Formation Of Quasicrystals Research Articles

Designing new quasicrystalline compositions in Al-based alloys

In the present work, we present and discuss the most important results that were obtained in the past few years related with the development of new quaternary quasicrystalline alloys and composites. We present the alloy design strategies that we have used and that led to the discovery of over 60 new quasicrystalline compositions, 2 new quasicrystal-forming systems and 1 new Al-matrix composite. New results are also presented and discussed here. Results of interest discussed in this work include: reassessment of quasicrystal and approximant phase formation on the Al–Co–Fe–Cr system; influence of Cr and Ni additions on the icosahedral Al–Cu–Fe quasicrystal stability; discovery of a decagonal Al–Ni–Co–Cr quasicrystal; composition range of formation of the decagonal Al–Cu–Fe–Cr quasicrystal using combinatorial strategies; fabrication of aluminum matrix composites reinforced with quasicrystals using conventional metallurgy fabrication methods.

Microstructure and Thermal Stability of Icosahedral Quasicrystals in Suction Casting Al-6 at.%Mn(-2 at.%Be) Alloys

Formation and microstructure of icosahedral quasicrystals in suction casting Al-6 at.%Mn(-2 at.%Be) alloys have been investigated by scanning electron microscopy, energy-dispersive spectrometer (EDS), x-ray diffraction (XRD), transmission electron microscopy, and differential scanning calorimetry (DSC). Based on the DSC analysis, isothermal annealing was designed, and XRD was performed to analyze the phase composition after heat treatment. The quasicrystalline microstructure of Al-6 at.%Mn(-2 at.%Be) alloys was obtained by suction casting. Be element addition in Al-Mn alloy modified the appearance of the quasicrystalline phases from hexagons to petals; meanwhile, the primary phase transformed from the Al6Mn compound to quasicrystalline approximant phase. Combined with XRD and scanning results show Be suppressed the formation of Al6Mn and promoted the formation of a quasicrystalline approximant phase. The thermal stability of the icosahedral phases contributes to a better performance of alloys at higher temperature. EDS analysis shows that the quasicrystalline phase is not a stoichiometric compound but a range of compositions.

An atomic scale study of two-dimensional quasicrystal nucleation controlled by multiple length scale interactions.

Formation of quasicrystal structures has always been mysterious since the discovery of these magic structures. In this work, the nucleation of decagonal, dodecagonal, heptagonal, and octagonal quasicrystal structures controlled by the coupling among multiple length scales is investigated using a dynamic phase-field crystal model. We observe that the nucleation of quasicrystals proceeds through local rearrangement of length scales, i.e., the generation, merging and stacking of 3-atom building blocks constructed by the length scales, and accordingly, propose a geometric model to describe the cooperation of length scales during structural transformation in quasicrystal nucleation. Essentially, such cooperation is crucial to quasicrystal formation, and controlled by the match and balance between length scales. These findings clarify the scenario and microscopic mechanism of the structural evolution during quasicrystal nucleation, and help us to understand the common rule for the formation of periodic crystal and quasicrystal structures with various symmetries.

Icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Y, Sm, Gd, Tb, Dy, Ho, Er, Tm) systems

The formation and stability of icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Y, Sm, Gd, Tb, Dy, Ho, Er, Tm) systems are studied in detail, with a focus on the effects of Mg substitution as well as the dependence on temperature and RE species. The results show that the compositional region of the icosahedral phase in the ternary phase diagram shrinks gradually as the RE element becomes smaller in atomic size. This phenomenon is correlated with the geometric ‘stability’ of a so-called Tsai-type cluster described as a packing of spheres that represent the atomic radii of the constituent elements. Moreover, the icosahedral quasicrystals are found to be stabilized at lower RE concentrations (12–13.5 at.%) and temperatures (T < 773 K) compared to their cubic approximants, contrary to earlier findings for the Cd-Mg-Yb system. Single grains of the icosahedral, 2/1 and 1/1 cubic approximant phases with, respectively, rhombic triacontahedron, octahedron and rhombic dodecahedron morphologies ranging ≈1.5–2.5 mm in diameter are further synthesized using a self-flux method. It is confirmed that the bounding facets of the single grains are {111} and {110} for the 2/1 and 1/1 cubic approximants, respectively, through orientation analysis using electron backscatter diffraction. Finally, microstructures involving the Cd-Mg-RE icosahedral quasicrystal and Cd-Mg hexagonal solid solution are analysed to show parallel alignment of 2-fold rotational axes of the former with the 6-fold and 2-fold rotational axes of the latter. This orientation relationship is further discussed in terms of the coincidence of interplanar spacings between the two phases.

