We have observed a metallic solid (Al-14-at.%-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice. The solid is metastable and forms from the melt by a first-order transition.

Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

The MN+1AXN phases: A new class of solids

Atomic-level structure and structure–property relationship in metallic glasses

Discrete Solitons in Optics

Theory of Microstructural Development during Rapid Solidification

We report herein the existence of a metallic solid which diffracts electrons like a single crystal but has point group symmetery rn35 (icosahedral) which is inconsistent with lattice translations. If the specimen is rotated through the angles of this point group (Fig. 1), selected-area electron diffraction patterns clearly display the six fivefold, ten threefold, and fifteen twofold axes characteristic' of icosahedral symmetry (Fig. 2). Grains up to 2 p, m in size with this structure form in rapidly cooled alloys of Al with 10—14 at. '/0 Mn, Fe, or Cr. We will refer to the phase as the icosahedral phase. Microdiffraction from many different volume elements of a grain and dark-field imaging from various diffraction spots confirm that entire grains have longrange orientational order. If the orientational order decays with distance, its correlation length is far greater than the grain size. We have thus a solid metallic phase with no translational order and with with long-range orientational order. The remarkable sharpness of the diffraction spots (Fig. 2) indicates a high coherency in the spatial interference, comparable to the one usually encountered in crystals. The diffraction data are qualitatively well fitted by a model consisting of a random packing of nonoverlapping parallel icosahedra attached by edges. The invariance of the local orientational symmetry from site to site and the finite number of possible translations between two adjacent icosahedra seem to be sufficient for insuring highly coherent interferences. Icosahedra are a common packing unit in intermetallic crystals with the smaller transition element at the center surrounded by twelve larger atoms arranged like the corners of an icosahedron. The symmetries of the crystals dictate that the several icosqhedra in a unit cell have different orientations and allow them to be distorted, leaving the overall crystal consistent with the well-known crystallographic point and space groups. Even though icosahedral symmetry is of great importance as an approximate site symmetry in crystals, it cannot survive the imposition of lattice translations: Crystals cannot and do not exhibit the icosahedral point group symmetry. Elementary crystallography indicates that fivefold

Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

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Indexing of icosahedral quasiperiodic crystals

The microstructure of rapidly solidified Al−Mn alloys containing 18 to 25.3 wt pct Mn was studied by transmission electron microscopy. One of the phases found in the microstructure exhibits icosahedral symmetry manifested in electron diffraction patterns having five-fold symmetry. A new structural concept is proposed to account for the observed electron diffraction patterns. The structure is assumed to be composed of many connected polyhedra. Although not forming a regular lattice, such structures are able to produce sharp diffraction peaks. The terminal stability and transformation of the icosahedral phase was also studied and reported.

The microstructure of rapidly solidified Al 6 Mn

Electron beam solidification passes have been performed on a series of Ag-Cu alloys between 1 wt pct Cu and the eutectic composition (28.1 wt pct Cu) at speeds between 1.5 and 400 cm per second. At low growth rates conventional dendritic or eutectic structures are obtained. The maximum growth rate of eutectic structure is 2.5 cm per second. At high growth rates microsegregation-free single phase structures are obtained for all compositions. The velocity required to produce this structure increases with composition for dilute alloys and agrees with the theory of absolute stability of a planar liquid-solid interface with equilibrium partitioning. For alloys between 15 and 28 wt pct Cu, the velocity required to produce the microsegregation-free extended solid solution decreases with composition and is related to nonequilibrium trapping of solute at the liquid solid interface. At intermediate growth rates for alloys with 9 wt pct Cu or greater, a structure consisting of alternating bands of cellular and cell-free material is obtained. The bands form approximately parallel to the local interface.

Dan Shechtman

Papers

Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

Indexing of icosahedral quasiperiodic crystals

The microstructure of rapidly solidified Al 6 Mn

The Effect of Rapid Solidification Velocity on the Microstructure of Ag-Cu Alloys