Formation Of Quasicrystals Research Articles

On electrochemical corrosion of mechano-activated and thermally processed AlxCryNiz 2D decagonal quasicrystalline structures and crystalline approximants

This article represents a pioneering study centered on the corrosion kinetics of untreated and thermally processed mechano-synthesized AlxCryNiz two-dimensional decagonal quasicrystalline structure and crystalline approximants. It sheds light on the distinguished corrosion behavior of untreated and heat-treated mechano-synthesized Al72Cr15Ni13 and Al86Cr12Ni2 alloys, including a wide diversity of miscellaneous intermetallic phases. A comprehensive characterization was performed to analyze crystallographic structure and thermal characteristics of AlxCryNiz powder particles. Electrochemical evaluations of the mechano-synthesized Al72Cr15Ni13 and Al86Cr12Ni2 specimens and their heat-treated counterparts were conducted under cyclic potentiodynamic polarization tests with 0.1 mol/L Na2SO4 (pH=2) and 3.5% NaCl (pH=8.5) electrolytes at room temperature, respectively. Al72Cr15Ni13 two-dimensional decagonal quasicrystalline phase was attained following 6 h mechano-synthesis and subsequent annealing treatment at 1035°C. There is no evidence of quasicrystal formation in the Al86Cr12Ni2 alloy system after 6 h mechano-synthesis and successive thermal processing at 445 and 570°C. In this study, we conducted the first investigation into electrochemical performance of both Al72Cr15Ni13 and Al86Cr12Ni2 intermetallics. Both Al72Cr15Ni13 and Al86Cr12Ni2 alloys develop a protective passive film in 0.1 mol/L Na2SO4 electrolyte. It was determined that 6 h mechano-synthesized Al72Cr15Ni13 sample, subjected to annealing at 1035°C, stands out in the Al-Cr-Ni alloy systems for applications necessitating exceptional corrosion resistance, passivation behavior, and minimal susceptibility to pitting corrosion when compared to other tested counterparts. This alloy is characterized by a corrosion current density of 3.73 µA/cm2 and a corrosion potential of -0.16 V(vs. Ag/AgCl), revealing a remarkably stable passive film up to a current density of 0.02 A/cm2 and a potential of 2.41 V(vs. Ag/AgCl) within 0.1 mol/L Na2SO4 medium. Likewise, it exhibited a drastically diminished corrosion current density of 11.65 µA/cm2 and a reduced corrosion potential of -0.27 V(vs. Ag/AgCl) within 3.5% NaCl electrolyte, attributed to the formation of two-dimensional decagonal quasicrystalline phase and hexagonal δ-Al3Ni2 crystalline approximant at 1035°C. It also encompassed a re-passivation current density and potential of 50.35 µA/cm2 and -0.04 V(vs. Ag/AgCl), respectively, within the latter solution. Its corrosion mechanism may be ascribed to a two-step surface precipitation process: initially, Al dissolves into a hydroxide, succeeded by the formation and precipitation of Al oxides, such as NaAlO2 and Al2O3∙xH2O.

Thunderstruck! A quasicrystal made by lightning

A material with characteristics between crystal and glass has been accidentally created by an electrical discharge (likely a lightning strike) in the Sand Hills of Nebraska. The material is a quasicrystal with 12-fold symmetry, impossible for ordinary crystals. Transient high-pressure and high-temperature conditions seem to ease the formation of quasicrystals in nature.

