Coincidence-site lattices as rational approximants to irrational twins

It is well known that sequences of crystals with Mackay icosahedral motif and increasing lattice parameters exist converging to the icosahedral quasicrystal in the limit. They are known as rational approximants. It has also been demonstrated that it is possible to create icosahedral symmetry by irrational twins involving five variants by 72° rotations around an irrational axis [τ 1 0] or an irrational angle of 44.48° around a rotation axis [1 1 1]. These twinned crystals do not share a coincidence site lattice. In this paper, it is demonstrated that the above twinning relationship arises in the limit of a sequence of coincidence site lattices starting with the cubic twins with Σ = 3 and extending through Σ = 7, 19, 49, 129, 337, …, ∞ created by rotation around [1 1 1] axis. It is also noted that the boundaries of higher CSL values (Σ > 7) are composed of a combination of structural units from Σ = 3 and Σ = 7 boundaries.     

A unified approach to complex crystalline and so-called quasicrystalline phases in aluminium alloys

Recent developments in the complex and controversial, but fertile and fascinating field of aluminium-transition metal alloys are reviewed with particular reference to the so-called quasicrystalline phases and their rational approximants. Pauling’s several approaches to icosahedral phases on the basis of twinning in cubic crystals with large unit cells are described and examined along with the difficulties in checking the structures proposed by him. A new unified crystallographic approach is presented by the author, starting with icosahedral atomic clusters in concerned alloy melts, and it is shown that this integral approach leads to a reasonably good understanding of the interrelationship between the numerous known solid phases in aluminium alloys, including icosahedral phases, decagonal phases and their rational approximants. DEDICATED TO THE MEMORY OF PROFESSOR LINUS PAULING (1901–1994).     

The deformation behavior of DyCu ductile intermetallic compound under compression

In this study polycrystalline specimens of as-cast DyCu with B2 crystal structure were compressed to different strains at room temperature to test if stress-induced phase transformation and twinning occur during deformation. In these tests DyCu exhibited high ductility with plastic strain as high as 35% and ultimate compressive strength of ∼790 MPa. X-ray diffraction and transmission electron microscopy (TEM) showed no indications that DyCu had undergone stress-induced phase transformation or twinning. 〈1 1 1〉-type dislocations have been observed to play an important role for imparting the ductile behavior. TEM analyses showed the presence of second phases, Dy₂O₃ and DyCu₂ within the DyCu. The mechanisms of ductility and impurity phase formation are discussed.     

Ordering transformation in icosahedral quasicrystals and related crystalline phases

Arcs of diffuse intensity appear in various shapes and positions in the diffraction patterns from the icosahedral phase, violating the parity rule for simple icosahedral (SI) symmetry. In the process of annealing treatment, the diffuse spots also evolve in the centre of the arcs and become sharp. These extra diffuse spots change the symmetry of the quasilattice fromP-type toF-type. The ordered and disordered structures in quasicrystal have been linked to the ordered and disordered structures present in the crystalline α (Al-Mn-Si) and α (Al-Fe-Si) alloys.     

Is the two dimensional organic conductor, τ-(EDO-S,S-DMEDT-TTF)2(AuCl2)1+y clean or dirty?

The transport properties of organic τ-type conductors seem to be very clean as well as very dirty depending on what we observe. To clarify this problem, we studied temperature and magnetic field dependence of resistivity, ρ(T, B), in τ-(EDO-S,S-DMEDT-TTF)₂(AuCl₂)_1+y. The properties that favor “probably dirty” are: i) stepwise ρ_a(T) increase below 20 K, which is suppressed by magnetic field, and ii) contrasted difference in ρ(T) as well as magnetization M(T) between field cooled (FC) and zero field cooled (ZFC). On the other hand, Shubnikov de Haas oscillations with very low Dingle temperature (T_D=1.5 K) are typical of clean system. Based on these observations, we conclude this system changes from “dirty” to “clean” system by increase of magnetic field.     

Is the Two Dimensional Organic Conductor, τ-(EDO-S,S-DMEDT-TTF)2(AuCl2)1+y Clean or Dirty?

The transport properties of organic τ-type conductors seem to be very clean as well as very dirty depending on what we observe. To clarify this problem, we studied temperature and magnetic field dependence of resistivity, ρ(T, B), in τ-(EDO-S,S-DMEDT-TTF)₂(AuCl₂)_1+y. The properties that favor “probably dirty” are: i) stepwise ρ_a(T) increase below 20 K, which is suppressed by magnetic field, and ii) contrasted difference in ρ(T) as well as magnetization M(T) between field cooled (FC) and zero field cooled (ZFC). On the other hand, Shubnikov de Haas oscillations with very low Dingle temperature (T_D = 1.5 K) are typical of clean system. Based on these observations, we conclude this system changes from “dirty” to “clean” system by increase of magnetic field.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

Phase transitions and hard magnetic properties for rapidly solidified MnAl alloys doped with C,B, and rare earth elements

