Precipitation hardening of alloys with structure modulated within the region of micro- and macroflow. I

The effect of precipitation of phase Co₃Ti on the change in mechanical properties, measured within the range of micro ( - 10^§-1), and macroflow ( = 10^–3) was studied at various stages of decomposition of the Co-Ni-Ti and Co-Ni- Ti-Al alloys. It was shown that in the region of microdeformation, a parabolic dependence () is observed, and the dependence of resistance to deformation on the grain size is expressed by Petch equation. It was shown that theoretical estimations with the use of Gerold -Haberkorn and Gleiter-Hornbogen theories are in agreement with the experimentally observed changes in macroscopic yield stress during the process of precipitation of Co₃Ti phase in the studied alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–52, September, 1972.     

Photothermal waves in a periodically modulated structure

The generation of thermal waves in a one-dimensional structure with a sinusoidal variation in thermal diffusivity can be described by an inhomogeneous Mathieu equation. An exact solution to the frequency-domain Mathieu equation can be found by using a variation of parameters method to give the alternating component of the temperature along the structure. From the theory of Mathieu functions a dispersion relation for the thermal waves is found, which does not display band gaps, but which shows damping that departs from that for thermal waves in a uniform medium.     

Incommensurate modulated magnetic structure in orthorhombic EuPdSb

Orthorhombic EuPdSb is known to undergo two magnetic transitions, at 12 K and at T _N≃ 18 K, and in phase III (T < 12 K), single crystal magnetisation data have shown that the spin structure is collinear antiferromagnetic, with magnetic moments along the crystal a axis. From a ¹⁵¹Eu M?ssbauer absorption study, we show that, at any temperature within phase III, all the moments have equal sizes, and that in phase II (12 K< T <18 K) the magnetic structure is modulated and incommensurate with the lattice spacings. The modulation is close to a pure sine-wave just below T _N = 18 K, and it squares up as temperature is lowered. We measured the thermal variations of the first and third harmonics of the moment modulation, and we could determine the first and third harmonics of the exchange coupling. We furthermore show that the antiferromagnetic-incommensurate transition at 12 K is strongly first order, with a hysteresis of 0.05 K, and that the incommensurate-paramagnetic transition at 18 K is weakly first order. Finally, we present an explanation of the spin-flop transition observed in the single crystal magnetisation data in phase III when || in terms of an anisotropic molecular field tensor. Received 17 January 2001 and Received in final form 20 March 2001     

On the particle hardening in Cu-Cd alloy single crystals

The transmission electron microscopy of Cu-Cd single crystals deformed previously was performed to explain the hardening effect measured. The increment of the critical resolved shear stress is explained by the size misfit effect of the observed particles.     

On the theory of modulated structures

Summary The reasons of the modulated structure formation through the second-order phase transition are briefly reviewed. Particular attention is paid to the relatively new case of the modulated structure formation due to the high-order invariants, linear in the order parameter gradients. Conditions of instability of the uniform state are discussed. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

Dislocation structure and deformation hardening of bcc metals

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 23–34, March, 1991.     

Laws of modulated structure formation in isomorphous decomposing alloys

Types and parameters of the space distribution of precipitating-phase particles in isomorphous decomposing alloys having a cubic crystalline lattice are determined. For this purpose, an analytical expression for the anisotropic elastic potential is derived, and the elastic energy of the various space distributions is calculated. Results of an electron-microscopy investigation of some isomorphous decomposing alloys are also reported.     

On the nature of the dispersion hardening of Cu-Al-Co alloys

The authors describe an investigation into the mechanism of strain hardening of Cu-8 at. % Al-2 at. % Co alloy strengthened by particles of the intermetallic compound CoAl. They show that within the range 77–573°K the temperature dependence of the yield point is determined by the temperature dependence of the shear modulus. At T > 573°K the reverse processes gain in importance and cause a sharp decrease in the coefficient of strain-hardening and a loss of plasticity. The investigation of the Bauschinger effect and its reversal showed that distant stresses, generated by Orowan loops, have a considerable effect on the strain-hardening process. The reversal processes and an increase in test temperature produced no qualitative change in the dislocation pattern.     

