Simple Exponential Form Research Articles

Hole traps of metastable iron-boron pairs in silicon

Hole traps of configurationally metastable iron-boron pairs in p-type silicon are studied using deep level transient spectroscopy, thermally stimulated capacitance, and single shot techniques combined with minority-carrier injection. Two levels at EV+0.53 and 0.48 eV are observed as the metastable pairs after the injection at 150 K. The level at 0.53 eV consists of two traps vanishing with different decay rates at around 220 K, while the level at 0.48 eV annihilates with simple exponential form. The decay rate for each trap has a thermal activation energy of ∼0.7 eV and shows a single jump process of interstitial iron from one configuration to another. These new traps of iron-born pairs are discussed with the aid of configuration-coordinate description within the framework of the simple ionic model.

On rotations as special cases of unitary transformations with some applications to the theory of spin

AbstractSome problems in elementary geometry are approached from the point of view of linear algebra and generalized to the theory of linear spaces of finite or infinite dimensions having a positive definite binary product. The angle ω between two elements of the linear space is defined from the concept of length by means of the cosine‐theorem. A rotation is then defined as a special case of a unitary transformation moving all elements the same angle ω, except that under certain circumstances, some elements may stay invariant. In the former case, one speaks of a rotation around an “external axis,” and in the latter case, of a rotation around an “internal axis” defined by the invariant elements. It is shown that the finite rotations U of both types may be expressed in the simple exponential form U = exp(iωm), where the “generator” m in the former case is an operator satisfying the relation m2 = 1, and in the latter case, m3 = m. The structure of the group of finite rotations in the former case is clarified in some detail. As an illustration of the theory, some applications to the three‐ and two‐dimensional spaces as well as to the theory of spin are given. The coupling between the ordinary three‐dimensional rotations and the spinor transformations is considered in somewhat greater detail.

The Dynamic Energy Release Rate for a Steadily Propagating Mode I Crack in an Infinite, Linearly Viscoelastic Body

An analysis is presented for the dynamic, steady-state propagation of a semi-infinite, mode I crack in an infinite, linearly viscoelastic body. For mathematical convenience, the material is assumed to have a constant Poisson’s ratio, but the shear modulus is only assumed to be decreasing and convex. An expression for the Stress Intensity Factor (SIF) is derived for very general tractions on the crack faces and the Energy Release Rate (ERR) is constructed assuming that a fully developed Barenblatt type failure zone with nonsingular stresses exists at the crack tip and the loadings have a simple exponential form. For comparative purposes, expressions for the ERR are derived for the special cases of dynamic steady-state crack propagation in elastic material and quasi-static crack propagation in viscoelastic material, both with and without a failure zone. Sample calculations are included for power-law material and a standard linear solid in order to illustrate the combined influence of inertial effects, material viscoelasticity, and a failure zone upon the ERR.

Surface composition and structure changes in GaAs compounds due to low-energy Ar+ ion bombardment

We have carried out an experimental study of the surface composition and structural changes of GaAs under Ar+ ion sputtering using Auger electron spectroscopy (AES) and reflection high-energy electron diffraction (RHEED). The Auger results show that preferential sputtering of As atoms takes place in the GaAs compound and that such a composition change with depth occurs in a simple exponential form with Ga enrichment on the top surface layer. The grown surface undergoes a C(4×4) reconstruction, and after Ar+ ion sputtering this GaAs(001)–C(4×4) structure disappears resulting in an amorphous halo. But the characteristic surface which has a superlattice of (011) on GaAs (001) was found after sputtering and postannealing.

Computer simulation of exciton trapping in Cu2+-doped crystals of (CH3)4NMnCl3 and (CH3)4NMnBr3 : Significance of trap efficiency in one-dimensional systems.

Computer simulations of exciton trapping in ${\mathrm{Cu}}^{2+}$-doped crystals of the highly-one-dimensional salts, tetramethylammonium manganese chloride (TMMC) and tetramethylammonium manganese bromide (TMMB), have been performed. The model, which assumes a slow interchain (three-dimensional) hopping process in conjunction with very rapid intrachain (one-dimensional) migration, treats inefficient as well as efficient trapping. The agreement between the simulated survival probabilities and the experimental decay curves is excellent. The results indicate that at room temperature in TMMC the intrachain exciton hopping frequency is on the order of ${10}^{12}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, the interchain hopping frequency on the order of 2\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, and the absolute efficiency of the ${\mathrm{Cu}}^{2+}$ traps between ${10}^{\mathrm{\ensuremath{-}}3}$ and ${10}^{\mathrm{\ensuremath{-}}4}$. The results for TMMB are qualitatively similar, but are not as definitive. The effect of a small three-dimensional component in a fast one-dimensional hopping process has been examined in the general case. In order for a decay curve to deviate from simple exponential form, the exciton migration has to be extremely anisotropic.

NMR study of the time evolution of the fractal geometry of cement gels.