MnAl alloys are attractive candidates to potentially replace rare earth hard magnets because of their superior mechanical strength, reasonable magnetic properties, and low cost. In this study, the phase transitions and magnetic properties of melt spun Mn₅₅Al₄₅ based alloys doped with C, B, and rare earth (RE) elements were investigated. As-spun Mn–Al, Mn–Al–C, and Mn–Al–C–RE ribbons possessed a hexagonal ε crystal structure. Phase transformations between the ε and the L1₀ (τ) phase are of interest. The ε → τ transformation occurred at ~500 °C and the reversed τ → ε transformation was observed at ~800 °C. Moderate carbon addition promoted the formation of the desired hard magnetic L1₀ τ-phase and improved the hard magnetic properties. The Curie temperature T _C of the τ phase is very sensitive to the C concentration. Dy or Pr doping in MnAlC alloy had no significant effect on T _C. Pr addition can slightly improve the magnetic properties of MnAlC alloy, especially J_S. Doping B could not enhance the magnetic properties of MnAl alloy since B is not able to stabilize either the ε phase or the L1₀ hard magnetic τ phase.     

Al基三元准晶相图的电子浓度特征

准晶是一种电子型金属间化合物，其形成及结构稳定性主要由电子浓度因素控制。三元准晶相图的电子浓度特征表明，三元准晶与其晶体学类似相一起位于一等电子浓度线附近，称为准晶等电子浓度线现象。同时，三元准晶与二元准晶的存在密切联系，它们同第三组元一起落在同一变电子浓度线上，称为准晶变电子浓度线现象，三元准晶的理想成分位于准晶等电子浓度线和准晶变电子浓度线的交点上，据此特征，区分了两种类型的Al-Ni-Fe三元十次准晶，它们的典型成分分别为：D-Al72.5Fe14.5Ni13(Al-Fe型）和D′-Al70.5Fe12Ni17.5(Al-Ni型）。     

Occurrence of faults/APBs in periodic to quasiperiodic transformations

The strip projection method has been used here to establish the structural relationships between various two dimensional quasiperiodic structures and certain well known periodic structures. These periodic structures, designated as unmodulated approximants, can transform into their quasiperiodic counterparts in a continuous fashion. The early stages of such transformations are characterized by the occurrence of faults or APBs. There is considerable high resolution electron microscopy (HREM) and electron diffraction evidence in favour of this in the case of the β-Mn to octagonal quasicrystal, the σ-phase to dodecagonal quasicrystal and the Al₅Ti₃ to quasiperiodic superlattice structure transformations.     

Effect of hydrogen on orientation dependence of critical shear stress and mechanism of straining in single crystals of stable stainless steel

The effect of hydrogen on the critical shear stress (τ_cr), dislocation structure, and mechanisms of straining (slip vs. twinning) in single crystals of Fe-26Cr-32Ni-3Mo (wt %) austenite stainless steel has been studied. It is shown for the first time that hydrogenation leads to the appearance of the orientation dependence of τ_cr, which is absent in the initial hydrogen-free crystals. This dependence of τ_cr is related to a decrease in the stacking fault energy, which determines a change of the mechanism of straining from slip to twinning.     

The hP1-type phases in alloys of cadmium,mercury, and indium with tin

The hP1-type phases in alloys of Cd, Hg, and In with Sn are stable in the valence electron concentration interval 3.80–3.95. Following a rule of Raynor, the axial ratioc/a decreases with increasing valence electron concentration,N _b ^/at . Using lattice constant measurements the rule is confirmed, and by using density measurements the absence of constitutional vacancies is verified. Thec/aN _b ^/at relation of the hP1 phases is similar toc/aN _b ^/at of InSn _m (03Sn. A bonding-type proposal, explaining the stability of these structures and the dependence of their axial ratio on valence electron concentration, is derived.     

Microwave dielectric properties of Ca4La2Ti5O17–LaAlO3 system ceramic materials

Compositions in the (1 − x) Ca₄La₂Ti₅O₁₇–xLaAlO₃ system were prepared in order to modify the positive temperature coefficient of the resonant frequency (τ _f ) of Ca₄La₂Ti₅O₁₇. The microwave dielectric properties and phase composition of this system ceramics were investigated. X-ray powder diffraction results showed that Ca₄La₂Ti₅O₁₇ and LaAlO₃ formed a solid solution only when x ≤ 0.2. The τ _f values showed a near linear decrease with increasing additions of LaAlO₃. It was observed that near zero τ _f value can be achieved as x = 0.64. The permittivity (ε_r) and the quality factor (Q × f) values exhibited a non-linear behavior with LaAlO₃ additions. The microwave dielectric properties were strongly correlated with composition, secondary phases and grain sizes. For practical application, a permittivity (ε_r) of 42, a quality factor (Q × f value) of 12,450 GHz and a temperature coefficient of resonant frequency (τ _f ) of ~0 ppm/°C for 0.36 Ca₄La₂Ti₅O₁₇−0.64 LaAlO₃ were proposed.     