Viscosity, undercoolability and short-range order in quasicrystal-forming Al-Cu-Fe melts

Understanding the mechanisms which relate properties of liquid and solid phases is crucial for fabricating new advanced solid materials, such as glasses, quasicrystals and high-entropy alloys. Here we address this issue for Al-Cu-Fe alloys which can serve as a model for studying microscopic mechanisms of quasicrystal formation. We study experimentally two structural-sensitive properties of the liquid – viscosity and undercoolability – and compare results with ab initio investigations of short-range order (SRO). It is shown that the main features of interatomic interaction in Al-Cu-Fe system, extracted from radial distribution function and bong-angle distribution function, are the same for both liquid and solid states. In particular, the system demonstrates pronounced effective repulsion between Fe and Cu as well as strong chemical interaction between Fe and Al. Analysis of orientational short-range order reveals existence in the supercooled liquid Fe-centered icosahedral clusters which are discussed in the literature as structural motifs of the quasicrystal phase. In the concentration region corresponding to the composition of the icosahedral phase, minima on the viscosity and undercoolability isotherms are observed which affect noticeably the initial stage of solidification. Thus, we argue that SRO and structural-sensitive properties of a melt may serve as useful indicators of solid phase formation.

Thermal spray coating of Al-Cu-Fe quasicrystals: Dynamic observations and surface properties

In this study, we prepared Al-Cu-Fe quasicrystals (QCs) via thermal spray coating after optimizing the process parameters. Both in-situ XRD and in-situ TEM were used to investigate the thermal stability of QC phase. These dynamic techniques uniquely allow for a direct observation of QC growth upon heating and cooling. We show that the cubic β-Al-Cu-Fe is the dominant phase at room temperature (initial stage), but with an increase in temperature, the QC takes over at 650 °C, consistent with thermodynamic calculations. Further increasing the temperature to 800 °C, the QC phase transforms into cubic β-Al-Cu-Fe such that the β-Al-Cu-Fe phase is the only phase in existence at 870 °C. Based on this result, we annealed the sample after thermal spray deposition for one hour at 650 °C, which yielded an almost pure QC coating. The contact angle (against water) before annealing was 50°±4° but improved dramatically to 130°±5° after annealing at 650 °C for 1 h. This study provides a better understanding of QC formation during heat treatment as well as that of other secondary phases. Furthermore, these results can be used to manufacture QC coatings with enhanced interfacial properties that are central to technological applications.

Phase Behaviors of Soft-core Particle Systems

This paper reviews some of our recent works on phase behaviors of particulate systems with a soft-core interaction potential. The potential is purely repulsive and bounded, i.e., it is finite even when two particles completely overlap. The one-sided linear spring (harmonic) potential is one of the representatives. This model system has been successively employed to study the jamming transition, i.e., the formation of rigid and disordered packings of hard particles, and establish the jamming physics. This is actually based on the “hard” aspect of the potential, because at low densities and when particle overlap is tiny the potential resembles the hard sphere limit. At high densities, the potential exhibits its “soft” aspect: with the increase of density, there are successive reentrant crystallizations with many types of solid phases. Taking advantage of the dual nature of the potential, we investigate the criticality of the jamming transition from different perspectives, extend the jamming scenario to high densities, reveal the novel density evolution of two-dimensional melting, and find unexpected formation of quasicrystals. It is surprising that such a simple potential can exhibit so rich and unexpected phenomena in phase transitions. The phase behaviors discussed in this paper are also highly regarded in polymer science, which may thus shed light on our understanding of polymeric systems or inspire new ideas in studies of polymers.

Formation of an Intermediate Valence Icosahedral Quasicrystal in the Au-Sn-Yb System.

