Concentration dependence of the lattice constant of disordered interstitial solid solutions

The lattice constant of the A-(C) interstitial solid solutions is calculated, and its dependence on the solution composition is determined for arbitrary concentration c_C of the C atoms and their arbitrary distribution over interstices of different types. For c _c ≪1, a linear dependence of the lattice constant on c_C is established, which is also observed experimentally. The influence of temperature redistribution of interstitial atoms over interstices of different types, leading to a specific nonlinear temperature dependence of the lattice constant, is investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–5, December, 2005.     

Luminescence properties of solid solutions of borates doped with rare-earth ions

The structural and luminescence properties of Lu _x Y_{1 ? x} BO₃ solid solutions doped with Ce³⁺ or Eu⁺³ have been investigated. It has been found that the solid solutions crystallize in the vaterite phase with a lutetium concentration x < 0.5. For a higher lutetium concentration x, the solid solutions contain an additional calcite phase with a content less than 5 wt %. The luminescence spectra are characterized by intensive impurity emission under excitation with the synchrotron radiation in the X-ray and ultraviolet spectral ranges. It has been shown that, as the lutetium concentration x in the Lu _x Y_{1 ? x} BO₃: Ce³⁺ solid solutions increases, the emission intensity smoothly decreases, which is associated with a gradual shift of the Ce³⁺ 5d(1) level toward the bottom of the conduction band, as well as with a decrease in the band gap. It has been established that, in the Lu _x Y_{1 ? x} BO₃: Eu³⁺ solid solutions with intermediate concentrations x, the efficiency of energy transfer to luminescence centers increases. This effect is explained by the limited spatial separation of electrons and holes in the solid solutions. It has been demonstrated that the calcite phase adversely affects the luminescence properties of the solid solutions.     

Low-temperature resistance fluctuation in disordered conductors

At low temperatures the electron elastic mean free path in a disordered conductor can become much smaller than the inelastic mean free path (or more precisely the Thouless length) which in turn may be comparable with, or even larger than the sample size. In this quantum regime, the electrical resistance is dominated by the coherence effects that eventually lead to the now well-known weak or strong localization. Yet another remarkable manifestation of the quantum coherence is that it makes the resistance non-additive in series and, more importantly, non-self averaging, thus replacing the classical Ohm’s law with a quantum Ohm’s law describing statistical fluctuations. In this paper, we report on some of our recent work on the statistics of these “Sinai” fluctuations of residual resistance for one and higher space dimensions (d). In particular we show that the physics at the mobility edge may be dominated by these fluctuations. We also show that an external electric field tends to harness these fluctuations. Some observational consequences such as 1/f-noise at low temperatures are discussed. Our approach is based on invariant imbedding extended by us for this purpose.     

Luminescence of solid cyclic polynitramines

The solid form of the cyclic polynitramines known as RDX and HMX have a weak absorption band in the near ultraviolet which is not observed in spectra of the solvated compounds. Fluorescence measurements on solid samples of these materials show a weak emission, the excitation spectrum of which corresponds to this absorption band. Phosphorescence measurements on the solids at 77 K reveal a long-lived emission, the excitation spectrum again corresponding to the weak absorption band. The absorption and the luminescence bands are attributed to charge-transfer self-complex formation in the solid state, and estimates of the energies of the emissive singlet and triplet excited states are given.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

Current noise and long time tails in biased disordered random walks

We calculate the mean velocity and the velocity correlation function for a random walk with a uniform bias on a disordered chain. We find a new long time tail in the velocity correlation function due to the combined effects of the bias and of the disorder in the site variables. This long time tail persists to a low-frequency cutoff inversely proportional to the square of the bias. By associating the velocity correlation function with the spectrum of current fluctuations, we calculate the excess low-frequency current noise associated with this long time tail. The spectrum of current fluctuations goes as(I ²/N)f ^–1/2, whereI is the DC current,N is the number of charge carriers, andf is the frequency. The possible connection to 1/f noise is discussed. The calculation is done by a perturbation expansion in the strength of the disorder, but is shown to be exact to all orders for weak enough bias.Supported by a fellowship of the German Academic Exchange Service (DAAD).Supported by the National Science Foundation through Grant No. DMR-8108328 and through the Cornell Materials Science Center.     

Anomalous diffusion and fluctuation effects in highly disordered media

The model of impurity transport in highly disordered fractal media is generalized with account taken of the superdiffusional behavior at large distances and fluctuative behavior at small distances. It is found that the impurity source power is renormalized due to the spatial fluctuations of medium characteristics. The renormalization coefficient K decreases dramatically with changing the source dimension R for R values smaller than the correlation length in the medium. In the same domain of R values, the coefficient K, together with the effective power, undergoes increasing statistical scatter.     

