Self-assembly of monatomic complex crystals and quasicrystals with a double-well interaction potential

For the study of crystal formation and dynamics, we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a decagonal, and a dodecagonal quasicrystal are self-assembled. In the case of the quasicrystals, the particles reorder by phason flips at elevated temperatures. During annealing, the entropically stabilized decagonal quasicrystal undergoes a reversible phase transition at 65% of the melting temperature into an approximant, which is monitored by the rotation of the de Bruijn surface in hyperspace.     

Energy characteristics of edge dislocations in quasicrystals

A model is developed for describing phason defects in quasicrystals in the form of dilation filaments. This model is used to calculate the energy of edge dislocations in quasicrystals including the interaction of this type of dislocation with its “intrinsic” phason defects and with the equilibrium phason defects present in a quasicrystal. It is shown that the contribution of “intrinsic” phason defects to the total energy of an edge dislocation in a quasicrystal is substantial. Fiz. Tverd. Tela (St. Petersburg) 39, 2003–2007 (November 1997)     

Growth of entropy stabilized quasicrystals

A simplified version of the model by Elser and Joseph for the process of growth of an entropically stabilized, two-dimensional quasicrystal with no dynamics in the bulk, is proposed. The phason fluctuations are modeled by a scalar field on a periodic lattice. The choice of the master equation for the growth is restricted by the requirement that its detailed balance solution describes the equilibrium fluctuations of the field with a quadratic Hamiltonian. The model is parametrized by the chemical potential bias and the microscopic surface tension coefficient . The phase diagram of the system on the plane (, ) shows several distinct regimes of growth, separated by relatively narrow transition zones. Within the regions corresponding to these regimes, the phason fluctuations do not depend on and . Analytic expressions for the spectra of phason fluctuations are obtained and confirmed by numerical simulation. Received 30 June 2000     

Phase diagram of a random tiling quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.     

Twelve-fold quasicrystal and its approximant of Ta62Te38 interpreted as modulated crystals

A transmission electron microscopy study reveals that the twelve-fold quasicrystal and its approximant in Ta62Te38 are crystals subjected to the structure modulation. It is composed of two modulated layers rotated by 30 degrees (or 90 degrees) to each other about their normal. Structures of the twelve-fold quasicrystal and its approximant can be related by modulation waves with the same directions but with slightly different wavelengths. The modulation is considered to be due to the rearrangement of atomic vacancies as a response to the occurrence of charge density waves.     

Simulation of the lattice dynamics of an Al-Cu-Fe icosahedral quasicrystal

The total and partial vibrational spectra of aluminum, copper, and iron atoms in an Al-Cu-Fe icosahedral quasicrystal are calculated by the recursive method. The calculations are based on the 1/1 crystal approximant. The interaction of atoms in the Al-Cu-Fe quasicrystal is described within the EAM model. The calculated spectra are in satisfactory agreement with the experimental data on neutron inelastic scattering.     

Interface of quasicrystal and crystal

A model on the coexisting phase of quasicrystal-crystal is proposed,with which we concretely investigate the interface effects for coexisting phases of one-dimensional orthorhombic quasicrystal-isotropic crystal and three-dimensional icosahedral quasicrystal-cubic crystal.The phason strain fields which play an important role in some processes are determined.Some factors affecting the strain fields,e.g.,the material constants of phonon,phason,phonon-phason coupling of the quasicrystal and the elastic modulus and the size of the crystal are also explored.     

Quasicrystals and related approximant phases in Mg-Zn-Y

As-cast microstructure of Mg-rich Mg(68)Zn(28)Y(4) has been investigated by a detailed transmission electron microscopy study. The as-cast Mg(68)Zn(28)Y(4) alloy consisted of three different types of phases: 10-20 m size primary solidification phase, dendritic phase grown from the primary phase and a eutectic structure formed at the later stage of solidification. The primary solidification phase has an icosahedral structure with a large degree of phason strain. 1/1 rhombohedral approximant phase with lattice parameters a=27.2 A and =63.43 degrees is first observed in Mg-Zn-Y system. The rhombohedral structure can be obtained by introducing phason strain in the six-dimensional face centered hyper-cubic lattice. The decagonal phase nucleates with orientation relationship with the icosahedral phase, and Mg(4)Zn(7) nucleates with orientation relationship with the decagonal phase, indicating a close structural similarity between the three phases. Gradual depletion of Y during solidification plays an important role in heterogeneous nucleation of decagonal and Mg(4)Zn(7) phases from icosahedral and decagonal phases, respectively.     