We report on the formation of a new icosahedral quasicrystal (iQC) in the Au-Sn-Yb alloy system. This iQC has a primitive icosahedral lattice with a lattice constant aico of 0.5447(7) nm and a composition that was determined to be Au60.0Sn26.7Yb13.3. X-ray absorption spectroscopy measurement of the near Yb L3 edge demonstrates that the Yb valence in the iQC is an intermediate valence between divalent (4f14) and trivalent (4f13) at ambient pressure and was determined to be 2.18+. The results are compared to those for a corresponding 2/1 cubic approximant crystal. The formation of this new iQC is discussed in terms of the atomic size factor (δ) and the valence electron-to-atom ratio (e/a).

Bridging the local configurations and crystalline counterparts of bulk metallic glass by nanocalorimetry

The structural understanding of crystallization in bulk metallic glasses (BMGs) has attracted much attention while rapid crystallization occurring under controllable conditions is less involved. In this study, a Ce68Al10Cu20Co2 (at.%) BMG was thermally devitrified by differential scanning calorimetry (DSC) and nanocalorimetry. At a heating rate of 10K/min by DSC, AlCe3 and Ce are the major crystalline phases after devitrification while Al13Co4 quasicrystals and Ce are the dominant phases in the crystallization products at a heating rate of 5000K/s by nanocalorimetry. Attributing to the covalent-like bond in Al–Co atom pairs, Al13Co4 quasicrystals precipitate in the primary crystallization and work as the precursors associating local atomic configurations in the glassy state with crystalline phases after crystallization. Attributing to the enhanced mobility of Cu atoms, compositional redistribution occurs in the as-cast sample. On nanocalorimetry heating, an unambiguous discrepancy in the nucleation and growth of the nano-sized Al13Co4 quasicrystals is thus triggered, contributing to an obvious difference in the crystal size. This research unveils the distinct crystallization behaviors of Ce-based BMG on rapid heating. The formation of quasicrystals demonstrates the multi-stage crystallization on rapid heating and bridges the structural gap between local atomic configurations of metallic glasses and crystalline phases.

Direct observation of growth and stability of Al-Cu-Fe quasicrystal thin films

Al-Cu-Fe based quasicrystal thin films exhibit unique surface and mechanical properties. To better understand the formation of the quasicrystal thin films, we observe direct growth of quasicrystals, prepared in a multilayer Al-Cu-Fe thin films with subsequent heat treatment, by in-situ synchrotron x-ray diffraction and in-situ transmission electron microscopy during heating and cooling. Using these two methods, we show that the ternary phase is more thermodynamically stable compared to the binary phases at temperature higher than 470 °C during the heating process, and quasicrystal formation occurs during the cooling process, specifically at 660 °C, after the sample has reached a liquid state. To distinguish quasicrystal from approximant crystals in the obtained thin film samples, we use high resolution x-ray diffraction to analyze the sample at room temperature. We reveal that the peak broadening increases monotonically along the twofold, threefold, and fivefold high-symmetry directions with the physical scattering vector but does not have systematic dependence on the phason momentum, which suggests that the thin film sample is indeed a quasicrystal instead of approximant crystals and it is almost free of phason strain. Our study provides a complete understanding of the growth mechanism for thin film Al-Cu-Fe quasicrystals, which is of particular importance for developing versatile applications of quasicrystal thin films.

Influence of minor additions on Icosahedral Short-Range Order (ISRO) and its consequences on nucleation and solidification growth kinetics in fcc alloys

The present contribution reviews the recent progress related to the influence of Icosahedral Short-Range Order (ISRO) and icosahedral Quasicrystals (i-QC) formation on the solidification of fcc alloys through minor solute element additions. From intensive crystallographic analysis of multi-twinned regions in as-cast Al-based and Au-based fcc alloys, Kurtuldu et al. have shown recently that a so-called “iQC-mediated” nucleation mechanism occurs when a few hundred ppm of Cr and Ir, respectively, are added to the melt [1] [2]. Similarly, it appears that the growth directions of dendrites in Al-Zn:Cr is also influenced by ISRO in the liquid, thus showing an attachment kinetics effect [3]. In a recent contribution, we have shown that iQC-mediated nucleation also occurs in pink gold alloys with Ir-additions, but two additional phenomena at high solidification speed [4]: (i) a spinodal-type decomposition of the liquid, leading to the formation of twinned Cu precipitates in addition to multi-twinned Au-rich grains; (ii) a change of the microstructure of the Au-rich grains, from 〈100〉 dendrites to 〈111〉 textured cells in the columnar zone.