Luminescence of Pr3+ ions in Y3Al5−xGaxO12 solid solutions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 5, pp. 774–778, November, 1991.     

A rigorous proof of the existence of band tails in disordered magnetic insulators

From the knowledge of the first moments of the density of states and, using a Lagrangian formalism, exact upper and lower bounds to the density of states of a simple hole in a magnetic insulator are calculated within the Hubbard model. These bounds provide a rigorous proof of the existence of band tails in the case of an antiferromagnetic spin arrangement in a simple cubic lattice. When the spin arrangement is random, the results suggest very strongly the existence of band tails.     

Simulation of two and three-dimensional disordered systems: Lifshitz tails and localization properties

Very large two and three-dimensional realizations of the Anderson model for localization are studied by solving the time-dependent Schrödinger equation. The density of states is calculated and Lifshitz tails extracted. Eigenstates at various energies are computed and analyzed. The localization length is determined as a function of the strength of the disorder and energy. For moderate disorder substantial deviations from results obtained by the strip-and-rod technique are found.     

Weak localization and fluctuation electron-electron interaction in disordered indium films

The effects of perpendicular magnetic fieldsH on the temperature dependence of the resistanceR(T) (T<20 K), the superconducting transition temperatureT _c and the fluctuation superconductivity (T«T _c ) have been investigated on high-resistance (R _>1 kOhm) indium films prepared by simultaneous condensation of the metal and hydrogen onto a substrate cooled to 5 K. AtT«T _c the resistance slightly decreased with rising temperature, in agreement with the weak localization and electron-electron interaction (EEI) theories. Processing of theR(T, H) curves in terms of the theories permitted the electron phase relaxation time (T) to be determined and the time _so of electron spin relaxation due to spin-orbital interaction (SOI) to be estimated. In the temperature rangeT–T _c /k the effect of the fluctuation EEI on conductivity was investigated. The contribution of the fluctuation EEI is shown to be given by a sum of two corrections: the Cooper and the Maki-Thompson ones. In the rangeT–T _c /k the influence of magnetic field was investigated on the transition from two-to zerodimensional fluctuations of the order parameter resulting from temperature increase in the rangeT>T _c . Increasing field was found to cause enlargement of the zero-dimensional fluctuation critical region and lowering of the fluctuation dimensionality alteration temperature, leading eventually to complete two-dimensional fluctuation suppression. The experimental dependencesT _c (H) experienced, in addition to orbital effects of the magnetic field, depairing effect of the field on electron spins. Thus the _so magnitude could also be estimated and proved roughly equal to _so determined from the analysis ofR(T, H)     

Coupling of fluctuation modes in the disordered strongly attractive Hubbard model

The coupling of two different types of soft modes related to interaction-generated superconducting and disorder-generated (pseudo)diffusive fluctuations in the large negative-U Hubbard model with random local energies is studied in the framework of a Grassmann field theoretic approach with modified semionic Matsubara frequencies. In leading loop order it is found that the sound-like order parameter phase fluctuation mode retains its massless nature with only its velocity being modified, as expected from the generalized Ward identity. The disorder-induced fluctuations which are originally completely local due to the locality of disorder correlations acquire true diffusive behaviour by interaction effects in the superconducting phase.     

Fluctuation kinetics of the hopping fluorescence quenching in disordered solid solutions: A theoretical model and experimental evidence

Fluctuation kinetics of the hopping fluorescence quenching in disordered solid solutions is investigated for the first time. Measurements were made in the chelated complexes of rare-earth ions [Y_1−xTb_x(pyca)₃(H₂O)₂]nH₂O used as chromophore. The Tb³⁺ ions and the OH^--ions of unbounded water molecules appear as fluorescent donors and randomly distributed acceptors, respectively, with the dipole-dipole interaction between them. The measured fluctuation kinetics is the kinetics of the Förster type but with larger decay amplitude. It begins almost immediately after the initial static stage of quenching, and lasts for the entire interval of measurements leaving no room at all for the well-known exponential kinetics with constant rate. Proposed theoretical explanation of the phenomenon is based on the solution of the closed many-particle integral equation for the observable kinetics of hopping fluorescence quenching. The methods for determination of the energy transfer microparameters by the measured fluorescence quenching kinetics are discussed.     

Quantum-ohmic resistance fluctuation in disordered conductors—An invariant imbedding approach

It is now well known that in the extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive thed-dimensional generalization of the above probability distribution, or rather the associated cumulant function—‘the free energy’. Ford=3, our analysis shows that the dispersion dominates the mobility edge phenomena in that (i) a one-parameterβ-function depending on the mean conductance only does not exist, (ii) one has a line of fixed-points in the space of the first two cumulants of conductance, (iii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one-dimensional system in the presence of a finite electric field. We find a cross-over from the exponential to the power-law length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a Poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.