First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants whose deterministic decoration of tiles by atoms can be extended quasiperiodically. Experimentally observed disorder corresponds to phason fluctuations. First-principles total energy calculations find many distinct tilings close to stability and suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B38Mg17Ru45 forms a metastable decagonal quasicrystal that may be thermodynamically stable at high temperatures.     

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.     

AlCuFe quasicrystals: Local electronic properties of these new industrial materials

We present room temperature ⁵⁷Fe Mössbauer centre (isomer) shift and electric field gradient (EFG) results in the Al_100-x-yCu_xFe_y icosahedral-quasicrystalline (i-) and crystalline phases. We have investigated the local electronic properties and atomic order along the existence domains of the quasicrystalline and approximant phases given by two close-lying parallel lines in the concentration diagram: the I-line, where the quasicrystal is stable, and the A-line, where the rhombohedral approximant is stable, and other high-order approximants (orthorhombic and pentagonal) as well as the quasicrystal phase are metastable. We have also studied a series of intermediate concentrations situated between the I- and A-lines retained in the metastable i-phase by quenching. It is found that the centre shift and EFG are linearly correlated to each other over the range of compositions and structures for both the I- and A-lines as well as the intermediate samples. This correlation results from systematic changes in the orbital occupations on Fe atoms with composition. We have investigated as well the new low-order cubic approximant phase containing Si. The results for this phase fall near to but not on the correlation line indicating small changes in the atomic binding as compared to the i- and high order approximant phases. In addition, we have studied several non-approximant phases which lie close to these phases in composition. The results for the non-approximant structures do not fall near the correlation line, indicating very different atomic binding.     

Crystallographic features of the approximant H (Mn7Si2V) phase in the Mn–Si–V alloy system

The intermetallic compound H (Mn₇Si₂V) phase in the Mn–Si–V alloy system can be regarded as an approximant phase of the dodecagonal quasicrystal as one of the two-dimensional quasicrystals. To understand the features of the approximant H phase, in this study, the crystallographic features of both the H phase and the (σ → H) reaction in Mn–Si–V alloy samples were investigated, mainly by transmission electron microscopy. It was found that, in the H phase, there were characteristic structural disorders with respect to an array of a dodecagonal structural unit consisting of 19 dodecagonal atomic columns. Concretely, penetrated structural units consisting of two dodecagonal structural units were presumed to be typical of such disorders. An interesting feature of the (σ → H) reaction was that regions with a rectangular arrangement of penetrated structural units (RAPU) first appeared in the σ matrix as the initial state, and H regions were then nucleated in contact with RAPU regions. The subsequent conversion of RAPU regions into H regions eventually resulted in the formation of the approximant H state as the final state. Furthermore, atomic positions in both the H structure and the dodecagonal quasicrystal were examined using a simple plane-wave model with 12 plane waves.     

Al70Co15Tb5Ni10合金中准晶T相和相关相的形成

 对Al₇₀Co₁₅Tb₅Ni₁₀合金进行了静高压（4.40 GPa）熔态（1 450 ℃）淬火（冷却速率为10² ℃/s）研究。首次在该系统中观察到准晶T相和一个新的十次准晶相关相形成。使用透射电镜对准晶相和准晶相关相进行了结构分析，得到了准晶相关相的晶胞参数。使用已有的理论模型对该相关相的形成进行了讨论。     

Ab initio calculations of the vibrational spectra of 1/1 approximant of i-AlCuFe quasicrystal

The partial and total densities of vibrational states of the 1/1 crystal approximant of the icosahedral i-AlCuFe quasicrystal are calculated using the method of pseudopotentials in the generalized gradient approximation (to describe the electronic states) and the frozen-phonon method (to determine the dynamic matrix). The results obtained agree well with experimental inelastic neutron scattering data, which indicates that the method of calculations is appropriate and could be used to calculate other crystal approximants.     

Structure and reflective properties of Al-Cu-Fe quasicrystalline thin film prepared by laser induced arc method

Al-Cu-Fe thin films were prepared by laser induced arc (laser-arc) method from a single source-Al63Cu25Fe12 alloy, which was proved to consist of quasicrystalline phase together with approximant phase. The composition of the deposited films meets the requirement for formation of icosahedral symmetry phase. Quasicrystalline phase was obtained after annealing the amorphous as-deposit film samples. The optical properties of the samples were investigated. Thin film samples of Al, Cu and Fe deposited under the same condition were employed for comparison. The results showed specific reflective properties of Al-Cu-Fe quasicrystal thin film in some wavelength range. The optical conductivity of the films exhibited a negative peak, centered about 440 nm in range of 190to 800 nm. The Al-Cu-Fe quasicrystal thin films could absorb almost all the ray in the wavelength range from 420nm to 450 nm. The ratio of absorption was greater than 99%.     

