Diffusion in Solids

In this work the Si self-interstitial-carbon interaction has been experimentally investigated and modeled. The interactions between self-interstitials, produced by 20-keV silicon implantation, and substitutional carbon in silicon have been studied using a Si 1Ϫy C y layer grown by molecular beam epitaxy ͑MBE͒ and interposed between the near-surface self-interstitial source and a deeper B spike used as a marker for the Si-interstitial concentration. The C atoms, all incorporated in substitutional sites and with a C-dose range of 7ϫ10 12 -4 ϫ10 14 atoms/cm 2 , trap the self-interstitials in such a manner that the Si 1Ϫy C y layer behaves as a filtering membrane for the interstitials flowing towards the bulk and, consequently, strongly reduces the boron-enhanced diffusion. This trapping ability is related to the total C dose in the Si 1Ϫy C y membrane. Substitutional carbon atoms interacting with self-interstitials are shown to trap Si interstitials, to be removed from their substitutional sites, and to precipitate into the C-rich region. After precipitation, C atoms are not able to further trap injected self-interstitials, and the interstitials generated in the surface region can freely pass through the C-rich region and produce B-enhanced diffusion. The atomistic mechanism leading to Si-interstitial trapping has been investigated by developing a simulation code describing the migration of injected interstitials. The simulation takes into account the surface recombination, the interstitial diffusion in our MBE-grown material, and C traps. Since the model calculates the amount of interstitials that actually react with C atoms, by a comparison with the experimental data it is possible to derive quantitative indications of the trapping mechanism. It is shown that one Si interstitial is able to deactivate about two C traps by means of interstitial trapping and C clustering reactions. The reaction causing trapping and deactivation is tentatively described.

The diffusion of ion beam injected self-interstitials (I) and their interaction with impurities in crystalline Si has been investigated and modeled. In particular, the I-substitutional carbon (C) interactions have been studied, using a molecular-beam-epitaxy grown Si 1Ày C y layer interposed between the shallow I-source and a deeper B-spike (marker for Iconcentration). Substitutional C atoms are shown to trap IÕs, to be removed from their substitutional sites, and to form stable precipitates into the C-rich region. The I-trapping mechanism was quantitatively studied by a simulation code. The reactions causing trapping and deactivation are described. In addition, the boron markers approach was extended to the two dimensional (2D) diffusion. High resolution scanning capacitance microscopy was used for quantitative measurements of the 2D boron transient enhanced diffusion induced on a boron delta array by the IÕs ion beam injected through a sub-micron dimension oxide mask. A simulation code was developed to describe the 2D I-diffusion and a quantitative description of the 2D I-evolution has been obtained. Source size effects have been found and modeled.

Scanning capacitance microscopy (SCM) has been applied to monitor the two-dimensional (2D) diffusion of Si self-interstitials (I ). A sub-micron laterally confined source has been generated by Si self-implantation through a sub-micron oxide mask. The structure was grown by molecular beam epitaxy on (0 0 1) Si, with three spikes of B at different depths used as markers for the interstitial concentration. The measured 2D SCM maps have been accurately quantified to 2D carrier concentration profiles, yielding quantitative information on the B diffusion induced by the I flux. The I supersaturation inside the wafer was monitored by the broadening and the consequent peak concentration lowering of the boron spikes. We show that the I depth-penetration strongly depends on the original source lateral size. Moreover, lateral diffusion of I has been observed, being independent of the source size.

We present a closed form for the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental ͑de͒mixing. To this end, we show that when chemistry is fast, the diffusion fluxes of elements and species enthalpies can be expressed as explicit linear functions of gradients of elemental mass fractions and temperature. Our formulation is a natural extension of classical work on local equilibrium flows by other authors and yields results equivalent with a recent fully rigorous mathematical theory in a straightforward and physically appealing manner. The obtained set of equations is well-suited for numerical implementations and does not require the computationally expensive evaluation of thermodynamic derivatives using finite differences. The new transport coefficients that appear in the equations allow quantitative predictions and help to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium.

We present a closed form for the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental ͑de͒mixing. To this end, we show that when chemistry is fast, the diffusion fluxes of elements and species enthalpies can be expressed as explicit linear functions of gradients of elemental mass fractions and temperature. Our formulation is a natural extension of classical work on local equilibrium flows by other authors and yields results equivalent with a recent fully rigorous mathematical theory in a straightforward and physically appealing manner. The obtained set of equations is well-suited for numerical implementations and does not require the computationally expensive evaluation of thermodynamic derivatives using finite differences. The new transport coefficients that appear in the equations allow quantitative predictions and help to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium.

