scholarly journals A cubic quasicrystal in a rapidly-solidified Mg-Al alloy

2014 ◽  
Vol 70 (a1) ◽  
pp. C91-C91
Author(s):  
Takeshi Kato ◽  
Takehito Seki ◽  
Eiji Abe
Keyword(s):  
Rotational Symmetry ◽  
Point Group ◽  
Physical Space ◽  
Al Alloy ◽  
Fold Axis ◽  
Cubic Symmetry ◽  
Quasiperiodic Structure ◽  
Diffraction Patterns ◽  
Analysis Of The Images ◽  
Rapidly Solidified

It is commonly accepted that the definition of quasicrystal should include a rotational symmetry forbidden in periodic crystals. On the other hand, the quasicrystal with a conventional point group is theoretically possible [1,2]. In a rapidly-solidified Mg-Al alloy, intriguing electron diffraction patterns (EDPs) were reported, which show a cubic symmetry with aperiodic arrays of Bragg reflections [2]. In the present work, we investigate the detailed structure of the rapidly-solidified Mg-Al phase based on direct structure observations using STEM. In a rapidly-solidified Mg-61 at.% Al alloy, 2-fold, 3-fold, and 4-fold EDPs are obtained (Fig. a), which shows that the structure has the cubic point group. However, the relevant diffraction spots are arranged aperiodically. Especially in the 2-fold EDP, a high density of the spots is observed, and the corresponding HADDF-STEM image shows several remarkable features (Fig. b). Two length scales, L and S, can be definitely observed, and they are arranged quasiperiodically along the 3-fold axis. Their arrangement can be well described by the hyperspace crystallography; a physical space tilted by the angle θ , where tanθ ∼ 1.4, successfully generates the observed quasiperiodic pattern. Simulated EDPs from a simple model without detailed atomic decoration reproduces fairly well the experimental patterns. Further analysis of the images reveals that the present quasiperiodic structure has similar local structure to the stable β-Mg2Al3phase; two lengths correspond to L and S may be reasonably defined. The quasicrystal with a cubic symmetry is unambiguously determined for the first time, based on a direct structural observation. The present results strongly suggest that the noncrystallographic rotational symmetry is not an essential factor to form the quasiperiodic structure, raising a very fundamental, universal question on the physical origin of a long-range order of condensed matters.

Interpretation of the Nano-Electron-Diffraction Patterns along the Five-Fold Axis of Decahedral Gold Nanoparticles

2011 ◽  
Vol 17 (2) ◽  
pp. 279-283 ◽  
Author(s):  
L.D. Romeu ◽  
J. Reyes-Gasga
Keyword(s):  
Gold Nanoparticles ◽  
Electron Beam ◽  
Electron Diffraction ◽  
Diffraction Pattern ◽  
Rotational Symmetry ◽  
Fold Axis ◽  
Double Refraction ◽  
Dynamical Diffraction ◽  
Refraction Effect ◽  
Diffraction Patterns

AbstractThe transition from 10-fold to 5-fold symmetry was observed during the analysis of nanodiffraction patterns of a gold decahedral multiple twinned nanoparticle of 15 nm in diameter. The analysis shows that as the convergence of the beam is increased, the rotational symmetry of the diffraction pattern shifts from 10- to 5-fold. The 10-fold symmetry predicted by Friedel's law is lost by the asymmetric shift of the diffraction spots, an effect that becomes more noticeable as the electron beam convergence increases. Dynamical and kinematical diffraction calculations indicate this decrease in symmetry is the result of a double refraction effect coupled with the variation of the dynamical diffraction conditions arising from a varying electron beam convergence.

TEM Study of Quasicrystals in Al-Mn-Fe Melt-Spun Ribbon

2012 ◽  
Vol 186 ◽  
pp. 255-258 ◽  
Author(s):  
Katarzyna Stan ◽  
Lidia Lityńska-Dobrzyńska ◽  
Jan Dutkiewicz ◽  
Lukasz Rogal ◽  
Anna Maria Janus
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Crystallographic Direction ◽  
Fold Axis ◽  
Orientation Relationships ◽  
Melt Spun ◽  
High Resolution Images ◽  
Different Shapes ◽  
Diffraction Patterns ◽  
Rapidly Solidified

Microstructure of rapidly solidified Al91Mn7Fe2 (at.%) alloy was investigated using SEM and TEM techniques. Quasicrystalline particles of different shapes and sizes embedded in the aluminium matrix were observed. Quasilattice constant was calculated as 0.461 Å. Additionally orientation relationships between matrix and quasicrystals particles were found based on electron diffraction patterns and high resolution images, such that: five-fold axis lie along [011] or [001] axes of the α-Al crystallographic direction.