Rational Design and Self-Assembly of Two-Dimensional, Dodecagonal DNA Quasicrystals.

Quasicrystals are a class of materials with long-range order but no translational periodicity. Though many quasicrystals have been discovered, rational design and engineering of quasicrystals remain a great challenge. Herein, we have developed a rational strategy to assemble two-dimensional (2D), dodecagonal quasicrystals from branched DNA nanomotifs. The key of our strategy is to balance the rigidity and flexibility of the motifs, which is controlled by the introduction of interbranch "bridges". By fine-tuning the experimental conditions, we are able to predictably produce either 2D quasicrystals or conventional crystals. This study presents a rational design, prediction and realization of quasicrystal formation.

Decagonal and Dodecagonal Quasicrystals Obtained by Molecular Dynamics Simulations**Supported by the National Natural Science Foundation of China under Grant No 11674102.

Double-well potentials are used for molecular dynamics simulation in monatomic systems. The potentials change as their parameters are adjusted, resulting in different structures. Of particular interest, we obtain decagonal and dodecagonal quasicrystals by simulations. We also verify the results and explain the formation of quasicrystals from the perspective of potential energy.

In-Situ observation of local atomic structure of Al-Cu-Fe quasicrystal formation

The phase and local environment, neighbouring atoms and coordination numbers (CN), for an Al-Cu-Fe multilayer were studied during heating (to 800 °C) and cooling (to room temperature) processes using in-situ X-Ray diffraction (XRD) and in-situ X-ray absorption spectroscopy (XAS) techniques to investigate the formation of Al-Cu-Fe quasicrystals (QCs). In-situ XRD clarified the transition of the ω-Al7Cu2Fe phase to a liquid state at the high temperature which transformed into the QC phase during cooling. The in-situ XAS showed a relatively small shift in distance between Cu-Al and Fe-Al during the phase evolution from RT to 700 °C. The distance between Cu-Cu, however, showed a significant increase from ω-phase at 700 °C to the liquid state at 800 °C, and this distance was maintained after QC formation. Furthermore, the CN of Fe-Al was changed to N = 9 during cooling. Through our observations of changes in CN, atomic distances and the atomic environment, we propose the local structural ordering of the quasicrystalline phase originated from a liquid state via ω-phase. In this study, we give a clear picture of the atomic environment from the crystalline to the quasicrystalline phase during the phase transitions, which provides a better understanding of the synthesis of functional QC nanomaterials.

Direct Observation of Growth and Stability of Al-Cu-Fe Quasicrystal Thin Films

Al-Cu-Fe based quasicrystal thin films exhibit unique surface and mechanical properties. To better understand the formation of the quasicrystal thin films, we observe direct growth of quasicrystals, prepared in a multilayer Al-Cu-Fe thin films with subsequent heat treatment, by in-situ synchrotron x-ray diffraction and in-situ transmission electron microscopy during heating and cooling. Using these two methods, we show that the ternary phase is more thermodynamically stable compared to the binary phases at temperature higher than 470 °C during the heating process, and quasicrystal formation occurs during the cooling process, specifically at 660 °C, after the sample has reached a liquid state. To distinguish quasicrystal from approximant crystals in the obtained thin film samples, we use high resolution x-ray diffraction to analyze the sample at room temperature. We reveal that the peak broadening increases monotonically along the twofold, threefold, and fivefold high-symmetry directions with the physical scattering vector but does not have systematic dependence on the phason momentum, which suggests that the thin film sample is indeed a quasicrystal instead of approximant crystals and it is almost free of phason strain. Our study provides a complete understanding of the growth mechanism for thin film Al-Cu-Fe quasicrystals, which is of particular importance for developing versatile applications of quasicrystal thin films.