Solid triblock copolymers can serve as the basis for membranes in such applications as separations and fuel cells. Diffusion of a low molecular weight penetrant in such a membrane is strongly affected by the morphology. The effect of the morphology on the translational motion of the penetrant can be directly assessed by pulse field gradient NMR measurements. The rotational and translational motion of 2,2,4-trimethylpentane (TMP) in a SEBS triblock will be characterized by NMR. TMP is primarily soluble in the rubbery EB phase of the SEBS triblock so that this phase then acts as the conductive component of the membrane.

Proton and sodium-23 spectra are reported on acid and sodium neutralized forms of the perfluorosulfonate ionomer (Nafion), respectively. This local structural view is compared with pulse field gradient diffusion measurements of water, methanol and dimethyl methylphosphonate (DMMP) in several Nafion films. Both the proton and sodium-23 spectra indicate that the counter ions are primarily in clusters or aggregates with no evidence for isolated ions. The proton resonance from the sulfonic acid group reflects hydrogen bonding but these protons rapidly exchange with sorbed water. There is also evidence for small amounts of water not in contact with the ionic clusters. Pulse field gradient diffusion measurements of water show little evidence of tortuous diffusion though a tortuous pathway might be expected for diffusion through domains of ionic clusters. A cast film shows greater evidence of a tortuous pathway than commercially prepared Nafion sheets though the level of tortuosity is still low. Methanol diffusion shows more tortuosity in both commercial films and cast films with the most tortuosity in a cast film containing fumed silica nanoparticles. Even greater tortuosity is observed for DMMP. The greatest tortuoisty is observed for DMMP in cast films with nanoparticles and this is an improvement in terms of potential applications of Nafion in chemical protection. Though the high-resolution proton spectra show only modest differences between commercial film, cast film and nanocomposite film, more significant structural changes on a larger length scale are detected in the pulse field gradient NMR experiments. Cast films may display more tortuous diffusion because of better-organized domains of ionic groups, backbone units and side chains even though this is not clearly indicated by focusing on the structure of the ionic cluster itself.

The Schottky defect formation process in MgO, CaO, SrO, and BaO i~ investigated using our recently introduced EPPI modeL3 We find that inclusion of quadrupolar interactions makes a substantial contribution to the formation energy by values ranging from 1.2 eV to 2.9 eV. The EPPI values of the enthalpies (hI) are 5.9 ,5.8 ,4.7 and 1.4 eV respectively for MgO, CaO, SrO, and BaO.The results of cation self diffusion experiments in MgO are reanalyzed to include the effects of impurity-vacancy association reaction. The analysis suggests the previous interpretation of the experimental data to be an oversimplification. Since the binding energy of an impurity-defect complex in MgO could be quite large, the effects of the association reaction on the defect densities are appreciable. On the basis of near complete association of the dominant tetravalent cation impurity , hI in MgO is found to be 5.8 eV which is in .good agreement with the theoretical value of the present work.

We investigate quantum transport characteristics of a ladder model, which effectively mimics the topology of a double-stranded DNA molecule. We consider the interaction of tunneling charges with a selected internal vibrational degree of freedom and discuss its influence on the structure of the current-voltage characteristics. Further, molecule-electrode contact effects are shown to dramatically affect the orders of magnitude of the current. Recent electrical transport measurements on suspended DNA oligomers with a complex base-pair sequence, revealing strikingly high currents, are also presented and used as a reference point for the theoretical modeling. A semiquantitative description of the measured I − V curves is achieved, suggesting that the coupling to vibrational excitations plays an important role in DNA conduction.

We provide experimental evidence of the distortion of a F profile by the presence of a CVD grown B box. After annealing, a depletion in the F profile is observed fitting the position of the immobile part of B profile. To study this phenomenon further experiments were designed and atomistic simulations were done using a recently developed F model. In this model F complexes with both Si interstitials (F-I) and vacancies (F-V) are included. The formation of Boron-Interstitial Clusters is found to reduce the local Si interstitials defect concentration. This feature may be responsible for the reported F distortion by the presence of a B box.