A Modulated quasi-crystalline structure in an Ai-Li-Cu-Mg-Zr alloy

1987 ◽  
Vol 45 ◽  
pp. 418-419
Author(s):  
J. P. Zhang ◽  
H. Q. Ye ◽  
K. H. Kuo ◽  
Z. Z. Jiang ◽  
L. D. Marks
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Point Group ◽  
Icosahedral Phase ◽  
Fold Axis ◽  
High Resolution Image ◽  
Translation Symmetry ◽  
Group 3 ◽  
Diffraction Patterns ◽  
Zr Alloy

Sainfort et. al. have observed a quasi-crystalline phase in normal equilibrium precipitates in Al-Li-Cu and Al-Li-Cu-Mg alloys produced by classical casting rather than rapid solidification. Hence the intergrowth of the icosahedral phase (I-phase) and the related crystalline structures and formation mechanism is a subject of some interest. By means of electron microscopy we have studied the I-phase precipitates extracted from an Al-Li-Cu-Mg-Zr alloy.The presence of I-phase was verified by selected area diffraction patterns shown in Fig. 1, showing the typical 5-fold and 3-fold symmetry of the point group 3 m 5, instead of ordinary translation symmetry, in (a) and (b) respectively. Fig. 2 is a high resolution image in a 2-fold axis of I-phase with the corresponding EM pattern inserted. The configuration of Fig. 2 shows not only the quasi-per iodic arrangement, but also a modulation in two directions perpendicular to this axis.

Friedel'S law breakdown and interpretation of stacking fault images in tetrahedral semiconductors

1987 ◽  
Vol 45 ◽  
pp. 318-319
Author(s):  
Rob. W. Glaisher ◽  
A.E.C. Spargo
Keyword(s):  
Relative Phase ◽  
Point Group ◽  
Binary Compound ◽  
Stacking Fault ◽  
Fold Axis ◽  
Atom Pair ◽  
Tetrahedral Semiconductors ◽  
Group Symmetries ◽  
Thin Crystal ◽  
Phase Differences

Images of <11> oriented crystals with diamond structure (i.e. C,Si,Ge) are dominated by white spot contrast which, depending on thickness and defocus, can correspond to either atom-pair columns or tunnel sites. Olsen and Spence have demonstrated a method for identifying the correspondence which involves the assumed structure of a stacking fault and the preservation of point-group symmetries by correctly aligned and stigmated images. For an intrinsic stacking fault, a two-fold axis lies on a row of atoms (not tunnels) and the contrast (black/white) of the atoms is that of the {111} fringe containing the two-fold axis. The breakdown of Friedel's law renders this technique unsuitable for the related, but non-centrosymmetric binary compound sphalerite materials (e.g. GaAs, InP, CdTe). Under dynamical scattering conditions, Bijvoet related reflections (e.g. (111)/(111)) rapidly acquire relative phase differences deviating markedly from thin-crystal (kinematic) values, which alter the apparent location of the symmetry elements needed to identify the defect.

Diffraction study on bainite of Cu-Al alloy

1990 ◽  
Vol 48 (4) ◽  
pp. 1006-1007
Author(s):  
Delu Liu ◽  
T. Ko
Keyword(s):  
Diffraction Study ◽  
Parent Phase ◽  
Al Alloy ◽  
Alloy Sample ◽  
Bright Field Image ◽  
Hexagonal System ◽  
Iced Brine ◽  
Diffraction Patterns ◽  
Zone Pattern ◽  
Stacking Structure

Structure of bainite in Cu-Al and Cu-Zn-Al alloys has been reported as 3R, 9R or 18R long period stacking structure (LPS) by X-ray and electron diffraction studies. In the present work, a Cu-25.5 (at)% Al alloy sample was heated at 900°C for 2 h then isothermally held at 450°C for 60 s before quenching into iced brine. FIG.1 shows a TEM bright field image of bainite plates (marked B) grown from grain boundary. The parent phase ( with DO3 structure ) has transformed to martensite (marked M ) during cooling from 450° C to 0°C. Both bainite and martensite plates have dense striations inside.Careful diffraction study on a JEOL 2000FX TEM with accelerating voltage 200 KV revealed (FIG.2) that the diffraction patterns contai_ning the same zone axis [001] ( hexagonal index ) or [111]c ( cubic index ) are from a bainite plate with obtuse V-shape. They are indexed as [010], [140], [130], [120], [230], [340] and [110] zone pattern for hexagonal system respectively.