The surface-induced nuclear-magnetization-resonance relaxation recovery of exchangeable water in cement pastes changes from a simple exponential form found in the "dormant" period to a "stretched"-exponential form in later stages of the hydration process. The results reflect the time evolution of the fractal geometry of hydrating cement gels and may help in differentiating between different possible models of cement hydration.

Emission dynamics from doped crystals of (CH3)4NMnBr3(TMMB)-exciton trapping in a one-dimensional lattice

The red emission from (CH3)4NMnBr3 (TMMB) crystals is quenched by small concentrations of Cu2+. The emission decay curves from TMMB crystals doped with Cu2+ deviate dramatically from simple exponential form. Consistent with the linear chain structure of TMMB, the decay curves are accurately described by expressions derived to treat exciton trapping in a one-dimensional lattice. The analysis of the data indicate that the intrachain exciton migration is rapid, with a hopping frequency at room temperature of 1011 to 1012 s−1. The temperature dependence of the emission decay curves is consistent with an energy barrier to migration of 600 to 700 cm−1. Interchain migration apparently makes a negligible contribution to exciton trapping in TMMB with the interchain hopping frequency estimated to be less than 102 s−1. Within the limits of the experimental data, energy transport in TMMB is perfectly one-dimensional.

Matrix element and transition rate for Auger neutralization of low energy ions near metal surfaces

A model for direct Auger neutralization of low energy ions near metal surfaces is outlined, and used to calculate the dependence of the transition rates for the H(ls)-Au and H(ls)-Al interactions on ion-surface separation. A one-parameter variational atomic state wavefunction is used in the calculation of the transition amplitude. The corresponding transition rate contains significant contributions from metallic electrons with a wide range of momenta, and a major contribution from transitions in which the Auger electron does not escape from the metal. The absolute transition rate is a sensitive function of the surface electron density profile model, but can be well represented, over a wide range of ion-surface separations S, by the simple exponential form A e − aS , where A and a are constants.

Matrix element and transition rate for Auger neutralization of low energy ions near metal surfaces

Abstract A model for direct Auger neutralization of low energy ions near metal surfaces is outlined, and used to calculate the dependence of the transition rates for the H(ls)-Au and H(ls)-Al interactions on ion-surface separation. A one-parameter variational atomic state wavefunction is used in the calculation of the transition amplitude. The corresponding transition rate contains significant contributions from metallic electrons with a wide range of momenta, and a major contribution from transitions in which the Auger electron does not escape from the metal. The absolute transition rate is a sensitive function of the surface electron density profile model, but can be well represented, over a wide range of ion-surface separations S, by the simple exponential form A e−aS, where A and a are constants.

Kinetics and energetics studies at surfaces and interfaces

The diffusion coefficient on a surface and the strain at a lattice‐mismatched interface are obtained employing a molecular dynamics simulation and an atomistic energetics calculation, respectively. It is found that (i) the diffusion coefficient exhibits a nonlinear Arrhenius behavior, (ii) the coverage dependence of the diffusion coefficient is independent of temperature and can be cast into a simple exponential form, (iii) the strain developed at the interface depends on the size of adsorbate clusters, and (iv) the critical size for the onset of pseudomorphism depends linearly on the relative strength between the adsorbate–adsorbate and adsorbate–substrate interactions.

Emission dynamics from doped crystals of (CH3)4NMnCl3 (TMMC): Exciton trapping in a one-dimensional lattice.

The emission decay curves from (${\mathrm{CH}}_{3}$${)}_{4}$${\mathrm{NMnCl}}_{3}$ [tetramethylammonium manganese chloride (TMMC)] crystals doped with small amounts of ${\mathrm{Cu}}^{2+}$ deviate dramatically from simple exponential form. Consistent with the linear chain structure of TMMC, the curves are adequately described by decay expressions derived for exciton trapping in one-dimensional systems. Analysis of the data indicates that exciton migration in TMMC is nearly one-dimensional with an intrachain hopping frequency at room temperature of ${10}^{11}$ to ${10}^{12}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ and an interchain hopping frequency of only ${10}^{2}$ to ${10}^{4}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. The presence of small concentrations of ${\mathrm{Cd}}^{2+}$, a scattering impurity, greatly reduces the rate of exciton trapping. The temperature dependence of the decay curves suggests an energy barrier of 800 to 1000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for migration along the chains in TMMC.