Transient enhanced diffusion of B in silicon is modelled at temperatures down to 500°C, using a simplified model of self-interstitial clusters to describe the time evolution of the self-interstitial supersaturation, S. The model is highly predictive, providing an accurate description of diffusion both in the peak and tail regions of B marker layers, over a wide range of annealing conditions. The model is well adapted for implementation into existing 2D commercial simulation tools. Fundamental parameters of atomic-scale B diffusion were extracted for the first time at T = 500°C, under both intrinsic and extrinsic conditions.

In this paper, we report a lattice-free kinetic Monte Carlo (KMC) result of boron diffusion at low temperatures 450 and 550 with vacancy + interstitialcy mechanism or vacancy + kick-out one with dilute self-interstitials (I) and vacancies (V) created in a B-doped marker layer (4×10 11 B/cm 2 per marker) by Si implantation (50keV, 10 11 /cm 2). In this type of KMC model, point defects and dopants are treated at an atomic scale while they are considered to diffuse in accordance with their event rates, which are given as input parameters from ab initio calculations or experimental data. Especially, the formation of clusters and extended defects, which usually control the annealing kinetics after ion implantation, is to be minimized in the range of low doses in an effort to create dilute concentrations of I and V. Therefore, simple vacancy and kick-out or interstitialcy mechanisms without interstitial clusters or extended defects are tested in these conditions and both are in a good agreement with the SIMS data. However, in these dilute concentrations vacancy mechanism plays a dominant role in B diffusion in place of the usual kick-out or interstitialcy mechanism in boron enhanced diffusion.

In this paper, since boron atoms tend to diffuse in the silicon crystal with complex cluster structures, KMC calculation requires an excessive CUP time during the transient stages. In this paper, we present a simplified atomistic model which includes the dominant B m I n clusters for fast Kinetic Monte Carlo (KMC) calculation. In this work, we propose two types of simplified atomistic models for B m I n clusters, which comprise a simple atomistic model (SAM) and minimized atomistic model (MAM). The proposed simplified atomistic cluster model reduces the computational burden by more than a factor of 10 even with keeping the accuracy of the full cluster model. From the investigation on the dominant B m I n clusters during annealing process, we could decipher the most probable process route for the evolution of clusters. Our KMC simulation revealed that B1 2 seems to act a dominant role at the beginning stage of annealing process while B 3 I becomes more dominant near the end. After the proposed models were verified with experimental SIMS data, we implemented boron diffusion using MAM in wafer considering the Ge-PAI. The results of our simulation agreed with SIMS data.

Albite flames result from the replacement of K-feldspar by albite through alkali exchange. In flame perthites from deformed granites within the Grenville Front Tectonic Zone, replacement is driven by retrograde breakdown of plagioclase and hydration of K-feldspar. Within the strain fabric of the host rock, albite flames preferentially form subparallel to the inferred maximum compression direction and also develop at high-stress points such as grain-to-grain contacts. Flame tips are generally parallel to the 'normal' perthite crystallographic direction, i.e. the Murchison plane, which is the orientation of the plane of minimum crystallographic lattice misfit between the albite and K-feldspar. We propose that the morphology of an albite flame is controlled by the coherent propagation of its tip into the Kfeldspar crystal lattice, and that the orientation of the flames with respect to the rock fabric is controlled by the differential stress imposed during metamorphism. This type. of replacement requires dry conditions in which there would be inefficient dissolution-reprecipitation along completely incoherent interfaces (normal replacement), and increased strength of feldspar. Under these conditions coherency is maintained to avoid a very large kinetic barrier. The differences in lattice misfit along the Murchison plane between K-feldspar and albite requires either high elastic strain energy (ifthe fit is coherent), or lattice dislocation energy (if the fit is semi-coherent). Such energy might be expected to inhibit the replacement growth of albite lamellae in a host feldspar. However, compression parallel to the Murchison plane reduces the lattice misfit along the compression direction. This results (1) in an increase in the Helmholtz free energy of the K-feldspar, and (2) in a reduction in the Helmholtz energy of the albite lamellae or of the semi-coherent interface. Thus, albite replacement allows a decrease in net free energy without the destruction of the alumino-silicate framework and is therefore favoured under conditions of high differential stress. Since flame growth is controlled by the imposed differential stress and not by strain in the host rock, flame perthite has potential as a palaeostress-direction indicator.

An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.