The relation between the glass forming ability and nucleation kinetics of metastable quasicrystals in Mg–Zn–Yb liquid

Bulk metallic glass (BMG), metastable quasicrystals (QCs) and two types of approximant phases concurrently form from the melt during cooling at different rates in a Mg–Zn–Yb model alloy. Such an enriched phase competition between various metastable and stable crystals has also been found during the heating of Mg–Zn–Yb metallic glass between the glass transition and liquidus temperatures. Metastable QC acts as a transient phase that nucleates first from the melt and subsequently transforms into an equilibrium approximant phase. During heating, a metastable approximant phase transforms into the Mg-QC phase mixture which then transforms into the Mg and equilibrium approximant eutectic microstructure. Nucleation kinetics of QCs is critical to analyze for further understanding the relation between QC formation and glass forming ability of the alloy. For this purpose, a metastable phase diagram for QCs has been determined using a novel experimental strategy via fast differential scanning calorimetry (FDSC). Along compositional line binding Mg to Zn17Yb3, one stable eutectic point, i.e. Mg68.6Zn26.7Yb4.7 at 390°C, and one metastable eutectic composition, i.e. Mg64.6Zn30.1Yb5.3 at 350°C, were determined during interrupted heating experiments. We have demonstrated that the glass forming ability of Mg–Zn–Yb alloys strongly depends on the metastable phase diagram of QCs and their nucleation kinetics. Nucleation of metastable QCs limits the metallic glass formation, therefore the bulk metallic glass forming compositional region was found to be below metastable hypoeutectic compositions.

Ball Milling and Consolidation Process of Al-Cr Powder Mixture—Microstructural Characterization

The interest in studying the synthesis of an Al–Cr alloy system by non-equilibria processes is due to the formation of metastable or quasicrystalline phases when rapid solidification has been utilized. Similarly, the formation of quasicrystals has been reported to a much lesser extent when the mechanical alloying technique was applied. In the present research, a mixture of powders of Cr and Al (both elements with a purity of 99.99%) with compositions of Al-5 and 7.5 at. % Cr was subjected to a ball milling process. Afterwards, the powder mixture was subjected to a consolidation process, conducted by pressing and sintering processes. The X-ray diffraction analyses revealed that during 20 h of milling there was no formation of metastable or quasicrystalline second phases detected. In addition, the X-ray diffraction peaks revealed that as milling time increased, the nanometric grain size decreased, and once the sintering treatment was applied, the crystallite size decreased following the same tendency. The dislocation density was estimated using the size of nanometric grains; this computation revealed that the dislocation density grew throughout the ball milling process; even after sintering, the multiplication of dislocations prevailed following the same tendency.

2D honeycomb transformation into dodecagonal quasicrystals driven by electrostatic forces

Dodecagonal oxide quasicrystals are well established as examples of long-range aperiodic order in two dimensions. However, despite investigations by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), low-energy electron microscopy (LEEM), photoemission spectroscopy as well as density functional theory (DFT), their structure is still controversial. Furthermore, the principles that guide the formation of quasicrystals (QCs) in oxides are elusive since the principles that are known to drive metallic QCs are expected to fail for oxides. Here we demonstrate the solution of the oxide QC structure by synchrotron-radiation based surface x-ray diffraction (SXRD) refinement of its largest-known approximant. The oxide QC formation is forced by large alkaline earth metal atoms and the reduction of their mutual electrostatic repulsion. It drives the n = 6 structure of the 2D Ti2O3 honeycomb arrangement via Stone–Wales transformations into an ordered structure with empty n = 4, singly occupied n = 7 and doubly occupied n = 10 rings, as supported by DFT.

Emergent time crystals from phase-space noncommutative quantum mechanics

It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position (qˆi) and/or momentum (pˆi) noncommutativity, i.e., from [qˆi,qˆj]≠0 and/or [pˆi,pˆj]≠0 (for i≠j). In such a context, a predictive analysis is carried out for the 2-dim noncommutative quantum harmonic oscillator through a procedure supported by the Weyl-Wigner-Groenewold-Moyal framework. This allows for the understanding of how the phase-space noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis also shows how the spontaneous formation of time quasi-crystals can arise.