A model of structure periodically modulated in three dimensions

A model of structure periodically modulated in three dimensions is calculated in the presented paper and applied to the alloy Cu₈₀Au₂₀. The existence and intensity of the side-bands of the Bragg lines appearing with hyperstructural lines on films of this alloy after heating to temperature on the border of the order-disorder transformation are explained by means of the given model and the value of the period of sinusoidal variation of the lattice parameter and scattering power is calculated.ikova 22, Brno, Czechoslovakia.The author thanks Mrs. V. Gregor and Mr. M. Jelínek who prepared the necessary pictures.     

Photonic crystal waveguides utilizing a modulated lattice structure

We experimentally demonstrate a new class of optical waveguide consisting of a-Si/SiO(2) autocloned photonic crystals with modulated lattice structure. The waveguide utilizes the macroscopic form birefringence of photonic crystals and confines light by the difference in the effective refractive index. A monopole modal field with spot diameters of 6.9 micromx6.5 microm was observed at a wavelength of 1.55 microm. The propagation loss of the waveguide at the wavelength was found to be ~4.2 dB/mm at most.     

Spontaneous phase transitions in magnetic films with a modulated structure

The influence of monoperiodic and biperiodic bias fields on the nucleation of domain structures in quasi-uniaxial magnetic films near the Curie point has been studied experimentally. The main types of observed nonuniform magnetic moment distributions have been established and chains of a devil’s staircase phase transitions are shown to be realized when the films are slowly cooled.     

Step-like structure and assisted tunneling in two coupled modulated waveguides

The propagation of an initially-localized optical beam along two coupled modulated waveguides is investigated. A universal step-like structure emerges in the propagation process once |d|\delta v/v₀|v_0| ~ 1 and T = 2 π/m v₀m v_0, both for the linear and nonlinear optical waveguides. The reason is that the coupling between the two waveguides can be completely suppressed at z = m T or (2 m+1)T/2. When the nonlinearity is strong, assisted tunneling can be found for the initially-localized optical beam by slightly increasing the strength of the modulation.     

On choosing the order parameter of modulated magnetic structures

Long-period modulated structures in the anisotropic Ising model with competing interactions (the ANNNI model) are studied by Monte Carlo methods. A new order parameter in the form of modulated phase amplitude is proposed for describing modulated structures. It is shown that the properties of the modulated phase-paramagnetic phase transition can be investigated by using the amplitude as the order parameter.     

Thermal expansion and elastic properties of the crystals with modulated structure

An experimental study of structure characteristics and elastic properties of the incommensurate crystals is reported.     

Polarization kinetics of a ferroelectric with complex modulated structure

Anomalous changes of the spontaneous polarization, the coercive field, and the spectrum of the distribution of polarization relaxation times in an electric field are detected in the ferroelectric TMA-ZnCl₄ at uniaxial pressures in the range where a transition arises to a nonuniform state with several coexisting waves of structural modulation. The anomalies are observed only in quasistatic and weak static fields and are due to a pressure-induced decrease of large potential barriers separating different metastable states of the structure. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 42–47 (10 July 1999)     

On the theory of magnetotransport in a periodically modulated two-dimensional electron gas

A semiclassical theory based on the Boltzmann transport equation for a two-dimensional electron gas modulated along one direction with weak electrostatic or magnetic modulations is proposed. It is shown that oscillations of the magnetoresistivity ρ_∥ corresponding to the current driven along the modulation lines observed at moderately low magnetic fields, can be explained as classical geometric resonances reflecting the commensurability of the period of spatial modulations and the cyclotron radius of electrons.     

Proposal of a new model for the modulated structure of α-uranium

The modulated structure of α-uranium is analysed in the framework of the theory of superspace groups. Arguments are given which lead to the (3 + 2)D superspace group Pmcm($\text{1}\text{2}$βγ) as the most probable one. The consequences for the structure are derived. The most important one is, that there are two independent atoms in the unit-cell, one with a displacement along b and c and the other with a displacement only along a. This model is quite different from that previously found, which has only one independent atom, and a modulation in all three directions.