We show that the solid-phase epitaxial regrowth of amorphous layers created by ion implantation in Ge results in the formation of extended defects of interstitial-type. During annealing, these defects evolve in size and density following, as in Si, an Ostwald ripening mechanism. However, this process becomes nonconservative as the annealing temperature increases to 600 °C. This suggests that the recombination/annihilation of Ge interstitial atoms becomes important at these temperatures. These results have important implications for the modeling of diffusion of implanted dopants in Ge.

In this paper, we showed that the maximum active P concentration of approximately 2 × 10 20 cm −3 exists during solid-phase epitaxial recrystallization (SPER). This maximum active concentration is close to the reported values for other active impurity concentrations during SPER. We introduced the concept of an isolated impurity that has no neighbor impurities with a certain lattice range. Assuming that impurities interact with three or four neighbor impurities, we can explain the activation phenomenon during SPER. According to our model, the isolated P concentration N iso has a maximum value of approximately 2 × 10 20 cm −3 at a total impurity concentration of approximately 10 21 cm −3 , and it decreases with a further increase in total impurity concentration. Deactivation occurs after the completion of SPER with increasing annealing time, and the active impurity concentration decreases with time but is always higher than the maximum diffusion concentration N Diff max. We also observed that N Diff max is independent of the annealing time despite nonthermal activation in the high-concentration region. We evaluated the dependence of N Diff max on annealing temperatures. We think that this N Diff max can be regarded as the electrical solid solubility N Esol that the active impurity concentration reaches in thermal equilibrium. We observed the transient enhanced diffusion (TED) after the completion of SPER, and that, the deactivation process continues during and after TED, and the corresponding diffusion coefficient is still much higher than that in thermal equilibrium even after TED has finished, which suggests that the deactivation process releases point defects.

We investigate quantum transport characteristics of a ladder model, which effectively mimics the topology of a double-stranded DNA molecule. We consider the interaction of tunneling charges with a selected internal vibrational degree of freedom and discuss its influence on the structure of the current-voltage characteristics. Further, molecule-electrode contact effects are shown to dramatically affect the orders of magnitude of the current. Recent electrical transport measurements on suspended DNA oligomers with a complex base-pair sequence, revealing strikingly high currents, are also presented and used as a reference point for the theoretical modeling. A semiquantitative description of the measured I − V curves is achieved, suggesting that the coupling to vibrational excitations plays an important role in DNA conduction.

In this study, deuteric coarsening of a lamellar cryptoperthite to a patch perthite has been experimentally induced for the first time. An homogeneous alkali feldspar, bulk composition Ab60Or40, was produced by molten salt ion-exchange with a gem quality orthoclase from Madagascar. This was then annealed isothermally for 32 days at 550 °C. This resulted in a coherent lamellar cryptoperthite (periodicity 28 nm) probably by spinodal decomposition and subsequent coarsening. The cryptoperthite was then reacted with 20 wt% H 2 O or 0.1 M HCl at 400 and 500 °C at 200, 400, and 1000 MPa for 96 h and for 192 h at 1500 MPa. At 1000 and 1500 MPa and 500 °C, the cryptoperthitic crystal fragments were partially replaced by a mosaic of albite and sanidine subgrains in the form of a patch perthite. Other than the Gibb's free energy of reaction as derived from the chemical potentials of the reactant and product phases, the second principle mechanism responsible for driving this reaction is interface-coupled dissolution-reprecipitation driven by a reduction in the coherency strain energy stored within the initial cryptoperthite. The main indicator of this is a change in the microtexture due to the destruction of the coherent lamellar cryptoperthite and its replacement by an assemblage of incoherent subgrains. Detailed mass balancing, based on XRD and EPMA data, indicate that conversion of cryptoperthite to patch perthite is not isochemical. Experimental formation of patch perthite appears to take place in two steps. Between the original cryptoperthite and the patch perthite, TEM investigation identified a "transition zone," characterized by a significant coarsening of the preexisting lamellar microstructure, without any sign of a loss in lattice coherency. This zone is probably the result of hydrous species diffusing into the cryptoperthite causing the H 2 O-enhanced diffusion of Na and K and hence lamellar coarsening. In the second step, this coarsened microstructure is replaced by the patch perthite. The polycrystalline patch perthite is characterized by a very complex distribution of albite and sanidine sub-grains. Even the larger albite or sanidine patches are polycrystalline. This inevitably results in a three-dimensional network of grain boundaries characterized by high defect densities resulting from the structural misfit between the albite and sanidine sub-grains. An increase in average grain size with distance from the interface indicates that secondary coarsening of the initially, very fine-grained intergrowth occurred. This was driven by the reduction of interface and surface energy similar to the coarsening observed in multiphase ceramics. In addition, the newly formed patch perthite is highly porous despite the fact that the results obtained in this study show that the replacement of cryptoperthite by patch perthite is nearly isovolumetric (∆V ∼-0.6%). The observed reaction-induced porosity results from differences in relative solubilities between the cryptoperthite and the patch perthite. Porosity abundance has been estimated at approximately 10 to 11 vol% based on the amount of quartz formed during the experiments. Three-dimensional investigations via FIB serial sectioning indicate almost no interconnectivity between pores. A consequence of albite and sanidine sub-grain coarsening is the constant redistribution of the porosity and the sub-grain boundaries within the patch perthite mosaic over time. This suggests that a dynamically evolving porosity could provide an important transport mechanism for fluid transport through rocks even when the abundance and interconnectivity of the reaction-induced porosity is low.

