Total Routhian Surface Calculations on Hf Isotopes

The two-dimensional total routhian surface calculations have been carried out to study the triaxial superdeformed structure of a neutron-rich nucleus ¹⁷³Hf firstly. In particular the effects of the rotational frequency ω and pairing-energy gap parameter Δ are discussed in detail in the course of shaping its triaxial superdeformation; additionally the neutron-shell correction energy is analyzed with emphasis in the confirmed triaxial superdeformed nucleus ¹⁷³Hf. Finally, more systematical results have been investigated for some confirmed superdeformed nuclei experimentally and a few predicted triaxial superdeformed nuclei theoretically with quadropole deformation ε₂≈0.4 and triaxial deformation γ≈20^º or 30^º in the Z=72 region.     

The effect of spurious motion on the collective potential energy surface

Energy corrections to the potential energy surface which are caused by spurious collective motions are investigated. We concentrate on spurious center-of-mass motion, rotational oscillations and spurious vibrations. It is shown that the effects are deformation dependent and thus, that the heights and curvatures of the potential energy surface are changed. The changes are of the order of 1–2 MeV in the range of deformation δ=0 to δ=±0.4.     

Spheroidal cap configurations of atomic clusters on planar surfaces

Deposited atomic cluster configurations are investigated under the hypothesis of spheroidal cap shapes being a stable geometry. The macroscopic-microscopic method is employed to calculate the deformation energy. A new specialized single-particle model is developed in order to account for the quantum effects, and the liquid-drop approach is used to calculate the macroscopic part of the energy. The minima within the total deformation energy are interpreted as equilibrium states of atomic clusters on surfaces. Calculations have been performed for the metallic clusters of Na with atom numbers N = 20, 70 and 200.     

Phase transformations and thermal stability of the structure of Ti<Subscript>3</Subscript>Al intermetallic compound at deuteration and plastic deformation

The structural transformations in Ti₃Al intermetallic compound at deuteration with concentrations x = 1.2 and 1.7, heating at 100–400°C, and shear deformation under pressure have been studied. It is established that at a given deuterium concentration deuterides with fcc and orthorhombic lattices are formed; under severe shear deformation, nanocrystalline and amorphous (or close to amorphous) deuterides arise. The reasons for the structure amorphization at deuteration and subsequent plastic deformation are discussed.     

探究弹簧自重对形变量的影响

在理论上,用2种方法研究了弹簧自重对形变量的影响,并用简单实验对该结论进行了论证,最终得出弹簧自身重力作用产生的形变量为x=G/2k的结论.应用该结论对习题进行了修正.     

Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.     

Axisymmetric vibration of continuous shallow spherical shells

The axisymmetric vibration of shallow spells supported along the outer periphery r = a and along an intermediate circle of radius r = b is considered. Shear deformation effects are included in the differential equations. This makes the analysis of higher modes more meaningful. Results are presented for three cases: (a) fixed edge condition at r = a; (b) simply supported condition at r = a; (c) free edge condition at r = a.     

Domain structures in rutile in ultrahigh-pressure metamorphic rocks from Dabie Mountains, China

According to the HRTEM study, the UHP jadeite-quartzite mineral (Rutile, TiO(2)) in Anhui Province, Dabie Mountains, China, has ultrastructures such as 011 two-dimensional commensurable modulated structures or superstructures, [011] twin domain structures, dislocations and crystal deformations. The SAED patterns and HRTEM images indicate the existence of the deformations and stacking faults on the interface of [011] twin crystal of rutile and its two-dimensional commensurate modulated structures with repetition period 0.753 nm (3d(011)) has tetragonal symmetry, cell parameters a = 3a0 = 1.377 nm (a0 = 0.459 nm), c = c0 = 0.3 nm. The modulated structures of rutile were probably caused by the isomorphic replacement of Ti(4+) and position modulation or occupation modulation of oxygen atoms in different degree; the deformation structures reveal that during the process of crystallization and mineralization, this mineral may be affected by the geological environment (such as temperature, pressure and stress), metamorphism and deformation.     

Hardening and softening during fatigue fracture

Summary The comparison of the change of hardness and plastic deformation amplitude at a constant stress loading or stress amplitude at a constant deformation loading during the fatigue process shows some singularity of the hardening and softening effects. These effects were investigated on mean carbon and low-alloyed steel and on globular cast iron.The fatigue fractures at cycle numbers 10⁴÷10⁶ under stresses below the yield strength predominate in the softening process, which arises after an inconsiderable hardness increase extends in the region to 0·2 from the fracturing cycle number. Under the stresses above the yield strength, which in some cases for annealed and coarse-grained states are below the fatigue limit, the hardening process predominates, followed by a hardness increase in the field up to 0·25 and above the fracturing cycle number.At low cycle fatigue fractures with cycle numbers < 10⁴ depending on the cyclic plastic properties of steels the fatigue process can be followed by a continuous hardening or softening till fracture. This process is characterized by the change of the deformation amplitude and a one-sided accumulation of plastic deformations at a constant amplitude of active stresses. The one-sided accumulation of deformations commonly ends in a quasistatic failure. Under loading with a constant deformation amplitude during softening a fatigue fracture takes place as a result of damage accumulation under the alternating stresses with amplitudes decreasing with cycle number.     

