Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals

The optical behavior of both synthetic and natural icosahedral and decagonal quasicrystals in the range 400–700 nm has been explored by repeated measurements of the reflectance values on crystallographically oriented fragments. We found differences in the optical behavior between natural and synthetic quasicrystals, and discuss the possible reasons to justify this feature. Natural quasicrystals, both icosahedral and decagonal, exhibit an almost identical chemical composition to their synthetic analogs, but seem to show a higher degree of structural perfection, as indicated from their electron and X-ray diffraction patterns. Such perfection is mainly due to the very low phason strain shown by the minerals with respect to the synthetic compounds and substantiates the differences in the measured reflectance values. The new finding constitutes significant new support for the original proposal that icosahedral and decagonal quasicrystals can be energetically stable states of matter, on the same footing as crystals. Electron diffraction pattern of icosahedrite (left) and decagonite (right). A high-resolution transmission electron image of icosahedrite is on the background.

Features of crystal structures of Al 65 Cu 20 Fe 15-x Mn x alloys have been investigated by transmission electron microscopy. Electron diffraction patterns obtained experimentally show that some alloys exhibit similar diffraction patterns to those of the decagonal quasicrystal, in addition to those taken from the icosahedral quasicrystal as well as the Al 3 Mn and Al 13 Fe 4 crystalline approximants. That is, there are both diffraction patterns showing a crystal period of 1.2 nm along one direction and a pseudo-tenfold one with an electron incidence parallel to it. From high resolution images taken in the present works, it was also found that these patterns originate from a single-state region. These results clearly imply that a structure characterized by these patterns can be identified as a two-dimensional modulated structure, which should be distinct from not only the icosahedral and decagonal quasicrystals but also the crystalline approximants.

We tried to grow Al–Pd–Mn icosahedral quasicrystal (IQC) by floating zone melting technique. Molten block of Al73.2Pd19.8Mn7.0 at around 1140 K was travelled through a bar of Al69.4Pd20.3Mn10.3 at the rate of 1.1 to 14 μm/s. The sample obtained (about 1 cm in diameter and about 6 cm in length) was cut in several slices and some of them were annealed at 1073 K for 20 hr in evacuated state. The bulk composition of the sample was Al69.6Pd20.3Mn10.1 and almost unchanged along the growth direction. The largest grain was about 5 mm in diameter and several tens of mm along the growth direction. The sample was made mainly of IQC of Al69.8Pd21.4Mn8.8, and a small amount of decagonal quasicrystal (DQC) of Al68.6Pd13.3Mn18.1 was seen as fine exsolution lamellae and grain boundary phase. The electron diffraction pattern taken along the two-fold symmetry axis showed that our IQC is F1 type of Ishimasa and Mori (1992). Micro-Vickers hardness (HV) was about 950 at 25 g, irrespective of annealed or as-solidified and of the presence or absence of DQC lamellae. HV decreased with increasing load, as reported formerly. The fracture toughness (KIC) of annealed sample with lamellae (2.1 MPam1⁄2) was about 1.5 times as large as that of annealed one without lamellae (1.3 MPam1⁄2) and as-solidified one with lamellae (1.4 MPam1⁄2).

Spin structure, magnetism, and cation distributions of NiFe2−xAlxO4 solid solutions

Using a statistical approach to diffraction analysis, it was shown that the scale of difficulty in the analysis of the diffraction image of a one-dimensional quasicrystal is not significantly different from the analysis of the diffraction image for a single slit. In both cases we get a rectangular probability distribution, for which the Fourier transform leads to analytical expressions on the envelopes of diffraction peaks expressed by means of simple trigonometric functions (sinc). The generalization to 2d (decagonal quasicrystals) and 3d (icosahedral quasicrystals) requires more complex calculations, but conceptually, it does not significantly differ from the calculations for model one-dimensional quasicrystals.