This paper discusses the effect of porosity and hydrostatic pressure on diffusion kinetics and equilibrium water uptake in a semicrystalline fluoropolymer. Water sorption experiments at atmospheric pressure and under water pressures up to 250 MPa were carried out during 18 months at 40°C on reference and porous samples. Porosity of samples was induced due to a cavitation process occurring at the highest triaxiality area of waisted and notched specimens during tensile tests. Water uptake was found to be very sensitive to porosity, showing an increase in samples with a high void fraction. On the other hand, water content decreased with increasing pressure suggesting a compaction of the porous space in which water can be stored. Two models describing this water uptake behaviour were considered. The first is a classical model which assumes that sorption occurs only by diffusion following Fick's law. Fick's model was found to be in agreement with the experimental results. A ''Langmuir-type'' sorption model was also proposed to describe water uptake in porous samples, considering a two-phase water transport mechanism: one portion of the absorbed water diffuses through the polymer matrix and the other portion is stored in voids. This model was implemented in a user subroutine using ABAQUS TM software and simulations were confronted to experimental sorption curves showing satisfactory agreements. The potential of the Langmuir-type sorption model resides on its availability to be coupled to a poro-mechanical model, in order to improve the understanding of coupling between the mechanical behaviour and water sorption mechanism in a porous polymer.

2014 Grâce à des mesures de fluage, nous effectuons le choix du coefficient de diffusion qui régit le comportement viscoplastique de CuAl (03B2). Les coefficients d'interdiffusion mesurés par Romig et Pimenov qui conduisent à des résultats significativement différents, sont pris en compte. L'analyse d'Ashby de l'équation de Dorn permet de choisir le coefficient de Pimenov et de relier le comportement en fluage haute température du CuAl (03B2) à des mécanismes de courts-circuits de diffusion. Notre travail montre que le facteur thermodynamique doit être intégré dans la corrélation fluage-diffusion. Abstract. 2014 With creep's measures, we choose the diffusion coefficient which governs the viscoplastic behaviour of CuAl (03B2). The interdiffusion coefficients of Romig and Pimenov which give significantly different results, are compared. The Dorn's equation analysis of Ashby allows to choose the Pimenov's coefficient and to rely the high temperature creep behaviour of CuAl (03B2) with mechanisms of short circuits of diffusion. Our work shows that the thermodynamic factor must be integrated in the correlation creep diffusion.

An exhaustive first-principles study of the energetics of B-Si interstitial complexes of various configurations and charge states is used to elucidate the diffusion mechanism of B in Si. Total energy calculations and molecular dynamics simulations show that B diffuses by an interstitialcy mechanism. Substitutional B captures a Si interstitial with a binding energy of 0.90 eV. This complex is itself a fast diffuser, with no need to first "kick out" the B into an interstitial channel. The migration barrier is about 0.68 eV. Kinetic Monte Carlo simulations confirm that this mechanism leads to a decrease in the diffusion length with increasing temperature, as observed experimentally.