Discovery of core-shell quasicrystalline particles

Submicron-sized quasicrystalline particles were obtained in an Al-Zn-Mg-Cu alloy produced by traditional melting. These particles consist of an Al-Fe-Ni core and a Mg-Cu-Zn shell and were found to be stable and embedded randomly in the Al matrix. The diffraction patterns of these core-shell particles reveal a decagonal core and an icosahedral shell with, respectively, ten- and five-fold axes aligned. High resolution scanning transmission electron microscopy of the Mg-Cu-Zn shell confirms the five-fold symmetry atomic arrangement and the icosahedral structure. It can therefore be concluded that Fe and Ni impurities play an important role in mediating the formation of such an unusual ternary core-shell quasicrystalline particle. These findings provide some novel insights in the formation of quasicrystals in traditional industrial Al alloys.

Freezing in two-length-scale systems: complexity, universality and prediction

Two-length-scale pair potentials arise ubiquitously in condensed matter theory as effective interparticle interactions in molecular, metallic and soft matter systems. The existence of two different bond lengths generated by the shape of potential causes complicated behavior in even one-component systems: polymorphism in solid and liquid states, water-like anomalies, the formation of quasicrystals and high stability against crystallization. Here we address general properties of freezing in one-component two-length-scale systems and argue that solidification of a liquid during cooling is essentially determined by the radial distribution function (RDF) of the liquid. We show that different two-length-scale systems having similar RDFs freeze into the same solid phases. In some cases, the similarity between RDFs can be expressed by the proximity of two dimensionless effective parameters: the ratio between effective bond lengths, λ, and the fraction of short-bonded particles φ. We validate this idea by studying the formation of different solid phases in different two-length-scale systems. The method proposed allows predicting effectively the formation of solid phases in both numerical simulations and self-assembling experiments in soft matter systems with tunable interactions.

Study of in situ formed quasicrystals in Al-Mn based alloys fabricated by SLM

Quasicrystal (QC) phases are often observed in Al-based alloys with Al content< 85 at%, and their particle size is typically greater than 0.3 µm. In this study, an in situ formed QC phase was observed in Al-4.1Mn-0.98Mg-0.8Sc-0.5Zr alloy (Al ≈ 96 at%) when processed using Selective Laser Melting (SLM). The particle size of the QC phase processed by SLM is 55–85% smaller than when processed by other methods, which is likely due to the lower Mn concentration and higher cooling rate. Moreover, the shape of the QC phase is spherical near the bottom of the melt pool and becomes a strip in the center of melt pool with the variation of solidification conditions. At higher cooling rates, it can be inferred that the formation of QCs is promoted while the growth of QC phase is effectively inhibited. According to calculations and electron spectroscopy (EDS) results, the possible chemical composition of the QC phase is considered as Al80Cu2.83Mn17.16 (at%) with an e/a of 1.9849 and Rav of ~1.4152 Å. During aging, a portion of the QC phase could transform into Al6Mn through a peritectoid reaction. The homogeneously dispersed QC transforms the Al6Mn into a finer and more dispersed phase. Consequently, the mechanical properties are cooperatively improved both by Al6Mn and the residual QC phase. After aging, the ultimate strength is 548.67 ± 4.66 MPa with an elongation of 12.2 ± 1.09%. These results indicate that SLM expands the formation range of QC and is an ideal processing route to fabricate in situ QC-strengthened Al-based alloys.

