Incompatibility and preferred morphology in the self-accommodation microstructure of β-titanium shape memory alloy

The frequency distribution of habit plane variant (HPV) clusters and the deviation from twin orientation relationships (ORs) at the junction plane (JP) are investigated by transmission electron microscopy together with theoretical evaluation of the kinematic compatibility (KC) at the JP in a β-titanium shape memory alloy. Even though there are more than 10 types of possible HPV clusters, only three types are formed. V-shaped couplings of HPVs by {111} type I twins (V_I: 49%) and by ?211? type II twins (V_II: 42%) are the predominant types. A triangular morphology due to coupling of {111} type I twins is observed with a frequency of only 9%. These preferred morphologies are well explained by the degree of incompatibility (the rotation necessary for compatible connection of HPVs). The exact twin OR and KC are maintained at the JP in a V_I cluster instead of KC at the habit plane (HP), whereas the JP in a V_II cluster is incompatible and the ?211? type II twin OR shows slight deviation at the JP by about 0.4°. The competition between KC at the JP and KC at the HP (invariant plane) is responsible for the frequency distribution of HPV clusters and the character of the interfaces in the self-accommodation microstructure.     

Energy barriers associated with slip–twin interactions

The energetics of slip–coherent twin boundary (CTB) interactions are established under tensile deformation in face centered cubic (fcc) copper with molecular dynamics simulations, exploring the entire stereographic triangle. The CTBs serve as effective barriers in some crystal orientations more than others, consistent with experimental observations. The resulting dislocation structures upon slip–twin reactions are identified in terms of Burgers vector analysis. Visualization of the dislocation transmission, lock formation, dislocation incorporation to twin boundaries, dislocation multiplication at the matrix–twin interface and twin translation, growth, and contraction behaviors cover the most significant reactions that can physically occur providing a deeper understanding of the mechanical behavior of fcc alloys in the presence of twin boundaries. The results make a distinction between deformation and annealing twins interacting with incident dislocations and point to the considerable role both types of twins can play in strengthening of fcc metals.     

Atomic-scale mapping of twins and relevant defective structures in Al20Cu2Mn3 decagonal approximant

Twins or multiple twins occur frequently in the orthorhombic Al₂₀Cu₂Mn₃ approximant of decagonal quasi crystal (DQC). Due to the specific structural units, the twins in the Al₂₀Cu₂Mn₃ approximant usually exhibit the glide-reflection characteristics. Using aberration-corrected transmission electron microscope at the atomic scale, we have observed not only glide-reflection twins but also simple mirror-reflection twins in the Al₂₀Cu₂Mn₃ approximant. The two twinning modes are found to coexist in the present sample. These twins exhibit variant configurations at the twin boundaries where the tessellations of local subunits are imaged at an atomic scale. At the twin boundaries, diversified tiles such as star-like (S), bowtie-shaped and boat-shaped (B) are observed. The diversified tiles stacking with various manners allow the coexistence of the DQC and the approximant. Furthermore, the variants of B and S tiles are also found.     

Sound radiation from point-excited structures: Comparison of plate and sphere

Acoustic radiation from a structure can be expressed in terms of “modal radiation” and “modal coefficients”. This paper investigates the contributions of these two modal properties to radiation excited by a point force. Sound radiation from two basic structures is considered: a baffled rectangular plate and a closed spherical shell. The plate behaviour is familiar, and governed by the relation between the natural frequency of a mode and its coincidence frequency. For a closed spherical shell, there are either zero or two “critical frequencies”, depending on the radius and thickness. When there are two the shell radiates well both above and below the two frequencies, and poorly in the frequency range between them.     

Hierarchical microstructure in structural phase transitions

We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T₀) we obtain the conditions under which branching of twins is energetically favorable. Above T₀ a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.     

Preparation and properties of binary metal monolayers: II. Pb and Sn on Al(100)

The growth modes, structures and thermal properties of binary monolayers of lead and tin on the (100) face of aluminium have been investigated by LEED and AES. Monolayers of pure lead and pure tin were also examined. Dense binary layers were formed by successive vapour deposition of the two elements. The compositions were accurately determined by AES. For the pure monolayers sharp changes in the sticking probability at half-monolayer coverage (detectable by AES) lead to accurate determinations of the densities of the complete monolayers. The LEED pattern for the pure lead monolayer can be interpreted in terms of a pseudo-hexagonal arrangement while that for tin shows intensity features that favour an arrangement of dense atomic chains. For the binary layers the apparent mesh parameter varies continuously as a function of composition between the values for the pure monolayers. Different variations in parameter are found, depending on which element is deposited first. It is deduced that the binary layers are formed of intimate mixtures of the coincidence meshes of the pure monolayer structures together with disordered regions. Each binary layer is characterized by a temperature for complete thermal desordering T_d. For tin-rich layers there are significant differences between values of T_d for “tin-first” and “lead-first” layers. A sharp minimum in T_d is observed for the composition Sn₄Pb.     