In this work, we investigate the interstitial injection into the silicon lattice due to high-dose, low energy arsenic implantation. The diffusion of the implanted arsenic as well as of boron, existing in buried ␦-layers below the silicon surface, is monitored while successive amounts of the arsenic profile are removed by low temperature wet silicon etching. From the analysis of the diffusion profiles of both dopants, consistent values for the interstitial supersaturation ratio can be obtained. Moreover, the experimental results indicate that the contribution of the implantation damage to the TED of boron, and thus the interstitial injection, is not the main one. On the contrary, interstitial generation due to arsenic clustering seems to be more important for the present conditions.

In this work, we investigate the interstitial injection into the silicon lattice due to high-dose, low-energy arsenic implantation. The approach consists in monitoring the diffusion of the arsenic profile as well as of the boron profile in buried δ-doped layers, when amounts of the as-implanted arsenic profile are removed by low-temperature wet silicon etching. The experimental results indicate that the contribution of the implantation damage to the transient enhanced diffusion of boron, and thus the interstitial injection, is not the main one. On the contrary, interstitial generation due to arsenic clustering seems to be more important for the present conditions.

We show that the solid-phase epitaxial regrowth of amorphous layers created by ion implantation in Ge results in the formation of extended defects of interstitial-type. During annealing, these defects evolve in size and density following, as in Si, an Ostwald ripening mechanism. However, this process becomes nonconservative as the annealing temperature increases to 600 °C. This suggests that the recombination/annihilation of Ge interstitial atoms becomes important at these temperatures. These results have important implications for the modeling of diffusion of implanted dopants in Ge.

By comparing diffusion coefficients D of bivalent cations Ba 2 +, Ca 2 +, Sr 2 + in NaCI crystals it was shown that in the temperature range above 550 ~ D (Ba z+) > D (Sr 2+) > D (Ca 2+) is valid. Temperature dependences of jump frequencies w 2 of these cations are described by w 2 (Ba 2+) = (2.

In this paper we discuss methods to obtain high dopant concentrations during processing of Si devices. The possibility of increasing the solubility of B in Si by misfit stress is investigated. The enthalpy of B atoms is calculated, with and without stess, using density functional theory. A second approach, the trapping of excess dopant atoms during deposition of Si, is also considered. For this purpose, the enthalpies of several dopant species in sites near the surface are calculated.

In this paper we discuss methods to obtain high dopant concentrations during processing of Si devices. The possibility of increasing the solubility of B in Si by misfit stress is investigated. The enthalpy of B atoms is calculated, with and without stress, using density functional theory. A second approach, the trapping of excess dopant atoms during deposition of Si, is also considered. For this purpose, the enthalpies of several dopant species in sites near the surface are calculated.

The evaluation of the energy of formation of point defects in silicates is developed using solid-state theory. The calculations require a proper treatment of the polarization effects in the crystal as well as the usual Coulomb and repulsion energy terms. The theory is applied to the calculation of point defects in forsterite. The Mg-O and O-O repulsion potential calculation uses the recent electron gas th€ory of Gordon and Kim (1972). The partly covalent Si-O bond is treated semi-enpirically. The relative importance of the various energy terms in the overall energy of formation is evaluated. The results show a marked di.fference between defects on the Ml and M2 octahedral sites, and among the three di.fferent oxygen sites of olivine. The energy differences are on the order of several electron volts. The implication of the results on the nature of defects and on the diflusion mechanism in olivines is then treated.

The chemically driven propagation of interacting parallel cracks in monoclinic alkali feldspar was studied experimentally. Single crystals of potassium-rich gem-quality sanidine were shifted towards more sodium-rich compositions by cation exchange with a NaCl-KCl salt melt at a temperature of 850 • C and close to ambient pressure. Initially, a zone with elevated sodium content formed at the crystal surfaces due to the simultaneous in-diffusion of sodium and out-diffusion of potassium, where the rate of cation exchange was controlled by sodium-potassium interdiffusion within the feldspar. A chemical shift of potassium-rich alkali feldspar towards more sodium-rich compositions produces highly anisotropic contraction of the crystal lattice. This induced a tensile stress state in the sodium-rich surface layer of the crystals, which triggered the formation of a system of nearly equi-spaced parallel cracks oriented approximately perpendicular to the direction of maximum shortening. Crack propagation following their nucleation was driven by cation exchange occurring along the crack flanks and was controlled by the intimate coupling of the diffusion-mediated build-up of a tensile stress state around the crack tips and stress release by successive crack propagation. The critical energy release rate of fracturing was determined as 1.8-2.2 J m −2 from evaluation of the near-tip J-integral. The mechanism of diffusion-controlled crack propagation is discussed in the context of high-temperature feldspar alteration.