Chapter 5 Magnetism and quasicrystals

A structural relationship between the μ-Al4Mn phase and the Λ-Al4Mn phase, which are approximants of icosahedral and decagonal quasicrystals respectively, was studied from the viewpoint of the modulated structure. The difference between these phases is basically understood by the difference in the ordered arrangements of atomic vacancies in the close-packed layers (or the modulation wave-vectors). The modulation is considered to be due to the rearrangement of atomic vacancies as a response to the occurrence of charge-density waves.

Publisher Summary This chapter reviews the current results about high-resolution electron microscopy studies on quasicrystals. From the results it can be concluded that structures of icosahedral and decagonal quasicrystals can be described as aperiodic arrangements of some atom clusters, which have the same symmetry as those of the quasicrystals, with definite linkages. There is variety in aperiodic arrangement of the atom clusters and atomic arrangements in the atom clusters, depending on quasicrystalline alloys. High-resolution electron microscopy is the most powerful tool for studying the varied structures. However, it has many limitations for carrying out precise structure analysis about atomic arrangements, because of its limited resolution compared with diffraction and the use of images projected along the incident beam. To proceed to the more precise structure analysis of the quasicrystals, combining high-resolution electron microscopy with the diffraction method becomes more important. The atomic arrangements of Al–Ni–Co, Al–Pd–Mn, and Al–Pd decagonal quasicrystals, were proposed using the results of x-ray diffraction.

Elementary excitations in quasicrystals

The formation of the icosahedral phase in an Al70Cu20Fe10 quasicrystal and the structural transition from the crystal praphase to the quasicrystalline phase are simulated and studied by means of X-ray absorption near edge structure spectroscopy. Al-Cu-Fe samples are fabricated by means of powder metallurgy. The ω phase of the praphase crystal forms following exposure at 500°C for 20 min; the quasicrystalline phase forms after exposure at 800°C for 2 h. The model of the structural transition from the crystal to quasicrystal is a diffusion displacement of aluminum atoms around iron atoms with the formation of an icosahedron with the iron atom at the center. The immediate environment of copper atoms consists mainly of aluminum and copper atoms, and no iron atoms are observed.