On twist quantizations of <Emphasis Type="Italic">D</Emphasis> = 4 Lorentz and Poincare algebras

We use the decomposition of o(3, 1) = sl(2; ℂ)₁ ⊕sl(2; ℂ)₂ in order to describe nonstandard quantum deformation of o(3, 1) linked with Jordanian deformation of sl(2; ℂ). Using the twist quantization technique, we obtain the deformed coproducts and antipodes, which can be expressed in terms of real physical Lorentz generators. We describe the extension of the considered deformation of D = 4 Lorentz algebra to the twist deformation of D = 4 Poincare algebra with dimensionless deformation parameter. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Evolution of the defect substructure in V-4Ti-4Cr alloy under severe plastic deformation

The evolution of the defect substructure in V-4Ti-4Cr alloy under its severe plastic deformation by torsion in Bridgman anvils is studied by transmission electron microscopy. Nanoband structural states with a dipole or multipole character of misorientations and a crystallite (or nanoband) size varying from several to several tens of nanometers form in the true logarithmic strain range e ≈ 3.0−6.6. Such crystallites form inside 100-nm submicrocrystallites or coalesce (at e ≥ 6) to yield mesobands with a pronounced vortex character of their propagation. The formation of these states is related to the activation (by the flows of nonequilibrium point defects in stress fields) of quasi-viscous deformation and lattice reorientation mechanisms, which provide the generation and propagation of partial disclination nanodipoles followed by the development of collective effects in a disclination substructure. These effects lead to the group motion of nanodipoles inside the mesobands.     

Study of nuclear-coulomb interference effects in inelastic deuteron scattering on 238U

The angular distributions of elastically and inelastically scattered deuterons from ²³⁸U at E = 17 MeV are compared to coupled-channel calculations. The cross sections at small scattering angles are strongly influenced by nuclear-Coulomb interference effects and allow a simultaneous extraction of nuclear (optical potential) and charge quadrupole deformation parameters. Two different deformed Coulomb potentials and the parameters of the optical model are discussed.     

Alpha-gamma angular correlation measurements as a sensitive method determining the sign of the nuclear quadrupole deformation

In-plane ²⁴Mg(α, α₁γ) angular correlations habe been measured at E_α = 104 MeV. The correlation parameters and the reaction amplitudes extracted from the data have been studied by a coupled-channel analysis. Drastic effects of the sign of the intrinsic quadrupole deformation are found.     

Isospin symmetry of odd-odd mirror nuclei: identification of excited states in N=Z-2 48Mn

Excited states have been observed in the N=Z-2 odd-odd nucleus 48Mn for the first time. Through comparison with the structure of 48V, a first high-spin study of an odd-odd mirror pair has been achieved. Differences between the T=1 analogue states in this pair have been interpreted in terms of Coulomb effects, with the aid of shell-model calculations in the full pf valence space. Unlike other mirror pairs, the energy differences have been interpreted almost entirely as due to a monopole effect associated with smooth changes in radius (or deformation) as a function of angular momentum. In addition, the large energy shift between analogue negative-parity states is interpreted in terms of the electromagnetic spin-orbit interaction in nuclei.     

Prediction of accidental cancellation of different deformation components and optimum fusion orientations

In view of the role of nuclear deformations in the fusion between spherical and deformed nuclei to form super-heavy elements, we try to understand how a cancellation of the different nuclear deformations could arise. We first investigated the correlation between the orientation variation of the deformed nucleus radius and the orientation Coulomb barrier distribution in presence of the higher order deformation components, β₆ and β₈, in addition to the lower order ones. This correlation has been reported in our previous work (Ismail and Seif, 2010) [1] in presence of the lower order (β₂, β₃ and β₄) deformations. Even if there are higher deformations, we found here that the simple expression which describes the deformed target nucleus can be used to predict with good accuracy the behavior of the fusion Coulomb barrier with both orientation and deformation as well as the optimum (cold or hot) fusion configurations. It can predict the orientations of compact and elongated configurations of the interaction and whether they are equatorial or polar or none of them. The value and sign of the deformation parameters ratios with respect to one of them have been used to classify these configurations. We applied the same correlation to predict successfully the mutual cancellation effects between the different deformation components up to β₈. Illustrative examples are given in which the cancellation, at some orientations, brings the fusion barrier back to the spherical case or keeps only the effect of quadrupole deformation, or the effects of both β₂ and β₄.     