Laboratory studies reveal the sensitivity of measured geophysical properties to solid-fluid, fluid-fluid, and solid-solid interfaces in granular and fractured materials. In granular materials, electrical properties and nuclear magnetic resonance relaxation times exhibit a strong dependence on the size and properties of the solid-fluid interface. The electrical and seismic properties of granular materials and the seismic properties of fractured materials reveal a dependence on the size or geometry of fluid-fluid interfaces. Seismic properties of granular and fractured materials are affected by the effective stress and cementing material at solid-solid interfaces. There have been some recent studies demonstrating the use of field-scale measurements to obtain information about pore-scale interfaces. In addition, a new approach to geophysical field measurements focuses on the geophysical response of the field-scale interface itself, with successful applications in imaging the water table and a redox front. The observed sensitivity of geophysical data to interfaces highlights new ways in which geophysical measurements could be used to obtain information about subsurface properties and processes.

We explore stochastic models for the study of ion transport in biological cells. Analysis of these models explains and explores an interesting feature of ion transport observed by biophysicists. Namely, the average time it takes ions to cross certain ion channels is the same in either direction, even if there is an electric potential difference across the channels. It is shown for simple single ion models that the distribution of a path ͑i.e., the history of location versus time͒ of an ion crossing the channel in one direction has the same distribution as the time-reversed path of an ion crossing the channel in the reverse direction. Therefore, not only is the mean duration of these paths equal, but other measures, such as the variance of passage time or the mean time a path spends within a specified section of the channel, are also the same for both directions of traversal. The feature is also explored for channels with interacting ions. If a system of interacting ions is in reversible equilibrium ͑net flux is zero͒, then the equivalence of the left-to-right trans paths with the time-reversed right-to-left trans paths still holds. However, if the system is in equilibrium, but not reversible equilibrium, then such equivalence need not hold.

Plane-wave reflection from a rough surface overlying a fluid half-space, with a sound speed distribution subject to a small and random perturbation, is considered. A theory based upon a boundary perturbation method in conjunction with a formulation derived from Green's function for the coherent field in the random medium have been applied to a typical oceanic environment to study their effects on the plane-wave reflection. By considering the coherent field itself, the plane-wave reflection may be obtained straightforwardly through a procedure consistent with the formalisms currently employed in rough surface scattering. The results show that both the rough surface and medium inhomogenieties may reduce the plane-wave reflection, however, the characteristics of the curves representing their effects are different, enabling us to identify the dominant scattering mechanism. The results for the coherent reflection due to the individual scattering mechanism are compatible with those found in the existing literature.

The authors study solute transport in periodic networks of channels. They identify the parameter regime where a local physical mechanism that occurs at the intersections of channels is the dominant cause of dispersion and obtain the macroscopic transport equation that the concentration of solute satisfies.

Thermal conductivity of mantle materials controlling the heat balance and thermal evolution of the Earth remains poorly constrained as the available experimental and theoretical techniques are limited in probing minerals under the relevant conditions. We report measurements of thermal conductivity of MgO at high pressure up to 60 GPa and 300 K via diamond anvil cells using the time-domain thermoreflectance technique. These measurements are complemented by model calculations which take into account the effect of temperature and mass disorder of materials within the Earth. Our model calculations agree with the experimental pressure dependencies at 300 and 2000 K for MgO. Furthermore, they predict substantially smaller pressure dependence for mass disordered materials as the mechanism of scattering changes. The calculated thermal conductivity at the core-mantle boundary is smaller than the majority of previous predictions resulting in an estimated total heat flux of 10.4 TW, which is c...

We study energy localization in a finite one-dimensional ⌽ 4 oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. On the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrödinger equation approximating the dynamics, to support and explain the numerical results.

We study the phase space region of two-and three-dimensional lattices where a transition from chaotic to ordered dynamics takes place when the energy is lowered. In this region we find coexistence of degrees of freedom ͑DOF's͒, endowed with different levels of chaos. The analysis of this complex dynamical pattern requires the introduction of diagnostic tools suitable for a characterization of single DOF's: coherence angles and coherence times. We find that the coherence times-which give a measure of the time each DOF needs to relax to equilibrium-are roughly proportional to the inverse of the specific energy. This may be useful to evaluate the reliability of statistical results obtained in computer experiments performed on condensed matter systems at low energy.