Optimal trapping wavelengths of Cs2 molecules in an optical lattice

The present paper aims at finding optimal parameters for trapping of Cs₂ molecules in optical lattices, with the perspective of creating a quantum degenerate gas of ground-state molecules. We have calculated dynamic polarizabilities of Cs₂ molecules subject to an oscillating electric field, using accurate potential curves and electronic transition dipole moments. We show that for some particular wavelengths of the optical lattice, called “magic wavelengths”, the polarizability of the ground-state molecules is equal to the one of a Feshbach molecule. As the creation of the sample of ground-state molecules relies on an adiabatic population transfer from weakly-bound molecules created on a Feshbach resonance, such a coincidence ensures that both the initial and final states are favorably trapped by the lattice light, allowing optimized transfer in agreement with the experimental observation.     

Boron implanted in silicon: Segregation at angular configurations of the silicon/silicon dioxide oxidation boundary

Based on computer simulation of the physicochemical segregation processes involving dopants implanted into a host material (silicon), the details of boron injection were investigated for four types of angular configurations (direct and inverse kinks and cavities of the “trench” and “square” types) of the “silicon/silicon dioxide” oxidation boundary. A complicated picture of the B distribution inside the Si and SiO₂ regions and at the SiO₂/Si front was obtained and analyzed in general terms.     

Kinetics of formation of green rust 2 in the steady acidic sulphated medium

The kinetics of formation of green rust 2, 4Fe(OH)₂.2FeOOH.FeSO₄.nH₂O, called “GR2, was followed by Mössbauer spectroscopy in the controlled aeration of a mixture of 0.4 M FeSO₄ and 0.4 M NaOH. Mössbauer spectra run at 78 K of the reaction products taken at different time intervals display an average of seven doublets. The initial products of reaction consists of a badly crystallized ferrous hydroxide, FE(OH)₂., called “FH”, which disappears first at about 1/3 of the total time of formation of GR2, and sulphated ferrous hydroxide, 4Fe(OH)₂.FeSO₄.nH₂O, called “SFH”. The kinetics of oxidation of SFH into GR2 can be described by a linear growth reaction and the transformation is considered to be in situ.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

Effect of initial orientation on twinning in commercially pure titanium

Abstract

The effect of initial orientation on twinning micro-mechanisms during tensile deformation of commercially pure titanium has been studied using micro focus X-ray diffraction and electron back scatter diffraction (EBSD) in a scanning electron microscope. Three orientations A, B and C obtained from a rolled and annealed block of commercially pure titanium were deformed in uniaxial tension till failure and the tested specimens were characterised with regard to bulk texture, microstructure and crystal orientation mapping using EBSD. Orientation B along the transverse direction in ND-TD plane exhibits higher strength and lower strain hardening compared to orientations A and C along the rolling direction in TD-RD and ND-RD plane, respectively. This is attributed to different texture of sample B compared to samples A and C leading to dissimilar twinning micro-mechanisms and characteristic variation in nature of twinning. It is observed that limited twin nucleation and prominent lateral growth plays a dominant role in orientation B while multiple twin nucleation with significant non-Schmid behaviour is dominant for the other two orientations. It is proposed from this study that conventional factors associated with twin formation like Schmid factor play a main role in twin nucleation and propagation, however, growth or lateral thickening of the twins is explained by elastic stiffness variation across twins and their parent grains.     

The activation and the spreading of deformation in a fully lamellar Ti–47 at.% Al–1 at.% Cr–0.2 at.% Si Alloy

The spreading of deformation in a lamellar Ti–47?at.% Al–1?at.% Cr–0.2?at.% Si alloy deformed under compression is studied at 25°C and 600°C. This microstructure is largely dominated by twin-related variants which are separated by either twin interfaces or thin α ₂ slabs. The alloy deforms at both temperatures by ordinary dislocations and twins. Deformation in a particular γ variant and its adjacent twin-related variant involves the same kind of glide system, either ordinary dislocations or twins. This property is found to be true for all twin-related lamellae. The occurrence of this correlated glide is explained by the introduction of the notion of pilot and driven orientations. The lamellar orientation in which the operating glide system is activated on the basis of Schmid factor considerations is termed the pilot orientation. It imposes its deformation system on to the twin-related lamella, called the driven orientation, whose deformation may not involve the slip system most favoured by the applied stress.     