Emergent Physics on the Route from Crystals to Amorphous Solids

Comprehensive SummaryBy introducing and gradually increasing the magnitude of disorder into both crystalline particle packings and crystalline networks, we realize the evolution from crystals to amorphous solids. The evolution of structures and mechanical properties during this process is expected to help us understand the physical origin of the peculiar properties of amorphous solids, e.g., the boson peak, so as to build up the bridge between well‐established physics of crystals and that of amorphous solids. To our surprise, this attempt also reveals some extraordinary phenomena, including the hidden order‐disorder transition from crystals to disordered crystals and the emergence of mechanical metamaterials with negative Poisson's ratios. What is the most favorite and original chemistry developed in your research group?Our favorite research findings are some extraordinary phase behaviors of soft‐core particle systems, including the discontinuous‐continuous transition of two‐dimensional melting, formation of quasicrystals and the transition from crystals to disordered crystals discussed in this article.How do you get into this specific field? Could you please share some experiences with our readers?I entered the field of soft matter during my graduate study at Yale University. I have been attracted by so many interesting and complex problems in soft matter. During the research, we keep meeting new phenomena and problems, which keep broadening my interest. Learning by doing is a good way to enjoy research.How do you supervise your students?I always assign one or two problems to beginners. The problems may not be very specific. My purpose is to encourage the students to work independently and cultivate their abilities of literature reading and finding and solving problems. I listen to their reports in weekly group meetings and discuss about their work whenever they come to show their progress or I have some new ideas. Once they achieve some significant progress, I will put more effort to help finalize their work.What is the most important personality for scientific research?Persistence.What are your hobbies?Jogging, walking, music, and movies.What is your favorite journal(s)?Physical Review series.

Formation and fluctuation of two-dimensional dodecagonal quasicrystals.

The self-assembly of two-dimensional dodecagonal quasicrystals (DDQCs) from patchy particles is investigated by Brownian dynamics simulations. The patchy particle has a five-fold rotational symmetry pattern described by the spherical harmonics Y55. From the formation of the DDQC obtained by an annealing process, we find the following mechanism. The early stage of the dynamics is dominated by hexagonal structures. Then, nucleation of dodecagonal motifs appears by particle rearrangement, and finally the motifs span the whole system. The transition from the hexagonal structure into the dodecagonal motif is coincident with the collective motion of the particles. The DDQC consists of clusters of dodecagonal motifs, which can be classified into several packing structures. By the analyses of the DDQC under fixed temperature, we find that the fluctuations are characterised by changes in the network of the dodecagonal motifs. Finally we compare the DDQCs assembled from the patchy particle system and isotropic particle system. The two systems share a similar mechanism of the formation and fluctuation of DDQCs.

Connecting short-range order for the liquid-solid transition of Al-Cu-Fe alloys

Liquid-solid transition processes have always been mysterious, especially those with the participation of quasicrystal (QC) structures, and are generally far less understood than the conventional solidification process. Here, the liquid structure variation of ternary QC-forming Al60Cu37Fe3 with crystal-forming Al50Cu40Fe10 alloy liquids was compared using synchrotron radiation based on high-energy X-ray diffraction (HE-XRD) and reverse Monte Carlo simulation (RMC). It was noted that the types of short-range order structures are almost the same in the Al60Cu37Fe3 and Al50Cu40Fe10 alloy liquids, while the former has more icosahedral short-range order (ISRO) and the latter has less. The medium-range order (MRO) was characterized by the cluster correlation method and visualization analysis. More obvious structural heterogeneity was found in the Al60Cu37Fe3 liquid, which is due to the strong correlation between clusters with high icosahedral order and the weak correlation between crystal clusters. Moreover, strongly correlated ISRO clusters can form icosahedral medium-range order (IMRO) structures by interpenetrating connections forming a stable structure upon cooling, and some other clusters can even enhance the IMRO stability. Such IMRO will be retained in the liquid upon cooling, leading to QC formation. All the findings provide a further understanding of the liquid-solid transition with ISRO participation.

Machine Learning to Predict Quasicrystals from Chemical Compositions (Adv. Mater. 36/2021)

Quasicrystals In article number 2102507, Kaoru Kimura, Ryo Yoshida, and co-workers demonstrate that machine-learning algorithms can predict the chemical composition of new quasicrystals. Furthermore, analyzing the input–output relationships black-boxed into the machine-learning model, they successfully identify nontrivial empirical equations interpretable by humans that describe the conditions necessary for stable quasicrystal formation. This is the first step toward understanding the formation mechanism of quasicrystals, which has been long sought in quasicrystal research.

