close to 31.71 °, which is the angle between a twofold and a fivefold axis in the m35 point group. In a conventional electron diffraction experiment, if the [001] axis of the crystal is rotated 31.71° around the [010] axis, these three zone axes would simultaneously satisfy the Bragg conditions and cannot be separated. Such superposition in the projected diffraction pattern, especially when the unit-cell is large, can yield a pseudo-fivefold symmetry which is indistinguishable with a true fivefold symmetry in SAD.


Author(s):  
Wang Rong ◽  
Ma Lina ◽  
K.H. Kuo

Up to now, decagonal quasicrystals have been found in the alloys of whole Al-Pt group metals [1,2]. The present paper is concerned with the TEM study of a hitherto unreported hexagonal phase in rapidly solidified Al-Ir, Al-Pd and Al-Pt alloys.The ribbons of Al5Ir, Al5Pd and Al5Pt were obtained by spun-quenching. Specimens cut from the ribbons were ion thinned and examined in a JEM 100CX electron microscope. In both rapidly solidified Al5Ir and Al5Pd alloys, the decagonal quasicrystal, with rosette or dendritic morphologies can be easily identified by its electron diffraction patterns(EDPs). The EDPs of the decagonal phase for the two alloys are quite similar. However, the existance of decagonal quasicrystal in the Al-Pt alloy has not been verified by our TEM study. It is probably for the reason that the cooling rate is not great enough for the Al5Pt alloy to form the decagonal phase. During the TEM study, a metastable hexagonal phase has been observed in the Al5Ir, Al5Pd and Al5Pt alloys. The lattic parameters calculated from the X-ray powder data of this phase are a=1.229 and c=2.647nm(Al-Pd) and a=1.231 and c=2.623nm(Al-Ir). The composition of this phase was determined by EDS analysis as Al4(Ir, Pd or Pt). It coexists with the decagonal phase in the alloys and transformed to other stable crystalline phases on heating to high temperature. A comparison between the EDPs of the hexagonal and the decagonal phase are shown in Fig.l. Fig. 1(a) is the EDPs of the decagonal phase in various orientions and the EDPs of the hexagonal phase are shown in Fig.1(b), in a similar arrangement as Fig.1(a). It can be clearly seen that the EDPs of the hexagonal phase, especially the distribution of strong spots, are quite similar to their partners of the decagonal quasicrystal in Fig.1(a). All the angles, shown in Fig.l, between two corresponding EDPs are very close to each other. All of these seem strongly to point out that a close structural relationshipexists between these two phases:[110]//d10 [001]//d2(D) //d2 (P)The structure of α-AlFeSi is well known [3] and the 54-atom Mackay icosahedron with double icosahedral shells in the α-AlFeSi structure [4] have been used to model the icosahedral quasicrystal structure. Fig.2(a) and (b) show, respectively, the [110] and [001] projections of the crystal structure of α- AlFeSi, and decagon-pentagons can easily be identified in the former and hexagons in the latter. In addition, the optical transforms of these projections show clearly decagons and hexagons of strong spots, quite similar to those in [110] and [001] EDPs in Fig.1(b). This not only proves the Al(Ir, Pt, Pd) metastable phase being icostructural with the α-AlFeSi phase but also explains the orientation relationship mentioned above.


1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.


1985 ◽  
Vol 58 ◽  
Author(s):  
Robert J. Schaefer ◽  
Leonid A Bendersky

ABSTRACTElectron beam surface melting has been used to study Al-Mn and Al-Mn-Si alloys subjected to a wide range of solidification conditions. Several of the reported equilibrium intermetallic phases are not found even at moderate growth rates. Beyond a composition-dependent critical velocity the equilibrium phases are all replaced by the quasicrystalline icosahedral and decagonal (T) phases. The icosahedral phase is favored over the T phase by higher solidification velocities. The addition of Si to Al-Mn alloys eliminates the T phase, but does not significantly facilitate the formation of the icosahedral phase by electron beam melting because the ternary α and β phases of Al-Mn-Si are able to grow rapidly into the electron beam melts.


1986 ◽  
Vol 20 (10) ◽  
pp. 1359-1360 ◽  
Author(s):  
G.V.S. Sastry ◽  
C. Suryanarayana

2008 ◽  
Vol 59 (10) ◽  
pp. 1119-1122 ◽  
Author(s):  
N.K. Mukhopadhyay ◽  
H.J. Chang ◽  
J.Y. Lee ◽  
D.H. Kim

2010 ◽  
Vol 1256 ◽  
Author(s):  
Sujata Mazumder ◽  
Jiten Ghosh

AbstractThe detailed structure of nanocrystalline BaTiO3 powder during ball milling has been studied using XRD & TEM. The study illustrates important advances in understanding atomic scale properties of this material. Ferroelectric BaTiO3 powder undergoes phase transformation along the sequence Cubic(Pm3m)-tetragonal(P4mm)-orthohombic (Amm2)-rhombohedral(R3m) structure when pressureless sintered samples are cooled from high temperature to low temperature. The high to low symmetry phases are not related to group subgroup symmetry as transformation is discontinuous and first order in nature and the twin relationship in the low symmetry is forbidden by Landau theory. In case of ball milled BaTiO3 powder a continuous and diffusionless phase transition occur via second order to and from a metastable intermediate phase. In this pathway crystallites in the aggregation are twinned and the twin structure is related to crystal point group m3m which in the present case is illustrated as having 6mm symmetry formed under low driving force. The unit cell evolution due to phase transition and the crystallographic relationship are established. The phase transformation, coalescence and twin structure of thermally annealed BaTiO3 nanocrystals under high vacuum has been investigated using in situ high temperature XRD. The structure analysis is performed with the use of the method of computer modelling of disorder structure and simulation of corresponding diffraction pattern.


1991 ◽  
Vol 6 (8) ◽  
pp. 1641-1649 ◽  
Author(s):  
S. Ebalard ◽  
F. Spaepen

A 1/1-type approximant to the AlCuCr icosahedral phase and approximants to a decagonal phase have been found in an as-cast Al65Cu20Cr15 ingot. Selected area electron diffraction indicates that the 1/1-type approximant consists of Mackay icosahedra arranged on a bcc lattice, similar to the α-AlMnSi cubic phase. Ordering of the glue atoms produces a base-centered orthorhombic superstructure, making the overall structure monoclinic P2/m, with lattice parameters a = 12.6 Å, c = 17.92 Å, and α = 90°.


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