TEM study of lanthanum aluminate

1990 ◽  
Vol 48 (4) ◽  
pp. 1060-1061
Author(s):  
C.Y. Yang ◽  
Z.R. Huang ◽  
Y.Q. Zhou ◽  
C.Z. Li ◽  
W.H. Yang ◽  
...  
Keyword(s):  
Domain Boundary ◽  
Point Group ◽  
Optical Microscope ◽  
Dark Field ◽  
Zone Axis ◽  
Superconducting Film ◽  
Ion Milling ◽  
Lanthanum Aluminate ◽  
Ring Diameter ◽  
Diffraction Patterns

Lanthanum aluminate(LaAlO3) single crystal as a substrate for high Tc superconducting film has attracted attention recently. We report here a transmission electron microscopy(TEM) study of the crystal structure and phase transformation of LaAlO3 by using Philips EM420 and EM430 microscopes. Single crystals of LaAlO3 were investigated first by optical microscope. Stripe-shaped domains of mm size are clearly seen(Fig.1a), and 90° domain boundary is also obvious. TEM specimens were prepared by mechanical grinding and polishing followed by ion-milling.Fig.lb shows μm size stripe domains of LaAlO3. Convergent beam electron diffraction patterns (CBED) from single domain were taken.Fig. 2a and Fig. 2c are [001] zone axis patterns which show a 4mm symmetry, and the (200) dark field of this zone axis gives 2mm symmetry(fig.2b). Therefore the point group of this crystal is either 4/mmm or m3m. The projection of the first order Laue zone(FOLZ) reflections on zero layer (fig. 2c) shows that the unit cell is face centered. A tetragonal unit ceil is chosen, with a=0.532nm and c=0.753nm, c being determined from the FOLZ ring diameter.

A Metastable Crystalline Phase Coexisted with the Decagonal Quasicrystals in Rapidly Solidified Al-Ir Al-Pd and Al-Pt Alloys

1990 ◽  
Vol 48 (1) ◽  
pp. 572-573
Author(s):  
Wang Rong ◽  
Ma Lina ◽  
K.H. Kuo
Keyword(s):  
Metastable Phase ◽  
Hexagonal Phase ◽  
Icosahedral Quasicrystal ◽  
Decagonal Quasicrystal ◽  
Decagonal Phase ◽  
Decagonal Quasicrystals ◽  
Pt Alloy ◽  
Pt Alloys ◽  
Diffraction Patterns ◽  
Rapidly Solidified

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.

scholarly journals Deep Neural Network Enabled Space Group Identification in EBSD

2020 ◽  
Vol 26 (3) ◽  
pp. 447-457 ◽  
Author(s):  
Kevin Kaufmann ◽  
Chaoyi Zhu ◽  
Alexander S. Rosengarten ◽  
Kenneth S. Vecchio
Keyword(s):  
Machine Learning ◽  
Electron Backscatter Diffraction ◽  
Group Identification ◽  
Point Group ◽  
Phase Identification ◽  
Space Group ◽  
Multiple Length Scales ◽  
Analysis Technique ◽  
Diffraction Patterns ◽  
Backscatter Diffraction

AbstractElectron backscatter diffraction (EBSD) is one of the primary tools in materials development and analysis. The technique can perform simultaneous analyses at multiple length scales, providing local sub-micron information mapped globally to centimeter scale. Recently, a series of technological revolutions simultaneously increased diffraction pattern quality and collection rate. After collection, current EBSD pattern indexing techniques (whether Hough-based or dictionary pattern matching based) are capable of reliably differentiating between a “user selected” set of phases, if those phases contain sufficiently different crystal structures. EBSD is currently less well suited for the problem of phase identification where the phases in the sample are unknown. A pattern analysis technique capable of phase identification, utilizing the information-rich diffraction patterns potentially coupled with other data, such as EDS-derived chemistry, would enable EBSD to become a high-throughput technique replacing many slower (X-ray diffraction) or more expensive (neutron diffraction) methods. We utilize a machine learning technique to develop a general methodology for the space group classification of diffraction patterns; this is demonstrated within the $\lpar 4/m\comma \;\bar{3}\comma \;\;2/m\rpar$ point group. We evaluate the machine learning algorithm's performance in real-world situations using materials outside the training set, simultaneously elucidating the role of atomic scattering factors, orientation, and pattern quality on classification accuracy.

X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

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