Machine Learning to Predict Quasicrystals from Chemical Compositions.

Quasicrystals have emerged as the third class of solid-state materials, distinguished from periodic crystals and amorphous solids, which have long-range order without periodicity exhibiting rotational symmetries that are disallowed for periodic crystals in most cases. To date, more than one hundred stable quasicrystals have been reported, leading to the discovery of many new and exciting phenomena. However, the pace of the discovery of new quasicrystals has lowered in recent years, largely owing to the lack of clear guiding principles for the synthesis of new quasicrystals. Here, it is shown that the discovery of new quasicrystals can be accelerated with a simple machine-learning workflow. With a list of the chemical compositions of known stable quasicrystals, approximant crystals, and ordinary crystals, a prediction model is trained to solve the three-class classification task and its predictability compared to the observed phase diagrams of ternary aluminum systems is evaluated. The validation experiments strongly support the superior predictive power of machine learning, with the overall prediction accuracy of the phase prediction task reaching ≈0.728. Furthermore, analyzing the input-output relationships black-boxed into the model, nontrivial empirical equations interpretable by humans that describe conditions necessary for stable quasicrystal formation areidentified.

Trace Element Conundrum of Natural Quasicrystals

We report laser ablation inductively coupled plasma mass spectrometry measurements of the trace element contents of the two naturally occurring quasicrystalline minerals, Al63Cu24Fe13 icosahedrite and Al71Ni24Fe5 decagonite, from their type locality in the Khatyrka meteorite. The isolated quasicrystal fragments were mounted separately from any matrix and are larger than the laser beam diameter. When the elements are sorted in order of volatility, a systematic and unique pattern emerges in both bulk natural quasicrystal specimens. They are highly depleted compared to primitive solar system materials (chondritic meteorites) in moderately refractory elements (those with 50% condensation temperatures near 1350–1300 K; V, Co, Mg, Cr) and significantly enriched in moderately volatile elements (those with 50% condensation temperatures between 1250 and 500 K; Sb, B, Ag, Sn, Bi). We compare the chondrite-normalized trace element patterns and ratios of the quasicrystals to those of scoriaceous cosmic spherules and other meteoritic components. The nonmonotonic shapes of the chondrite-normalized trace element patterns in both icosahedrite and decagonite are incompatible with a single condensation process from the gas of the solar nebula. Previous transmission electron microscopy studies show that the natural quasicrystals contain 3–5 vol % of silicate and oxide nanoparticle inclusions, which we consider to be the main host of the measured trace elements. On this basis, we construct a three-stage model for the formation of the quasicrystals and their inclusions: a high-temperature condensation stage and a low-temperature vapor-fractionation stage to make nanoparticles, followed by a third stage that leads to the formation of quasicrystals incorporating the two different types of nanoparticles and their incorporation into the CV chondrite parent body of the Khatyrka meteorite.

Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain

Quasicrystals have been discovered in a variety of materials ranging from metals to polymers. Yet, why and how they form is incompletely understood. In situ transmission electron microscopy of alloy quasicrystal formation in metals suggests an error-and-repair mechanism, whereby quasiperiodic crystals grow imperfectly with phason strain present, and only perfect themselves later into a high-quality quasicrystal with negligible phason strain. The growth mechanism has not been investigated for other types of quasicrystals, such as dendrimeric, polymeric, or colloidal quasicrystals. Soft-matter quasicrystals typically result from entropic, rather than energetic, interactions, and are not usually grown (either in laboratories or in silico) into large-volume quasicrystals. Consequently, it is unknown whether soft-matter quasicrystals form with the high degree of structural quality found in metal alloy quasicrystals. Here, we investigate the entropically driven growth of colloidal dodecagonal quasicrystals (DQCs) via computer simulation of systems of hard tetrahedra, which are simple models for anisotropic colloidal particles that form a quasicrystal. Using a pattern recognition algorithm applied to particle trajectories during DQC growth, we analyze phason strain to follow the evolution of quasiperiodic order. As in alloys, we observe high structural quality; DQCs with low phason strain crystallize directly from the melt and only require minimal further reduction of phason strain. We also observe transformation from a denser approximant to the DQC via continuous phason strain relaxation. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality--just like their alloy quasicrystal counterparts.