The dynamics of an isolated polymer chain has irreversible aspects that lead to the decorrelation of configurational properties over time. For simple mechanical models with time reversible equations of motion, the irreversibility is a consequence of the chaotic nature of the dynamics which, for a many body system, is expected to result in ergodic mixing. Here we study a fixed bond length N-mer interaction-site chain with fixed total energy and angular momentum. For N ജ 4 the equations of motion for such a chain are nonintegrable and chaotic dynamics is expected. We directly assess the ergodicity of short repulsive Lennard-Jones chains by comparing phase space and time averages for structural and energetic properties. The phase space averages are determined from the exact microcanonical partition function while the time averages are obtained from molecular dynamics ͑MD͒ simulations. For N = 4 and 5 we find that our exact phase space averages agree with the MD time averages, as expected for an ergodic system. The N = 3 system is integrable and thus displays regular dynamics for which time averages are found to depend on initial conditions. In all cases, the total angular momentum is found to have a large effect on both the average chain conformation and the partitioning of the total energy between potential, vibrational, and rotational contributions. Compared to a nonrotating chain, a small to moderate angular momentum slightly speeds up the internal chain dynamics, while a large angular momentum dramatically slows the internal dynamics.

The dynamics of an isolated polymer chain has irreversible aspects that lead to the decorrelation of configurational properties over time. For simple mechanical models with time reversible equations of motion, the irreversibility is a consequence of the chaotic nature of the dynamics which, for a many body system, is expected to result in ergodic mixing. Here we study a fixed bond length N-mer interaction-site chain with fixed total energy and angular momentum. For N ജ 4 the equations of motion for such a chain are nonintegrable and chaotic dynamics is expected. We directly assess the ergodicity of short repulsive Lennard-Jones chains by comparing phase space and time averages for structural and energetic properties. The phase space averages are determined from the exact microcanonical partition function while the time averages are obtained from molecular dynamics ͑MD͒ simulations. For N = 4 and 5 we find that our exact phase space averages agree with the MD time averages, as expected for an ergodic system. The N = 3 system is integrable and thus displays regular dynamics for which time averages are found to depend on initial conditions. In all cases, the total angular momentum is found to have a large effect on both the average chain conformation and the partitioning of the total energy between potential, vibrational, and rotational contributions. Compared to a nonrotating chain, a small to moderate angular momentum slightly speeds up the internal chain dynamics, while a large angular momentum dramatically slows the internal dynamics.

It is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the number of particles N as well as with the energy. Our results are conclusive. For N ജ 2 the spectra of these systems exhibit Poisson fluctuations provided that we consider sufficiently high excitation energies. Nevertheless, when the mean field is chaotic there exists a critical energy scale L c ; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.

We investigate quantum transport characteristics of a ladder model, which effectively mimics the topology of a double-stranded DNA molecule. We consider the interaction of tunneling charges with a selected internal vibrational degree of freedom and discuss its influence on the structure of the current-voltage characteristics. Further, molecule-electrode contact effects are shown to dramatically affect the orders of magnitude of the current. Recent electrical transport measurements on suspended DNA oligomers with a complex base-pair sequence, revealing strikingly high currents, are also presented and used as a reference point for the theoretical modeling. A semiquantitative description of the measured I − V curves is achieved, suggesting that the coupling to vibrational excitations plays an important role in DNA conduction.

An exhaustive first-principles study of the energetics of B-Si interstitial complexes of various configurations and charge states is used to elucidate the diffusion mechanism of B in Si. Total energy calculations and molecular dynamics simulations show that B diffuses by an interstitialcy mechanism. Substitutional B captures a Si interstitial with a binding energy of 0.90 eV. This complex is itself a fast diffuser, with no need to first "kick out" the B into an interstitial channel. The migration barrier is about 0.68 eV. Kinetic Monte Carlo simulations confirm that this mechanism leads to a decrease in the diffusion length with increasing temperature, as observed experimentally.

A theory is developed for generating short time, monostatic reverberation realizations caused by three-dimensionally distributed volume inhomogeneities in stratified media. A wave number integral approach to treating the propagation to and from the scatterers, combined with a two-dimensional spectral representation of the azimuthally averaged scatterer realizations and a novel numerical implementation, combine to yield an efficient, high fidelity reverberation simulator for predicting monostatic backscatter from horizontally stratified sediments.