Two-dimensional pentagon quasicrystal in an Al-Co-Ni-Tb alloy obtained by quenching under high static pressure

A transmission electron microscopy study of quasicrystals was carried out in Al-Co-Ni-Tb alloy which was obtained by quenching under high static pressure and a new two-dimensional pentagonal quasicrystal was discovered. An unique five-fold axis is observed in its diffraction patterns and the periodicity along the five-fold axis is 0.4 nm. Another feature of the pentagonal phase is that no extinction exists in the diffraction patterns along the direction perpendicular to the five-fold axis. A comparison of the high resolution electron microscopy images of the pentagonal phase and the decagonal quasicrystal is given. The effect of high pressure is discussed.     

Optical properties of chromium-doped transparent alumina xerogels

Optical properties of chromium-doped transparent alumina xerogels have been studied in the ultraviolet, visible and near infra-red regions. The coordination, valence state and symmetry of crystal field around the transition metal ion is found to change in different transition phases of the xerogel in accordance with the earlier conclusion that the metal ion penetrates into the alumina matrix and occupies aluminium sites. In boehmite and α-Al₂O₃ chromium is essentially in trivalent state, octahedrally coordinated, whereas in the transitionγ andδ phases tetrahedrally coordinated hexavalent state appears to be dominant. This agrees with the spinel structure expected for the transition phases.     

Orthorhombic rational approximants for decagonal quasicrystals

An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are explained elsewhere. In this work a comparison is made between the two models bringing out their equivalence. Further, using the concept of average lattices, a modified model is proposed.     

Metastable phases in vapour-deposited Al-Ru alloys

Vapour deposition of two Al-Ru alloys containing 10 and 15wt% Ru resulted in the formation of supersaturated solid solutions. Electron microscopy and electron diffraction techniques have been used to characterize this as-quenched structure and also those formed on subsequent decomposition. Elevated-temperature (650–800 K) annealing treatments resulted in the formation of a metastable intermediate phase. Electron diffraction evidence suggested that this phase can be assigned a simple cubic structure either of the Mo₃N₂-type witha=0.42 nm or of the Mg₂Zn₁₁-type witha=0.84 nm. Further annealing led to the formation of the equilibrium AI and AI₆ Ru phases. The morphology and structural features of transformation products and the crystal structure details of the metastable intermediate phase have been discussed.     

Pressure-dependent electronic properties of MgO polymorphs: a first-principles study of Compton profiles and autocorrelation functions

The first-principles periodic linear combination of atomic orbitals method within the framework of density functional theory implemented in the CRYSTAL06 code has been applied to explore effect of pressure on the Compton profiles and autocorrelation functions (AF) of MgO. Calculations are performed for the B1, B2, B3, B4, B8₁, and h-MgO polymorphs of MgO to compute lattice constants and bulk moduli. The isothermal enthalpy calculations predict that B4 → B8₁, h-MgO → B8₁, B3 → B2, B4 → B2, and h-MgO → B2 transitions take place at 2, 9, 37, 42, and 64 GPa, respectively. The high-pressure transitions B8₁ → B2 and B1 → B2 are found to occur at 340 and 410 GPa, respectively. The pressure-dependent changes are observed largely in the valence electrons Compton profiles, whereas core profiles are almost independent of the pressure in all MgO polymorphs. Increase in pressure results in broadening of the valence electrons Compton profiles. The principal maxima in the second derivative of Compton profiles shifts toward high-momentum side in all structures. Reorganization of momentum density in the B1 → B2 structural phase transition is seen in the first and second derivatives before and after the transition pressure. Features of the AFs shift toward smaller distances when pressure increases.     

Synthesis of the B1-type tantalum nitride by shock compression

B1-type tantalum nitride (polycrystalline bulk state) was synthesized by shock compression. Shock-compression recovery experiments of the porous sample of tantalum nitride with a hexagonal structure (CoSn-type) were performed in the impact-velocity range up to 1.5kms^–1. The instrumental chemical analysis, X-ray and electron diffraction experiments were carried out on the recovered tantalum nitride sample and the combustion-synthesized B1-type sample for comparison. The recovery rate of the B1 -type phase increased with increasing porosity, impact velocity and impactor thickness; among these above all the effect of porosity was most remarkable. Almost 100% recovery rate was achieved for the powder of 70% porosity impacted by a 2 mm thick tungsten plate with velocities above 1.4 kms^–1. It was confirmed by chemical analysis that the nitrogen content did not change by shock compression. The chemical formulae of the shock-synthesized and combustioned-synthesized B1-type phases were estimated to be TaN_0.96–0.99 and TaN_{1.13–1.16, 1.27–1.30}, respectively. The lattice parameter of the shock-synthesized B1 -type (Fm3m) phase was a_o=0.43363- + (1) nm. The results of X-ray and electron diffraction experiments also supported that the shock-synthesized B1-type tantalum nitride has a good stoichiometry compared with the combustion-synthesized ones.