Quasicrystal formation in binary soft matter mixtures

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with integral equation theory. Quasicrystal formation requires particle ordering with two characteristic lengthscales in certain particular ratios. How the lengthscales are related to the form of the pair interactions is reasonably well understood for one component systems, but less is known for mixtures. In our model mixture of big and small colloids confined to an interface, the two lengthscales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively. The small-small lengthscale is not significant. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors.

Electric field assisted alignment of monoatomic carbon chains

We stabilize monoatomic carbon chains in water by attaching them to gold nanoparticles (NPs) by means of the laser ablation process. Resulting nanoobjects represent pairs of NPs connected by multiple straight carbon chains of several nanometer lengths. If NPs at the opposite ends of a chain differ in size, the structure acquires a dipole moment due to the difference in work functions of the two NPs. We take advantage of the dipole polarisation of carbon chains for ordering them by the external electric field. We deposit them on a glass substrate by the sputtering method in the presence of static electric fields of magnitudes up to 105 V/m. The formation of one-dimensional carbyne quasi-crystals deposited on a substrate is evidenced by high-resolution TEM and X-ray diffraction measurements. The original kinetic model describing the dynamics of ballistically flowing nano-dipoles reproduces the experimental diagram of orientation of the deposited chains.

Solidification of Metallic Alloys: Does the Structure of the Liquid Matter?

In 1952, Frank (Proc R Soc Lond Ser-Math Phys Sci 215:43–46, 1952) already postulated that Icosahedral Short Range Order (ISRO) of atoms in the liquid could possibly explain the large nucleation undercoolings measured in metallic alloys by Turnbull and Fisher (J Chem Phys 17:71–73, 1949). About thirty years later, this conjecture was proven to be key for the understanding of Quasicrystals (QC) formation (Shechtman et al. in Phys Rev Lett 53:20, 1951–3, 1984). More recently, it has been found that a few tens to thousand ppm of solute elements in Al-base and Au-base alloys can influence the nucleation and growth of the primary fcc phase via mechanisms involving ISRO and QC formation. ISRO has also been found to limit the mobility, and thus diffusion, of atoms in the liquid. This can lead to out-of-equilibrium conditions, e.g., the formation of metastable phases or supersaturated solid solution, at reduced velocity compared to alloys where ISRO is not predominantly present. Finally, there are several experimental evidences that ISRO is also responsible for twinned dendrites formation in Al alloys. The present contribution summarizes these recent findings and points out the implications that these might have in the field of solidification and additive manufacturing.

Growth modes of quasicrystals involving intermediate phases and a multistep behavior studied by phase field crystal model

Understanding the microscopic kinetics of quasicrystal formation via nucleation and growth is crucial. Here, we report unusual pathways to nucleation and growth of dodecagonal quasicrystals via a phase field crystal model incorporating a two-length-scale potential. Under certain thermodynamic parameters, both quasicrystal growths via heterogeneous and homogeneous nucleation may be associated with a multistep behavior and the transient appearance of triangular and intermediate phases, different from classical nucleation pathways. The metastable intermediate phase spontaneously occurs to bridge the triangular phase and quasicrystal nuclei of different orientations to reduce the total free energy of the system. Decomposition of an undercooled fluid phase into quasicrystal phase shows a multistep pathway wherein the triangular phase and the intermediate phase may occur faster than the quasicrystal phase, when the growth rate of one length-scale ordering is significantly different from the other and the subsequent competing and coupling of both length scales are involved. The calculated structure factor, radial distribution function, and the aperiodic tiling structure of the intermediate phase explain why it appears during the quasicrystal formation.