Formation Of Quasicrystals Research Articles

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of phi = pi/ radical18 approximately 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Growth of large single-grain quasicrystals in the Ag–In–Yb system by Bridgman method

Well-defined single-grain Ag–In–Yb icosahedral quasicrystals of order of centimeter have been grown by the Bridgman method. The scanning electron microscopy (SEM) observation showed that the compositional distribution in the single-grain quasicrystals is uniform and Laue X-ray diffraction measurements verified the formation of single-grain icosahedral quasicrystals. The natural growth direction of the single-grain quasicrystals is close to a direction parallel to a 2-fold axis. It turns out that the Yb content in the initial melt limited within 15–16 at.% is a critical factor determining the formation of single-grain quasicrystal. Based on the experimental result, the mechanism of the growth of single-grain quasicrystal and formation of intermediate zone between quasicrystal and approximant phases are discussed.

Phase formation and structures of quasicrystals and approximants in the Zn–Mg–(Ti, Zr, Hf) system

The compositional regions for primitive (P) and face-centered (F) icosahedral quasicrystals (iQc) have been determined to be around Zn 84Mg 9Zr 7 and Zn 75Mg 18Zr 6, respectively. A 1/1 approximant of the F-type iQc was found to have a composition around Zn 77Mg 18Zr 5. A similar tendency has been verified for the Zn–Mg–Hf system. No stable iQc was observed in the Zn–Mg–Ti system. High-resolution X-ray measurements performed with synchrotron radiation showed that the stable iQcs are highly ordered and contain less phason disorder. High-angle annular dark field (HAADF) scanning transmission electron microscopy observation of the 1/1 Zn–Mg–Hf approximant effectively revealed the Hf positions in the structure, whose local contrasts can be reasonably interpreted by a structural model where icosahedral and dodecahedral Hf clusters are mutually interpenetrated. Similar appearances of local contrasts were frequently observed in HAADF images of the F-type iQc, indicating that the iQc structure is also build up of icosahedral clusters that are almost identical to those in the 1/1 approximant.

Quasicrystals formation in ball-milled Al-Cu-Cr powders

Al67Cu20Cr13 and Al75Cu10Cr15 alloys were produced by mechanical alloying from elemental powders. As-milled samples consist of the initial elemental phases. Phase transformations at heating were analyzed by differential scanning calorimetry and X-ray diffraction analysis. Annealing of as-milled powders in the temperature range of 500 to 550 °C results in the formation of binary and ternary compounds including the decagonal quasicrystalline phase that was found to be stable at least up to 800 °C.

Processing and characterization of rapidly quenched Ti-based alloys: Influence of solidification rate on the as-quenched structures

Abstracts From technological viewpoint, icosahedral Ti–Zr–Ni phase may give challenging opportunities as novel hydrogen storage and hydride battery. Nevertheless, from the structural standpoint, the phase selection criterion as function of solidification route remains unclear. A series of Ti 45 Zr 38 Ni 17 alloys, known to provide stable and well-ordered quasicrystals, was produced by planar flow casting using different processing parameters. From structural characterization, it appears that, at high cooling rate, i.e. high wheel speeds, or for the highest temperature of the melt, the as-quenched sample exhibits a mixture of nanoscale β and amorphous phases. The icosahedral phase precipitates when decreasing the wheel speed, from lower temperatures of the melt or after annealing a crystallized amorphous matrix. The reproducible formation of quasicrystals, observed in the amorphous matrix containing β particles, corroborates the competition between icosahedral and body-centered cubic (bcc) phases during the solidification process. These results are promising since it could be possible to control volume fractions of these two phases by choosing well-fitted thermal treatments so that quasicrystals mechanical properties should be improved by dispersion of a stable bcc phase.

Formation of decagonal quasicrystals in mechanically alloyed Al–Cu–Cr powders

Abstract Mechanical alloying was applied to form a decagonal phase in the Al–Cu–Cr system. Elemental powders of Al67Cu20Cr13, Al75Cu10Cr15, Al65Cu24Cr11, Al69Cu21Cr10 and Al78Cu10Cr12 compositions (in at%) were mechanically alloyed in a planetary ball mill. Annealing in the temperature range of 500 to 550 °C results in the formation of binary and ternary compounds including the decagonal quasicrystalline phase that was found to be stable at least up to 800 °C and was present in various amounts in all investigated alloys. No icosahedral quasicrystalline phase was found in the samples. The maximum content (95 vol%;) of decagonal quasicrystalline phase was observed for Al69Cu21Cr10 compound annealed at 635 °C. Further increase in the annealing temperature results in the quasicrystalline phase transformation into ψ-Al65Cu25Cr10 phase, which is an approximant phase to icosahedral quasicrystal.