Composition-dependent electrical resistivity in an Al-Re-Si 1 /1-cubic approximant phase: an indication of electron confinement in clusters

We report the synthesis of alpha-AlReSi and show that it is a 1/1-cubic approximant phase of the icosahedral quasicrystal with a = 12.9 A. The trend of the resistivity of the new approximant phase shows a nonmetallic character, similar to those seen in the stable icosahedral phases. The resistivity depends sensitively on the Re concentration and the nonmetallic transport is observed only at the Re concentration close to 17.4 at. %, where the transition metal sites in the icosahedral cluster are exclusively occupied by Re atoms. In view of a recent ab initio calculation, the present result suggests strongly the formation of the virtual bound states, or confinement of electrons, in the icosahedral clusters of transition metal atoms.     

Continuous transformation from quasicrystals to approximants in Al–Cu–Fe alloys

Continuous transformation of icosahedral quasicrystals as observed in Al-Cu-Fe alloys proceeds through intermediate modulated structures towards rational approximants with a rhombohedral structure. Corresponding to the diffuse scattering in the electron diffraction during the transformation, a tweed contrast emerges throughout the icosahedral phase matrix. High-resolution electron microscopy reveals a complex modulated structure which tends to evolve into rhombohedral microdomains. The observed distortion of the reciprocal quasilattice due to the structural modulation has been simulated on a computer by introducing linear phason strains into the quasicrystals.     

Dynamic behaviour of the icosahedral Al——Pd——Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al--Pd--Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon--phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.     

Intermediate stages of a transformation between a quasicrystal and an approximant including nanodomain structures in the Al-Ni-Co system

Transition states between decagonal quasicrystal and periodic approximants are studied in the Al-Ni-Co system at a measured composition of Al_71.3Ni_11.3Co _17.4 by high-resolution transmission electron microscopy and electron diffraction. The nanodomain structures appearing after annealing at 1270 K show periodic fluctuations coherently embedded in domains with the coarse order of a one-dimensional quasicrystal. Further annealing at lower temperatures changes the features of nanodomain structures and results in an increase in more periodic structures. These can be strongly disordered and full of defects but tiling analysis and electron diffraction patterns show that they correspond to locked phason strain values of two closely related periodic approximants. We conclude that the periodic approximants do not result from a continuous increase in phason strain but from the growth of seeds with a locked phason strain.     

Degree of structural perfection of icosahedral quasicrystalline grains investigated by synchrotron X-ray diffractometry and imaging techniques

A study of the structural perfection of icosahedral quasicrystalline grains of various alloys (Al-Pd-Mn, Zn-Mg-RE (RE L rare earth) and Al-Cu-Fe), grown by different slow solidification techniques (Czochralski, Bridgman, flux and annealing) was performed using high-resolution diffraction, including recording rocking curves combined with X-ray topography and phase contrast radiography, at a third-generation synchrotron radiation source (European Synchrotron Radiation Facility, Grenoble, France). For Al-Pd-Mn, additional coherent diffraction and diffuse scattering measurements were also carried out. After evaluating the potentialities of the techniques used, in the light of the criteria defined for crystals, it is shown that the structural perfection of icosahedral quasicrystals is quite comparable with that of metallic crystals but is considerably influenced by either uniform phason strains which can destroy the quasiperiodic long-range order, or by long-wavelength phason fluctuations leading to diffuse scattering. The structural perfection was also found to be extremely variable across the as-grown quasicrystalline grains and to be dependent on the presence and characteristics of inhomogeneities (pores and precipitates) often included in the quasicrystalline matrix. Regarding the grains that we used, it has been impossible to distinguish a clear influence of either the type of alloy or the growth method. It has, however, been noticed that Al-Pd-Mn and Al-Cu-Fe grains appeared less defective than Zn-Mg-RE grains and that the microstructure of these latter grains looks like that of crystals grown by the same technique. Annealing and mechanical polishing effects have also been analysed in the case of Al-Pd-Mn grains. It appeared that annealing improves the quasicrystalline lattice perfection by lowering phason strains insofar as no precipitates are nucleated. Mechanical polishing can introduce defects, located at the external surfaces, having the shape of bands.