Theoretical considerations regarding pulsed CO2 laser annealing of silicon

We present a calculation of the surface temperature and investigate the “thermal runaway” phenomenon during pulsed CO₂ laser (λ = 10.6 μm) annealing of silicon. In calculating the temperature variation of free carrier absorption in n-Si, we have taken into account acoustic deformation potential scattering, optical deformation potential scattering, and ionized impurity scattering. The deformation potentials are adjusted to fit the experimentally observed values at 300°K. Also, we discuss the contribution of free carrier absorption during annealing with a Nd:glass laser (λ = 1.06 μm).     

Hot deformation in nanocrystalline Ndben Feben B backward extruded rings

Radially oriented Nd-Fe-B rings are prepared by backward extrusion of fine grained melt-spun powder. Melt-spun powder with the nominal composition of Nd_30.5Fe_bal.Co_6.0Ga_0.6Al_0.2B_0.9 (wt%) is used as starting material. The effects of process variables, such as deformation temperature (T_d), strain rate (ε) and height reduction (Δh%), on the magnetic properties of the rings are investigated. A scanning electron microscope (SEM) equipped with an energy spectrum device is used to study the metallograph and microfracture of the extruded rings. The B_r and (BH)_max reach the optimum values at T_d=800℃, ε =0.01 mm/s, and Δh% =70%. It is found by SEM observations that the particle boundaries, which seemingly correspond to the interfaces of the starting melt-spun powders, emerge after the corrosion of metallography specimens. This is helpful for studying the effects of powder-powder interface on the local deformation and deformation homogeneity in the rings. For different spatial positions of the extruded rings, there are characteristic metallographies and microfractures. The upper end of the rings has the least deformation and worst texture, and therefore the worst magnetic properties. The magnetic properties in the radial direction increase slightly along the axis from the bottom to the middle, then steeply decrease at the upper end of the ring. The deformation and the formation-of-texturing processes are discussed. The deformation and the texturing formation of melt-spun Nd-Fe-B alloys probably involve grain boundary sliding and grain rotation, the solution-precipitation process and preferential growth of Nd₂Fe₁₄B nanograins along the easy growth a-axis.     

Microscopic analysis of the double backbending in the nucleus 160Yb

The Hartree-Fock-Bogolyubov cranking method is applied to analyze the double backbending effect recently observed in ¹⁶⁰Yb. The model Hamiltonian used contains the deformed Woods-Saxon potential and monopole pairing terms. The deformation is parametrized in terms of quadrupole and hexadecapole degrees of freedom. The particular values of the deformation employed are calculated by making use of the Strutinsky method. Calculations are performed selfconsistently using a fast convergent iteration procedure. The parameters of the Woods-Saxon and pairing potentials are taken from independent investigations and are not adjusted here. The backbending effects occurring at $\text{I = 10–14}\text{h}\text{?}\text{and}\text{I = 26–28}\text{h}\text{?}$ are reproduced without any free parameter and are associated to the gapless superconductivity (particle alignment) taking place for neutrons and protons, respectively. The corresponding microscopic structure rearrangements of the rotational states are illustrated and discussed.     

Some Nonlinear Rock Behavior Effects

The nonlinear rock behavior effects observed in loading diagrams are analyzed which are usually ignored in conventional models of elastoplastic media. The initial deformation stage and unloading of rock samples are considered. The nonlinear behavior on these loading stages is interpreted from the viewpoint of partial closure of cracks initiated during deformation beyond the elastic limit or in earlier loading history. Phenomenological relations are derived to account for the discussed nonlinear effects in numerical modeling. The postcritical deformation stage corresponding to the stage of strain localization and main crack formation is studied. Corrections are made to provide a more accurate determination of model parameters.     

Dynamics of plastic deformation: Waves of localized plastic deformation in solids

Conclusions It has been shown here that a localized plastic deformation in structurally inhomogeneous media can be of a wave nature and can propagate in the form of nonlinear plastic waves, not only at the microscopic level but also at the mesoscopic level. It has been established that there is an interrelationship between this new effect and grain-boundary slippage (an effect which has been under study for a long time) and also with certain types of quasiviscous fracture in plastically deformable materials.We have discussed certain specific practical problems in the mechanics of plastic deformation, and for certain types of fracture. In the future, these problems will be discussed at a more profound level and in greater detail, because of experimental studies which are presently being carried out on the dynamics of deformation for various types of loading and fracture [17, 18, 31]. We hope that the approach proposed here for a theoretical study of the localization of deformation and fracture can be taken to study such effects as splitting off [31], the influence of defect fluxes on grain-boundary slippage [22], superplasticity [23], the behavior of tectonic faults and boundaries of various types [32], electroplastic and magnetoplastic effects, and high-temperature localization of deformation [25].The general nature of the approach proposed here results from the circumstance that a localization of deformation is present explicitly or implicitly during plastic deformation, and the behavior of this deformation plays a role of fundamental importance in the propagation of plastic deformation through a material.The author wishes to thank V. E. Panin for a constant discussion of this problem and I. O. Nedavnii for carrying out the numerical calculations.V. V. Kuibyshev Tomsk State University. Institute of Strength Physics and Materials Science. Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 19–41, April, 1992.