Nano quasicrystal formation and local atomic structure in Zr–Pd and Zr–Pt binary metallic glasses

Abstract Formation of the nanoscale icosahedral quasicrystalline phase (I-phase) in the melt-spun Zr70Pd30 and Zr80Pt20 binary metallic glasses were reported. Local atomic structure in the glassy and quasicrystal (QC)-formed states were also analyzed by XRD and EXAFS measurements in order to investigate the formation mechanism of QC phase. The distorted icosahedral-like local structure can be identified around Zr atom in the Zr70Pd30 metallic glass. In the QC formation process, a change of local environment around Zr is detected, in which the approximately one Zr atom substitutes for one Pd atom. In contrast, since the local environment around Pt atom is remaining during the QC precipitation, it is suggested that the stable icosahedral local structure is mainly formed around a center Pt atom in the glassy state in Zr80Pt20. We also found that the local environment around Zr atom significantly changes during the quasicrystallization in the alloy. These results differ from those in the Zr70Pd30 metallic glass.

Formation and Properties of Quasicrystals

This article summarizes the general structural features and important properties of quasicrystals, a relatively new class of materials belonging to solid-state substances. Quasicrystals, which have a long-range quasiperiodic order but no three-dimensional translational periodicity, are structurally different from both conventional crystals and glassy solids. Although applications are still highly limited, quasicrystals are attracting significant attention as a structual constituent of mixed-phase materials exhibiting high strength together with certain ductility and can be applied as structural materials.

Fascinating quasicrystals

It took Dan Shechtman more than two years to get his discovery of an Al-Mn phase with icosahedral diffraction symmetry and sharp Bragg reflections published. A paradigm shift had to take place before this novel ordering state of matter - seemingly contradicting crystallographic laws - could be accepted. Today, more than 25 years later, the existence of quasicrystals is beyond doubt. However, not everything is settled yet. All the factors governing formation, growth, stability and structure of quasicrystals are still not fully understood, nor is it resolved whether their structures are strictly or only on average quasiperiodic, and it is still an open question why only quasicrystals with 5-, 8-, 10- and 12-fold rotational symmetry have been experimentally observed so far. These points will be addressed in this review article.

Thermodynamic Study of Liquid, Crystalline and Quasi-Crystalline Al-Mn Phases

Thermodynamic properties of liquid, intermetallic, and quasi-crystalline phases of the Al-Mn system have been studied using two experimental techniques: integral effusion method and Knudsen-cell mass spectrometry. The functions of the liquid phase followed the laws of associated solution and indicated that three type complexes, AlMn, Al2Mn, and Al5Mn, existed in the melt. Phase equilibria calculated using this model and the intermetallic compounds thermodynamic characteristics were in close agreement with phase diagram. The decagonal phase was found to be more stable than the icosahedral quasi-crystals. The calculated enthalpies of the quasi-crystalline phase transformation to the equilibrium crystals were close to the available literature information. The difference between the Gibbs energies of both type quasi-crystals and equilibrium crystalline compositions increases with decreasing temperature. This evidence favors the conclusion that the stabilization of quasi-crystals is entropic in nature and that the quasi-crystalline state, similar to the glassy state in metallic alloys, is only intermediate between liquid and crystals. The conditions of the quasi-crystals formation were found to be closely related to a certain type of the chemical short-range order in liquid, namely to significant mole fraction of the Al5Mn associative complexes.

Deformation behavior, corrosion resistance, and cytotoxicity of Ni‐free Zr‐based bulk metallic glasses

Two Ni-free bulk metallic glasses (BMGs) of Zr(60)Nb(5)Cu(22.5)Pd(5)Al(7.5) and Zr(60)Nb(5)Cu(20)Fe(5)Al(10) were successfully prepared by arc-melting and copper mold casting. The thermal stability and crystallization were studied using differential scanning calorimetry. It demonstrates that the two BMGs exhibit very good glass forming ability with a wide supercooled liquid region. A multi-step process of crystallization with a preferential formation of quasicrystals occurred in both BMGs under continuous heating. The deformation behavior of the two BMGs was investigated using quasi-static compression testing. It reveals that the BMGs exhibit not only superior strength but also an extended plasticity. Corrosion behaviors of the BMGs were investigated in phosphate buffered solution by electrochemical polarization. The result shows that the two BMGs exhibit excellent corrosion resistance characterized by low corrosion current densities and wide passive regions. X-ray photoelectron spectroscopy analysis revealed that the passive film formed after anodic polarization was highly enriched in zirconium, niobium, and aluminum oxides. This is attributed to the excellent corrosion resistance. Additionally, the potential cytotoxicity of the two Ni-free BMGs was evaluated through cell culture for 1 week followed by 3-(4,5-Dimethylthiazol-2-yl-)-2,5-diphenyltetrazolium bromide assay and SEM observation. The results indicate that the two Ni-free BMGs exhibit as good biocompatibility as Ti-6Al-4V alloy, and thus show a promising potential for biomedical applications.