Thermal Spray Coating of Al-Cu-Fe Quasicrystals: Dynamic Observations and Surface Properties

In this study, we prepared Al-Cu-Fe quasicrystals (QCs) via thermal spray coating after optimizing the process parameters. Both in-situ XRD and in-situ TEM were used to investigate the thermal stability of QC phase. These dynamic techniques uniquely allow for a direct observation of QC growth upon heating and cooling. We show that the cubic s-Al-Cu-Fe is the dominant phase at room temperature (initial stage), but with an increase in temperature, the QC takes over at 650°C, consistent with thermodynamic calculations. Further increasing the temperature to 800°C, the QC phase transforms into cubic s-Al-Cu-Fe such that the s-Al-Cu-Fe phase is the only phase in existence at 870°C. Based on this result, we annealed the sample after thermal spray deposition for one hour at 650°C, which yielded an almost pure QC coating. The contact angle (against water) before annealing was 50°±4° but improved dramatically to 130°±5° after annealing at 650°C for one hour. This study provides a better understanding of QC formation during heat treatment as well as that of other secondary phases. Furthermore, these results can be used to manufacture QC coatings with enhanced interfacial properties that are central to technological applications.

Formation and microstructure of quasicrystals in suction cast Al‐6 wt.% Mn alloys with additions of nickel and iron elements

AbstractThe formation and microstructure of quasicrystals in suction cast Al‐6 wt.% Mn‐2 wt.% TM (TM = Ni, Fe) alloys were investigated by transmission electron microscopy, scanning electron microscopy, energy dispersive spectrometry, and X‐ray diffraction. The suction cast Al‐6 wt.% Mn‐2 wt.% Ni alloy consists of a single decagonal phase of Al56Mn11Ni2, whereas the Al‐6 wt.% Mn alloy with 2 wt.% iron addition comprises a primitive icosahedral phase and a decagonal phase of Al40Mn7Fe2. Thus, the addition of nickel or iron favors quasicrystal formation in the suction cast Al‐6 wt.% Mn alloys. Based on a 4 : 1 matching ratio of aluminum atoms to heavier atoms, the approximate electron to atom ratio is 1.85 in two decagonal phases of Al56Mn11Ni2 and Al40Mn7Fe2. Various morphologies of quasicrystals with a size of more than 5 μm were observed in the microstructure of suction cast Al‐6 wt.% Mn‐2 wt.% TM (TM = Ni, Fe) alloys. The decagonal Al40Mn7Fe2 phase nucleates epitaxially and grows on the icosahedral phase.

Influence of Minor Additions on Icosahedral Short-Range Order (ISRO) and Its Consequences on Nucleation and Solidification Growth Kinetics in fcc Alloys

The present contribution reviews the recent progress related to the influence of icosahedral short-range order (ISRO) and icosahedral quasicrystal (iQC) formation on the solidification of fcc alloys through minor solute element additions. From intensive crystallographic analysis of multi-twinned region in as-cast Al-based and Au-based fcc alloys, it has been shown recently that a so-called iQC-mediated nucleation mechanism occurs when a few hundred ppm of Cr and Ir, respectively, are added to the melt (Kurtuldu et al. in Acta Mater 61(19):7098–7108, 2013; Acta Mater 70:240–248, 2014). Similarly, it appears that the growth directions of dendrites in Al–Zn/Cr are also influenced by ISRO in the liquid, thus showing an attachment kinetics effect (Kurtuldu in Influence of trace elements on the nucleation and solidification morphologies of fcc alloys and relationship with icosahedral quasicrystal formation, 2014). Similar observations have been made recently in pink gold alloys with Ir additions, when the solidification speed is increased (Zollinger et al. in Acta Mater, 2018).

Dirac fermions in quasicrystalline graphene

Quasicrystals Quasicrystal lattices, which can have rotational order but lack translational symmetry, can be used to explore electronic properties of materials between crystals and disordered solids. Ahn et al. grew graphene bilayers rotated exactly 30° that have 12-fold rotational order. Electron diffraction and microscopy confirmed the formation of quasicrystals, and angle-resolved photoemission spectroscopy revealed anomalous interlayer electronic coupling that was quasi-periodic. The millimeter-scale layers can potentially be transferred to other substrates. Science , this issue p. [782][1] [1]: /lookup/doi/10.1126/science.aar8412

Structural crossover in a model fluid exhibiting two length scales: Repercussions for quasicrystal formation.

We investigate the liquid state structure of the two-dimensional model introduced by Barkan etal. [Phys. Rev. Lett. 113, 098304 (2014)10.1103/PhysRevLett.113.098304], which exhibits quasicrystalline and other unusual solid phases, focusing on the radial distribution function g(r) and its asymptotic decay r→∞. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is ≈1.932. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the nonequilibrium growth or decay of small-amplitude density fluctuations in a bulk fluid.