A. S. Luk’yanenko

Energy features of an adiabatically loaded anharmonic oscillator

An excited anharmonic oscillator is considered under conditions of adiabatic (i.e., slow, as compared to the oscillation period) loading with an external force tending to a constant value at long times. The energy characteristics of the adiabatically loaded anharmonic oscillator, such as the instantaneous energy of the oscillator, the maximum kinetic (oscillation) energy, and the kinetic and potential energies averaged over the period, are analytically calculated as a function of the steady-state force. The analytical results are confirmed by the data of numerical calculations. It is established that the external force gives rise to a redistribution of the average kinetic and potential components of the initial energy of the anharmonic oscillator and that the transferred energy portions at a small external force considerably exceed the average work done by the external force.

Self-similar evolution of the surface morphology of a stressed amorphous alloy foil

A time-ordered sequence of topographic images of a stressed amorphous Fe70Cr15B15 ribbon is presented. It is shown that the surface of this material (unlike polycrystalline metal foil) has a fractal structure due to the nonequilibrium conditions of its formation. As a tensile stress of about 500 MPa is applied to the surface, the fractal dimension of the surface increases from 1.21±0.02 to 1.34±0.03, then drops to 1.12±0.03, and finally increases to 1.22±0.02. In about 1.5 hours, a complex surface morphology characterized by a roughness amplitude of several tens of nanometers evolves into a regular pattern of shear bands with amplitude of about 300 nm. Self-affine changes in surface morphology are explained by competition between several processes, including crack propagation, surface smoothing, and self-diffusion.

The effect of uniaxial tension on the relief geometry of the surface of an Fe77Ni1Si9B13 amorphous alloy

The effect of uniaxial tension in a wide range of applied stress (0–3 GPa) on the surface topography of an Fe77Ni1Si9B13 amorphous alloy was studied by scanning tunneling microscopy. It was found that the distributions of the surface defects with respect to lateral and vertical dimensions exhibit a change manifested by an increase in the proportion of large-scale defects and in the fractal dimension of the surface with increasing load. It is suggested that this surface relief is formed by a diffusion mechanism and that the observed effects are involved in the fracture focus nucleation on the sample surface.

Diffusion healing of the radiation defects during ion bombardment of a Ge(111) crystal face

The kinetics of ion-bombardment-induced damage and thermal annealing of a Ge(111) single crystal surface is studied by electron energy loss spectroscopy. The activation energy for the diffusion healing of radiation defects formed on the Ge(111) surface bombarded with 3-keV Ar+ ions is estimated at Q=0.3 eV.

Self-similar relief structures on a deformed crystal surface

The formation of self-similar roughnesses on a deformed Ge(111) single crystal surface was observed by two independent methods: scanning tunneling microscopy and low-energy electron diffraction. In the interval of loads studied, the geometric relief parameters—lateral and vertical roughness dimensions—were in a certain ratio (5: 1). It is suggested that this surface relief is formed by a diffusion mechanism.

Features of Defect Formation on a Deformed Si(111) Surface

Dynamics of the surface relief on a Si(111) single crystal face of a sample subjected to biaxial lateral extension after mechanical or chemical polishing was studied using scanning tunneling microscopy. In both cases, despite certain differences, the sample surface shows evidence of relief dynamics on a nanometer scale and exhibits a fractal character of the spatial structure formed in late stages of the process.

On the statistical distribution in a deformed solid

A modification of the Gibbs distribution in a thermally insulated mechanically deformed solid, where its linear dimensions (shape parameters) are excluded from statistical averaging and included among the macroscopic parameters of state alongside with the temperature, is proposed. Formally, this modification is reduced to corresponding additional conditions when calculating the statistical sum. The shape parameters and the temperature themselves are found from the conditions of mechanical and thermal equilibria of a body, and their change is determined using the first law of thermodynamics. Known thermodynamic phenomena are analyzed for the simple model of a solid, i.e., an ensemble of anharmonic oscillators, within the proposed formalism with an accuracy of up to the first order by the anharmonicity constant. The distribution modification is considered for the classic and quantum temperature regions apart.

Correlated transformation of the microrelief of the stressed surface of an amorphous alloy

Samples of Fe70Cr15B15 and Fe77Ni1Si9B13 amorphous alloy foils are loaded at tensile stresses of 0.2–1.2 GPa under constant strain or constant stress conditions. The submicroscopic profiles of the surface are recorded on a scanning tunneling profilometer. The “instantaneous” or extended (in time) transformation of the surface relief is statistically described by calculating the autocorrelation functions of the change in the relief height along two-dimensional scanning paths parallel to the loading axis. The autocorrelation functions thus constructed allow one to estimate the correlation radii of the surface profile, i.e., typical scales of relief components (holes, protuberances, flat regions). The performed analysis has revealed a considerable spatial correlation (∼2 × 103 nm) between the relief components in both initial (unloaded) foils. The application of the tensile load leads to an immediate increase in the roughness of the relief and a sharp decrease in the correlation radius. Subsequently, the relief does not remain stable and changes as a result of competing processes, such as microcrack growth, leveling of bends, and nucleation of kink bands. The behavior of the autocorrelation functions adequately reflects the transformation of the surface profile.

Energy criterion for relief formation on a strained surface

The strain-induced roughening revealed by scanning tunneling microscopy on the surface of elastically strained Ge(111) crystals and Fe70Cr15B15 amorphous alloy foils is discussed. It is demonstrated that the strained-induced roughening can be considered a channel for a decrease in the elastic energy of the strained surface. The diffusion mechanism of relief formation on a strained Ge(111) surface is proposed and justified.

Peculiarities of the Ge(111)-(2×8) crystal face structure studied by electron energy loss spectroscopy

The dispersion of surface plasma oscillations of a Ge(111)-(2×8) single crystal face was studied by electron energy loss spectroscopy. The experimental data are indicative of a reduced density in the surface layer, which confirms the existing adatom model of the 2×8 surface superstructure.