Formation of quasicrystals and metallic glasses in relation to icosahedral clusters

It has been widely accepted that quasicrystals and at least some metallic glasses are built up with icosahedral clusters. Information about the cluster structures can be obtained from crystalline counterparts. In this paper, we will describe the formation rules of bulk metallic glasses, originally developed for quasicrystals, by combining cluster structures with phase diagram features. We will introduce the e/a-constant and e/a-variant criteria for ternary systems, and e/a-constant and atomic size constant criteria for quaternary systems. We will show how the glass forming composition optimization is realized by applying these rules in the Zr–Al–Ni and Zr–Al–Ni–Cu systems. In both systems the optimized glass-forming composition is related to a common binary icosahedral cluster Zr9Ni4 derived from the fcc Zr2Ni phase. A novel route to reach amorphous forming composition is also attempted by mixing Al-based quasicrystal-forming compositions with Zr.

Formation of icosahedral quasicrystals in (Ag,Au)-based ternary systems

We investigated the phase constitution of rapidly solidified (Ag,Au)-based ternary alloys at various compositions of (M,X)85.7RE14.3 (M=Ag, Au, X=Al,Ga,In, RE=Er,Lu). It is found that an icosahedral phase is formed at an average electrons per atom ratio close to 2.0 as well as at the composition ratio of (M,X)6RE, suggesting that these factors have crucial roles in the stability of the icosahedral phases. It is also found that the trend of the icosahedral phase formation in the Au-based alloys is quite different from that in the Ag-based alloys.

Unusual devitrification behaviour in rapidly solidified Ti 45Zr 38Ni 17 alloy

In this study, Ti 45Zr 38Ni 17 ribbons have been elaborated using planar flow casting method ( v quenching = 10 6 K s −1). The rapidly quenched samples, displaying a dispersion of nanoscaled β phase particles in an amorphous matrix, have been extensively characterised using transmission electron microscopy (TEM) and X-ray diffraction (XRD). Devitrification behaviour, investigated by four-probe resistivity measurements and differential scanning calorimetry as well as high resolution TEM analysis, revealed the formation of nanometric quasicrystals (QC) during the first exothermic phase transformation as well as the precipitation of omega domains inside β particles. On the basis of these data, it has been noticed that nanoscaled β metastable particles had adopted the same temperature dependence as β metastable bulk. Furthermore, particular orientation relationships have been observed for QCs in the vicinity of β particles which have suggested probable influence of crystalline structure on the QCs growth, although the presence of such peculiar materials after annealing treatment could be mainly explained by an icosahedral short-range order prevailing in Ti–Zr–Ni melt and favouring their nucleation.

A study of thermodynamic properties and association in the Al-Cu melt and their relation to quasicrystal formation conditions

A study of thermodynamic properties and association in the Al-Cu melt and their relation to quasicrystal formation conditions

Effect of Co substitution for Ni on the Ti–Zr–(Ni, Co) pseudo-ternary quasicrystal formation

A series of alloys designed along a Ti 9(Ni,Co) 4–Zr e/ a-variant line in the Ti–Zr–(Ni, Co) pseudo-ternary alloy system, are investigated by XRD and TEM. Experimental results show that bulk icosahedral quasicrystals (IQC) prepared by copper mold suction casting, can be obtained in a large region from Ti 55Zr 20(Ni,Co) 25 to Ti 34.6Zr 50(Ni,Co) 15.4 with Ni/Co ratio equal to 3/1, and in a sharply diminished region from Ti 48Zr 30(Ni,Co) 22 to Ti 42Zr 40(Ni,Co) 18 with decreased Ni/Co ratio equal to 2/2 or 1/3. Ti 48Zr 30Ni 16.5Co 5.5 is the optimal quasicrystal-forming composition, where a nearly pure bulk IQC phase is achieved. The stepwise substitutions of Co for Ni in this pseudo-ternary system contribute to the formation of Ti 2Ni, fcc-Zr 2Ni, C14-type Laves and β-(Ti, Zr) solid solution phases. However, these substitutions greatly reduce the forming ability of the IQC phase. It is suggested that Co is essentially unfavorable to Ti/Zr-based quasicrystal formation.