In the pressent work the propagation of cracks in two-dimensional decagonal and three-dimensional icosahedral model quasicrystals under mode I loading is studied by means of molecular dynamics simulations. The dependence on temperature, applied load and underlying structure has been investigated in particular. The samples are endowed with an atomically sharp crack and loaded by linear scaling of the displacement field. Subsequently the response of the system is monitored by molecular dynamics simulations. In the decagonal systems three different regimes of propagation are discernable with increasing temperature: For low temperatures the crack velocity grows monotonically with the applied load. We observe that the crack follows the path of dislocations nucleated at its tip. For temperatures above 30% of the melting temperature the crack does not remain atomically sharp but is blunting spontaneously. In the temperature range between 70% and 80% of the melting temperature the quasicrystal fails by nucleation, growth and coalescence of micro voids. This gradual, dislocation-free crack extension is caused by plastic deformation which is mediated by localized rearrangements comparable to so-called shear transformation zones. These are also observed in amorphous solids. In conclusion at low temperatures the crack propagates along crystallographic planes just like in periodic crystals, whereas a glass-like behavior is dominant at high temperatures. In the icosahedral quasicrystals brittle fracture without any crack tip plasticity is observed irrespective of the orientation of the cleavage plane and the propagation direction. The fracture surfaces are not flat but show a pronounced roughness on the atomic scale, comparable to that observed experimentally. The magnitude of the roughness depends on both the cleavage plane and the propagation direction. The clusters inherent in the structure are not strictly circumvented but are cut to some extent by the moving crack. However, a detailed analysis of the fractured samples indicates that the roughness of the fracture surfaces can be assigned to the occurrence of the clusters. In der vorliegenden Arbeit wird die Ausbreitung von Rissen unter Modus-I-Belastung mittels molekulardynamischer Simulationen in zweidimensionalen dekagonalen und dreidimensionalen ikosaedrischen Modellquasikristallen studiert. Dabei wird speziell die Abhangigkeit der Ausbreitungsmechanismen von der Temperatur, der auseren Last und der zugrundeliegenden Struktur untersucht. Die Proben werden mit einem atomar scharfen Riss versehen und durch lineare Skalierung des Verschiebungsfeldes belastet. Anschliesend wird die Antwort des Systems in molekulardynamischen Simulationen verfolgt. In den dekagonalen Systemen lassen sich mit steigender Temperatur drei unterschiedliche Bereiche der Rissausbreitung beobachten: Fur tiefe Temperaturen steigt die Rissgeschwindigkeit kontinuierlich mit der angelegten Belastung. Wir beobachten, dass der Riss Versetzungen folgt, die von der Rissspitze nukleieren. Fur Temperaturen uber 30% der Schmelztemperatur bleibt die Rissspitze nicht atomar scharf, sondern stumpft spontan ab. Im Temperaturbereich zwischen 70% und 80% der Schmelztemperatur versagt der Quasikrsitall durch Nukleation, Wachstum und Koaleszenz mikroskopischer Poren. Dieses Porenwachstum ist mit plastischer Verformung vor der Rissspitze verbunden, die durch lokale Umordnungsprozesse verursacht wird. Diese sind vergleichbar mit sogenannten Schertransformationszonen, die auch in amorphen Strukturen beobachtet werden. Zusammenfassend lasst sich feststellen, dass sich der Riss bei tiefen Temperaturen wie in periodischen Kristallen entlang kristallographischer Ebenen ausbreitet, wahrend bei hohen Temperaturen ein glasartiges Verhalten dominiert. In den ikosaedrischen Quasikristallen wird unabhangig von der Spaltebene und der Ausbreitungsrichtung ein sprodes Bruchverhalten ohne Anzeichen fur Versetzungsemission beobachtet. Die Bruchflachen zeigen eine ausgepragte Rauigkeit auf atomarer Skala, die sich gut mit experimentellen Ergebnissen vergleichen lasst. Die Rauigkeit hangt hierbei sowohl von der Wahl der Spaltflache, als auch von der Ausbreitungsrichtung ab. Die in der Struktur enthaltenen globularen Strukturen werden nicht strikt umlaufen, sondern zu einem gewissen Grad durch den fortschreitenden Riss durchtrennt. Eine detaillierte Analyse der Spaltproben zeigt jedoch, dass sich die Rauigkeit der Spaltflachen auf die globularen Strukturen zuruckfuhren lasst.

Stable decagonal and icosahedral quasicrystals

Using different thickness of pure nickel as interlayer, hot isostatic pressing (HIP) diffusion bonding between TC4 prealloyed powders and GCr15 bearing steel have been performed at the temperature of 850 °C, under pressure of 150 MPa for 2 hrs. The diffusion bonding joints gained have been observed and analyzed by optical microscopy, electron microprobe and X-ray diffraction. The result of observation by optical microcopy indicates that, at the interface of TC4 and interlayer, many connecting arcs have been formed, and these arcs gradually disappear with thickness of pure nickel increasing. The result of observation by electron microprobe reveals that, during the process of HIP diffusion bonding, nickel atoms have a short diffusion distance in the zone of GCr15, whereas they diffuse a comparatively long distance in zone of TC4. The observation also find that the distributions of elements of titanium, iron and chrome vary in different area of zone of pure nickel, which results in the formation of different type of intermetallics. Thus, the contact of titanium atom and iron atom can be avoided with certain thickness of pure nickel as interlayer. When thickness of interlayer is large than 120 um in this test, the combination of titanium atom and iron atom will be avoided and intermetallics such as TiFe and TiFe2, are disappeared. These rules mentioned above also have been confirmed by the analysis of X-ray diffraction.

We analyze in detail the results of experimental investigations of the evolution of the thermal vibration spectra for iron atoms in iron monosilicide FeSi depending on two external parameters, viz., temperature T (in the range 46–297 K at pressure P = 0.1 MPa) and pressure P (in the range 0.1 MPa–43 GPa at temperature T = 297 K), obtained by nuclear inelastic scattering of synchrotron radiation. The decrease of the atomic volume is accompanied by a rearrangement of the phonon spectrum, which is manifested, in particular, in the splitting of the low-energy peak in the spectrum and in an increase of the energy for all phonons. The changes of the average energy of the iron atom vibrational spectrum and of the Debye energy with decreasing atomic volume are analyzed. Different versions of FeSi electron spectrum variation, which can be used to explain the observed phonon anomalies, are considered.