Structure and phase composition studies of partially stabilized zirconia

Zirconia single crystals doped with 2.8, 3.2, 3.7, and 4.0 mol % of Y₂O₃ have been studied. The phase composition and structure have been studied by X-ray diffraction analysis and transmission electron microscopy. It has been established that all investigated samples has two ZrO₂ tetragonal phases with tetragonality c/a = 1.006–1.007 and c/a = 1.014–1.015 independent of the stabilizing impurity content. The former phase is not transformed, whereas the latter is transformed into a monoclinic one. In all cases the samples have a developed twin structure. Twinning hierarchy is observed: there are first-, second-, third-order, etc., twins, each of them containing the next-order twins inside them. Elastic stress relaxation occurs by twinning rather than by generation of dislocations. The stabilizing impurity content affects the structure nonmonotonically; the minimum dimensions of the twin lamellas refer to the Y₂O₃ concentration of 3.2 mol %.     

Change in grain-boundary ensemble upon the A1 → L12 phase transition in Ni3Mn alloy

The grain structure of Ni₃Mn alloy is investigated in the states with short-range and long-range atomic orders that arise at the A1 → L1₂ phase transition. It is found that in ordering annealing, new boundaries of a general type form, the fraction of special-type boundaries (including twin boundaries) is reduced, the share of high-energy special boundaries with Σ > 11 increases, and the alloy’s texture is transformed into a “gray” texture.     

Diffraction de neutrons dans CoCl2, 6D2O determination de ses structures cristallographique et magnetique

We have performed neutron diffraction experiments on a CoCl₂, 6D₂O monocrystal. We show that a crystallographic transition from the C 2/m monoclinic structure to the P $\text{1}$ triclinic structure occurs at T = Tmt = 73.5K., together with a twinning of the monocrystal. We describe the two possible twins (four types of domains) related to the loss of the initial monoclinic symmetry, say of the elements 2 and m : either m becomes twin plane (Albite twinning) or 2 becomes twin axis (Pericline twinning). Each domain has an antiferromagnetic structure P 2a T, with an easy magnetization axis tilted from the ac plane by an angle φ = (30 ± 4)°, its component on this plane making an angle φ = (3.5 ± 2)° with the c axis.     

Soliton-soliton and wave-soliton collisions in Skyrme-likeσ-models

A skyrme-like version of the (2+1)-dimensional classical σ-model is considered. Some aspects of solitonsoliton collisions are studied using both the numerical and phenomenological approaches. In particular, the problem of 90° scattering of solitons in the head-on collisions is analyzed. Properties of the two-soliton configurations forυ～υ _cr are discussed in terms of a specific solution, which may be called a “disoliton”. This solution corresponds to a saddle point in the space of field configurations and is unstable with respect to the decay into two well separated solitons. Different classes of field configurations, which may be called “one-dimensional” wave packets, are also studied as well as the interaction of these wave packets with a soliton.     

Deformation twinning in boron carbide particles within nanostructured Al 5083/B4C metal matrix composites

The presence of deformation twins is documented in boron carbide reinforcement particles within a nanostructured Al 5083/B₄C metal matrix composite. High resolution transmission electron microscopy analysis suggests that these are (0001) twins. This work discusses the mechanisms responsible for their formation based on crystallographic analysis and mechanical loading conditions. Specifically, we propose that there are two potential models that can be used to describe twin formation in boron carbide particles. The structural models involve slip in the 1/3[1100] (0110) or 1/3[0110] (0110) planes of C–C–C chains and the appropriate reconfiguration of B–C bonds. Analysis of the loading conditions experienced by the boron carbide particles indicates that local high stress intensity and the presence of a high shear force around the boron carbide particles are two factors that contribute to twin formation.     

MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative

This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducting and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number “Re”, fractional parameter “α”, effective permeability “K_eff” and the time “t”, on the fluid's motion are observed.     

3D numerical analysis on mechanisms of flow and heat transfer in a square channel with right triangular wavy surfaces

Numerical investigations on thermo-hydraulic performance and mechanisms of flow and heat transfer in a square channel heat exchanger inserted with right triangular wavy surfaces are examined. The influence of the flow attack angles (30°, 45° and 60°) is investigated for laminar flow (Re = 100–2000). The configurations of the right triangular wavy surfaces are varied as inclined and V-shaped wavy surfaces (the pointing of V-tip with downstream and upstream called “V-downstream” and “V-upstream”, respectively). The insertions of the wavy surfaces in the channel heat exchanger are divided into two types: middle and diagonal insertions. The computational results reveal that the maximum thermal enhancement factor, TEF, is around 2.31 for the 30° V-downstream wavy surface with diagonal insertion at Re = 2000.