Formation of AlCuFe icosahedral quasicrystal by mechanical alloying: XAFS and XRD studies

The structural evolutions of the mechanically alloyed ternary Al 70Cu 20Fe 10 powders with the milling times and the annealing treatment were studied by X-ray diffraction (XRD) and X-ray absorption fine structure (XAFS). It was found that during the milling process, only Cu can incorporate into the lattice of Al to form an Al 2Cu compound or an AlCu solid solution, depending on the milling times. However, Fe remains the original structure of bcc α-Fe. Annealing treatment at 700 °C for 4 h can drive the α-Fe to react with the Al 2Cu compounds and AlCu solid solution, and the main products of the annealed Al 70Cu 20Fe 10 (10 h) and the annealed Al 70Cu 20Fe 10 (40 h) are the icosahedral Al 65Cu 20Fe 15 quasicrystal and the Al(Cu, Fe) solid solution, respectively. The local structural disorders around Fe and Cu atoms in the icosahedral QC phase is about 50% larger than those of the Al(Cu, Fe) solid solution.

Ionic Strength-Induced Formation of Smectite Quasicrystals Enhances Nitroaromatic Compound Sorption

Sorption of organic contaminants by soils is a determinant controlling their transport and fate in the environment. The influence of ionic strength on nitroaromatic compound sorption by K+- and Ca2+ -saturated smectite was examined. Sorption of 1,3-dinitrobenzene by K-smectite increased as KCl ionic strength increased from 0.01 to 0.30 M. In contrast, sorption by Ca-smectite at CaCl2 ionic strengths of 0.015 and 0.15 M remained essentially the same. The "salting-out" effect on the decrease of 1,3-dinitrobenzene aqueous solubility within this ionic strength range was <1.5% relative to the solubility in pure water. This decrease of solubility is insufficient to account for the observed increase of sorption by K-smectite with increasing KCl ionic strength. X-ray diffraction patterns and light absorbance of K-clay suspensions indicated the aggregation of clay particles and the formation of quasicrystal structures as KCI ionic strength increased. Sorption enhancement is attributed to the formation of better-ordered K-clay quasicrystals with reduced interlayer distances rather than to the salting-out effect. Dehydration of 1,3-dinitrobenzene is apparently a significant driving force for sorption, and we show for the first time that sorption of small, planar, neutral organic molecules, namely, 1,3-dinitrobenzene, causes previously expanded clay interlayers to dehydrate and collapse in aqueous suspension.

Mode localization and band-gap formation in defect-free photonic quasicrystals

Defects in photonic crystals are local regions in which the translational symmetry is broken. The same definition can be applied to photonic quasicrystals except in this case the symmetry is the 2pi/n rotational symmetry, where n is the rotational fold number. In this context, if no such defects are present, the structure is called "defect-free". Even though photonic quasicrystal patterns can be defect-free, localized modes can still exist in such structures. These modes resemble those of a central potential that suggests that localization in photonic quasicrystals are actually "extended" modes of the rotational symmetry. A possible connection is suggested between these localized modes and short-range dependence of the photonic band gap (PBG). Such a connection implies a tight-binding description of PBG formation of photonic quasicrystals - making them more similar to electronic semiconductors than regular photonic crystals.

Formation and magnetic properties of p-type icosahedral quasicrystals in Zn–Fe–Sc–L (L = Ho, Er, Tm) alloys

Icosahedral quasicrystals containing heavy lanthanoids L, namely Ho, Er or Tm, have been discovered in the Zn77Fe7Sc16– x L x alloy systems. The solubility limit of the lanthanoid is approximately half of the Sc atoms. All these quasicrystals belong to p-type and are stable at approximately 973 K. The temperature dependence of the magnetic susceptibility of the Zn77Fe7Sc8Tm8 quasicrystal follows the Curie–Weiss law and exhibits spin-glass-like behaviour with a freezing temperature of 9 K. The Curie constants obtained by Curie–Weiss fit are larger than those calculated by the Lande g-factor of free Tm3+ ions based on Hund's rule, assuming all magnetization is caused by Tm atoms only. It is deduced that both Tm and Fe atoms exhibit magnetic moments. This is the first example of a stable icosahedral quasicrystal containing two types of magnetic atoms: Fe and the lanthanoids.