Nickel, copper, and zinc atoms (M) are good complexing agents relative to ethylenediamine (En) and to Edta (H4L). The nickel and copper atoms are coordinated in a series of dinuclear complexes containing both ligands (L 4and En) only by L 4or by En: Ni2(L)(En).4H20 [1], Niz(L)(En)z.4HzO [2], Cu2(En)9.(L).6H20 [3] The formation of the mixed dinuclear complex, Cu~(L)(En)2.2H20, in which both copper atoms are coordinated with En and L 4was established on the basis of chemical and spectral data [4, 5]. In the study of the competitive complexation of Ni, Cu, and Zn in aqueous solutions containing only the L 4ligand or both L 4and En, we examined ZnCu(L).6H~O (I), ZnNi(L).6H2:) (II), and CuNi(L)(En)~.nH~O, where n = 2 (III) [6] and n 4 (IV) [7]. In the present work, we give the x-ray diffraction data for ZnCu(L)(En)2-4H20 (V) and atomic coordinates of ZnM(L).6H20, where M Cu (I) and Ni (II), which were omitted in our previous communication [8]. The unit cell parameters for monoclinic crystals of V are as follows: a = 10.356(3), b = 11.849(6), c = 10.082(2) A,/~ = 104.570(3) ~ V = 1197(1) A s, deale = 1.69 g/cm 3, Z = 2, space group P21. The exposure of the monocrystal was carried out on a CAD-4/SDP-t55 automatic diffractometric system using AMoK a radiation, graphite monochromator, and o,,--(n/6)20 scanning. A total of 3834 reflections were measured, of which 2283 reflections had I > 3o(I). Treatment of the experimental data and the structural calculations were carried out using the ENX-SDP program. The structure was solved by the heavy atom method. The coordinates of the nonhydrogen atoms and then the hydrogen atoms were determined from successive electron density maps. The refinement was carried out anisotropically for the nonhydrogen atoms and isotropically for the hydrogen atoms taking account of secondary extinction (c = 3.3617x10 -7) and a unified weighting scheme (w i = 1), R = 0.046, R w -0.050, and S = 0.729. The coordinates of the nonhydrogen atoms in I, II, and V are given in Table 1. The hydrogen atom coordinates in V are given in Table 2. The hydrogen atoms were not determined in the structures of I and II. Complexes V and IV are isostruetural. The structure of V consists of neutral binuclear [ZnL--CuEnz.HzO] complexes and water of crystallization molecules. As in IV, the Cu atom is coordinated by En, while the L 4ligand coordinates the Zn atom. The structure of the ZnL and CuEnz.HzO fragments is ordinary (see Fig. 1). No significant differences were observed in the bond lengths and angles in V and IV. The equatorial plane in the distorted octahedron of the Zn atom is formed by 03, 05, O7, and N5 while the axial apices are occupied by Ol and N6. The distortion of the octahedron is characterized by the following parameters: the equatorial plane is tetrahedrally distorted and the mean deviation of the atoms is +0.113 A. The zinc atom extrudes from the equatorial plane by 0.174 A toward O1. The bond angles are significantly distorted: O3ZnO5, 86.9(3); O3ZnN5, 80.9(3); O5ZnO7, 91.0(3); O7ZnN5, 100.3(3); O1ZnN6, 157.5(2)*. The equatorial plane of the copper square bipyramid is formed by the nitrogen atoms of the ethylenediamine rings E 1 and E 2. The water molecule in the bipyramid is closer the ideal axial position than O1. The OwlCuN(1-4) bond angles are 89.7,87.7, 87.6, and 89.7(3)*, while the OICuN(I-4) bond angles are 94.1, 96.0, 88.7, and 86.4(3)* The OICuOwl bond angle is 174.9(3)*.