Crystalline Approximants Research Articles

Quasicrystals and crystalline approximants

Over the past seven years, many examples of periodic crystals closely related to quasicrystalline alloys have been discovered. These crystals have been termed approximants, since the arrangements of atoms within their unit cells closely approximate the local atomic structures in quasicrystals. This colloquium focuses on these approximant structures, their description, and their relationship to quasicrystals.

Localized Magnetic Moments and Spin Freezing in Al-Based Amorphous, Quasicrystalline and Crystalline Approximant Phases

Al-based amorphous and quasicrystalline alloys have been prepared by high-rate sputtering and melt-quenching, respectively. The Al 67 Cu 20 Mn 13 crystalline approximant phase also has been made by annealing the quasicrystalline counterpart. The formation of the localized magnetic moments of 3d metals in the Al matrix is difficult except for Mn. The ratio of the magnetic Mn atoms estimated from the saturation magnetization and the Curie constant in the quasicrystalline phase is smaller than that in the amorphous phase. In the crystalline approximant phase, the ratio is comparable to that in the amorphous phase, but the average magnetic moment of magnetic Mn atoms is much smaller than that in the amorphous and quasicrystalline phases

Observation of lattice fringes in an approximant to the AI-Co-Cu decagonal phase

Lattice fringes for the C-orthorhombic crystalline approximant to the Al-Co-Cu decagonal phase were imaged. The relative orientations between various sets of equivalent lattice fringes reveal clearly the twinning in this approximant. Moreover, the fringe imaging provides detailed information concerning the sizes and the shapes of the twin variants in this structure

Structure and stability of quasicrystals: Modulated tiling models.

A modulated tiling model for the structure of an icosahedral quasicrystal of the Al-Zn-Mg class is proposed. Idealized structure models for quasicrystals are constructed on the basis of three-dimensional Penrose tilings with a Henley-Elser decoration of the basic structural units. The stability of these structures is investigated by an isothermal molecular-dynamics annealing of a hierarchy of crystalline approximants to the quasiperiodic structure, based on realistic pair forces derived from pseudopotential theory. We find that quasicrystals are stable only at compositions leading to an electron-per-atom ratio of e/A\ensuremath{\approxeq}2.1--2.2, thus confirming the existence of a Hume-Rothery or Peierls mechanism for the stability of quasicrystals. Because of the large number of different atomic environments in quasicrystals, any set of interatomic forces leads to a displacive modulation of the idealized quasiperiodic structure. For a stable quasicrystal, the displacement field has the symmetry of the quasilattice. The structural characteristics of the displacively modulated Penrose tilings are investigated in detail. We show that the modulation of the structure substantially improves the agreement of the models with experimental observation.

NMR study of the electronic properties and stability of quasicrystals.

We have studied by NMR the electronic properties of the stable quasicrystalline phases Al 57 Cu 10.8 Li 32.2 and Al 62 Cu 25.5 Fe 12.5 and of two crystalline approximants, the bcc R phase Al 56 Cu 12 Li 32 and the rhombohedral Al 62.8 Cu 26 Fe 11.2 phase. Low values of the density of states at the Fermi level are observed in the crystalline as well as in the quasicrystalline phases. The existence of a pseudogap at the Fermi level is therefore not a consequence of the quasiperiodicity

Orthorhombic crystalline approximants of the Al-Mn-Cu decagonal quasicrystal

Abstract Two orthorhombic Al–Mn–Cu phases, π-Al20Mn3Cu2 and Y-AlMnCu, with large lattice parameters were found to coexist with the decagonal quasicrystal in Al10Mn3Cu0.1-0.2 alloys and they were shown to be crystalline approximants of the latter. These two phases have similar structural subunits and a close orientation relationship. They twin easily and the twin boundary of the π phase is a layer of the π phase and vice versa. Therefore, these two phases intergrow frequently and both translational and rotational twin domains are abundant.

Structural repeat units and repeat schemes for the Al-Cu-Co decagonal phase and its crystalline approximants

Abstract Several repeat units and repeat schemes for the Al-Cu-Co decagonal phase and its crystalline approximants are proposed. An inherent strain is introduced into the structure through repetition of these units. The transition from the crystalline to the quasicrystalline state appears to be due to an increase in twinning, which reduces this strain.

Intermediate structures and crystalline approximants in the I→α transformation of Al-(Mn,Fe)-Si alloys

Intermediate structures and crystalline approximants in the I→α transformation of Al-(Mn,Fe)-Si alloys

Stable one-component quasicrystals.

The lowest-energy structures associated with a commonly used effective metallic pair potential are found for a wide range of values of the three parameters required by the potential. The structures tested include most of the lattices favored by the elements, the Bravais lattices with variable c/a and b/a ratios, and a number of candidate three-dimensional one-component quasicrystal structures. One of the quasicrystals is the stable structure for a region of parameter space close to the virtual-crystal parameters appropriate to the observed simple-metal quasicrystals. Energies are also evaluated for some crystalline approximants to the quasicrystals, and these structures are found to be lower in energy than the quasicrystal only for a small portion of the region of quasicrystal stability, although it is still possible that sufficiently high-order approximants are lower in energy over the entire region.

Universal pseudogap at Fermi energy in quasicrystals.

The electronic structures are calculated for several crystalline approximants of quasicrystals, AlCuLi and AlFe. The densities of states of these systems, and also of AlMn, suggest universality of the pseudogap at the Fermi energy in quasicrystals. The pseudogap satisfies a Hume-Rothery--type relation. The origin of the pseudogap is attributed to strong electron scattering by the lattice and the pseudogap causes an enhancement of cohesive energies. The characteristics of the states in the pseudogap and the electric resistivity are also discussed.

特集・準結晶研究の発展 準結晶の電子構造

Abstract The electronic structures are calculated for crystalline approximants of icosahedral quasicrystals, i-AlMn and i-AlCuLi. The density of states shows, commonly, a large depression, called a pseudogap, at the Fermi energy. The origin of the pseudogap is attributed to the electron-lattice interaction known as the Hume-Rothery mechanism. The density of states has also a structure of dense and fine spiky peaks. These may cause a large effective mass and may be one of the causes of abnormal transport phenomena and optical conductivity in quasicrystals.