Intramolecular vibrational energy redistribution in CHCl3: A theoretical analysis

The mechanism of intramolecular vibrational energy redistribution (IVR) in the vibrationally excited chloroform (CHCl3) has been studied theoretically. An analytic form of potential energy function was constructed with the aid of quadratic and cubic force constants calculated by ab initio MO method. Classical trajectory methods were applied to simulate the IVR process from the high CH stretch overtone states and the results were analyzed in terms of the moments of energy in each vibrational mode. The overtone absorption line shapes were also calculated. The results obtained are summarized as follows: (1) The IVR process is characterized by the two different time scales. The energy transfer from the CH stretch to the CH bend occurs rapidly, while it takes a longer time to complete the energy flow into the low frequency CCl vibrations. (2) There is a discontinuous transition of the mechanism of IVR between v=3 and 5. Above v=5, the energy in the CCl vibrations increases monotonically and the distribution in each mode can be represented by a simple exponential form, while the amount of energy transferred into the CCl modes is negligibly small for v=1–3.

An exponential alternative to the Fulton-Gouterman transformation

The Fulton-Gouterman transformation (1961) diagonalises special electron-phonon systems with respect to the electronic subsystem, but the transformation operator cannot be written in a simple exponential form. An alternative unitary transformation, displaying a simple exponential form, is presented.

Low momentum transfer elastic scattering at the CERN proton-antiproton collider

Proton-antiproton elastic scattering was measured at the CM energy √s = 546 GeV in the four-momentum transfer range 0.03<−t<0.32GeV 2 For −<0.15GeV 2 the data are well described by a simple exponential form exp( bt) with slope parameter b=15.2±0.2 GeV −2. This value is significantly larger than the one measured in the region 0.21<−t<0.50 GeV 2.

Vibrational state dependence of radiationless processes in 1B2u benzene

An extensive examination of the vibrational state dependence of fluorescence lifetimes in supersonic jet-cooled 1B2u benzene, and the inferred vibrational state dependence of the nonradiative rate constants, are reported. The qualitative features of our results agree with those obtained from previous investigations using room temperature vapor phase samples. The spectral simplification achieved in the supersonic jet expansion has, however, allowed measurement of the fluorescence lifetimes of a number of 1B2u vibrational levels not previously studied. These data indicate that excitation of ν4, ν5, ν8, and ν10 result in enhanced nonradiative decay, which suggests that these vibrations are promoting modes. A previously unobserved sensitivity of the nonradiative rate constant to the vibrational angular momentum of the initially excited level has been demonstrated. Finally, fluorescence decays which do not have simple exponential form have been observed from vibrational levels in the vicinity of the ‘‘channel three’’ region. We discuss the significance of all of these observations in terms of the existing theory of radiationless processes and with respect to other recent experimental investigations.

Drop Velocity from an Ink-Jet Nozzle

An empirical equation is presented which predicts the velocity produced by a pressurized ink-jet nozzle. This equation, which has a simple exponential form, expresses the velocity in terms of two empirical constants; the fluid parameters of pressure, viscosity, and density; and the nozzle parameters of length and diameter. Velocities calculated with this equation are compared graphically to several sets of experimental data.

A study of QCD scaling violations by direct resolution of Altarelli-Parisi type equations

We present a detailed study of scaling violations for non-singlet, singlet and glue distribution functions in the framework of several approximation schemes of QCD. Our formalism consists of direct resolution of the Altarelli-Parisi type equations and leads to a simple exponential form for the function q( x, Q 2). This form is very suitable for the analysis of experimental data and for the exploration of different evolution schemes. In particular, we examine the implications on the QCD scaling parameter Λ and the gluon parameter n G.

Fast neutron transport in selected materials relevant to large volume minerals analysis

The behaviour of the fast neutron flux in a number of materials has been studied for a point source and it has been shown that fluxes computed by using a discrete ordinates code (ANISN) fit a simple exponential form reasonably well. When allowance is made for the collided component in the flux by artificially adjusting the source intensity and energy spectrum it is found that the exponential attenuation form provides an accurate description of the total flux for most materials. Sensitivity factors have been derived which enable elemental concentrations to be obtained when applied to fast neutron induced γ-ray spectra.

Potential Flow over Weirs of Moderate Curvature

A review is given of some salient studies of critical flow over round-crested weirs, in particular Lenau's extension of Matthew's results. The basic equations of two-dimensional, incompressible, potential flow are recapitulated and applied to general free-surface, gravity flows. Approximate solutions in the form of series expansions about the free surface for ψ, l n v, and Θ in terms of x and y are derived. An assumed free surface profile of simple exponential form is investigated and is shown to represent a weir type of flow provided certain relationships exist between the free surface equation parameters. These are related to the ratio of total head above crest to radius of curvature of that crest (H/R) and the coefficient of discharge and the weir surface profile are deduced as series functions of that ratio. Compatibility with the Lenau theory is shown. This method brings out both the attractions and difficulties inherent in an inverse method remaining within a cartesian framework.

An approximate method for estimating multiquantum transition probabilities in molecular collisions

A simple algebraic formula is given to allow an estimation of multiquantum transition probabilities in molecular collisions from a knowledge of the one- and two-quantum probabilities. The result is based on a simple exponential form for the probabilities often used in the moment method of analysis. Reasonably accurate vibrational energy transition probabilities are obtained for collinear atom-diatom collisions.