The treatment and the solution of the mixing equations with composition dependent atomic volumes

Abstract

The computer program IMPETUS calculates sputter depth profiles by solving Fokker-Plank type equations for mixing. In the standard model, the effective volume of the mixing constituents is taken to be constant throughout the mixing regardless of the composition of their atomic environment. Experimentally measured values for atomic densities of materials and compounds indicate that this assumption is not correct and that non-constant atomic volumes need to be considered. Although the way in which the variation of the volumes take place is not known, the present work is aimed at developing the treatment of Fokker-Plank type equations such that composition dependent effective atomic volumes can be included. The complexity of the equations and a method for solution together with its application for a simple case are explained in this paper     

Elastic properties of nanostructured materials with layered grain boundary structure

Atomistic calculations of the elastic constants for a bulk nanostructured material that consists of a layered structure where alternating layers meet along high angle grain boundaries and where atoms interact via a Lennard-Jones potential are presented. The calculations of the elastic constants were performed in the frame of homogeneous deformations for a wide range of layer widths ranging from 2.24 up to 74.62 nm. The results showed that the relaxation of the atomic structure affects the elastic constants for the cases where more than 5% of atoms are located in the GB region. Also it was found that the way that external stresses are applied on the system affects the values of the obtained elastic properties, with the elastic constants related to the characteristic directions of the grain boundary being the most affected ones. The findings of this work are of interest for the fabrication methods of nanostructured materials, the measurement methods of their elastic properties as well as multiscale modeling schemes of nanostructured materials.     

Grain-boundary dislocations and enhanced diffusion in nanocrystalline bulk materials and films

A theoretical model is suggested which describes the transformations of grain-boundary dislocation walls and their influence on diffusion processes in nanocrystalline materials fabricated under highly non-equilibrium conditions. It is shown that the decay of boundary dislocation walls of finite extent, occurring via the climb of boundary dislocations and the corresponding emission of vacancies, is capable of highly enhancing the grain-boundary diffusion in nanocrystalline materials. The enhanced diffusion, in turn, strongly affects the deformation behaviour of nanocrystalline materials. In the case of nanocrystalline films deposited on to substrates, the effects of misfit stresses on the transformations of boundary dislocation walls and the diffusion are analysed. It is demonstrated that the mean diffusion coefficient in a nanocrystalline film may increase by approximately several orders of magnitude owing to misfit stresses.     

Diffusion mechanisms in the Fe_3Si alloys

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Diffusion mechanisms in the Fe3Si alloys

In this paper,the possible reascon for the high thermal vacancy concentration and the low migration barriers for the Fe atorn diffusion in the stoichiometric DO3 structure Fe3Si have been discussed.The high thermal vacancy conenrrarion was attributed to the compression of Fe-Fe atcmic pairs and the tension of Fe-Si atomic pairs in Fe75Si25.The deformations (compression or tensicn)of the atompairs incrcase the interatomic potentials and thus dercrease the enthalpies of vacancy formation.The low minration bamiers for the Fe atom diffusion in Fe75Si25 were related to the symmetric property of the triangualar bamiers.Additionally.it was considered that the Si atoms in Fe3Si could probably migrate via nearest-neighbour jumps without disturbing the long-range order of atomic arrangements,provided that during the diffusion process the residence time on the antistructure sites is very short.     

Volume dilatation in a polycarbonate blend at varying strain rates

Impact loaded polymers show a variety of strain-rate dependent mechanical properties in their elastic, plastic and failure behaviour. In contrast to purely crystalline materials, the volume of polymeric materials can significantly change under irreversible deformations. In this paper, uni-axial tensile tests were performed in order to measure the dilatation in the Polycarbonate-Acrylnitril-Butadien-Styrol (PC-ABS) Bayblend T65. The accumulation of dilatation was measured at deformation speeds of 0.1 and 500 [mm/s]. Instrumented with a pair of two high-speed cameras, volume segments in the samples were observed. The change in volume was quantified as relation between the deformed and initial volumes of the segments. It was observed that the measured dilatations are of great significance for the constitutive models. This is specifically demonstrated through comparisons of stress-strain relations derived from the two camera-perspectives with isochoric relations based on single-surface observations of the same experiments.     

Influence of difference in the atomic volumes of the components on the mutual diffusion in liquid binary alloys

Expressions relating the partial diffusion coefficients, macroscopic flow velocity, and mutual diffusion coefficient are obtained. Unlike the known Darken relations, the relations obtained take into account the difference in the atomic volumes of the solution components. The influence of the volume factor is more pronounced when the component concentrations are significantly different.     

Elastic-Plastic Analysis for Functionally Graded Thick-Walled Tube Subjected to Internal Pressure

The elastic-plastic response of the functionally graded thick-walled tube subjected to internal pressure is investigated by using the relation of the volume average stresses of constituents and the macroscopic stress of composite material in micromechanics. The tube consists of two idealized isotropic elastic-plastic materials whose volume fractions are power functions of the radius. As the internal pressure increases, the deformations of one phase and two phases from elastic to plastic are analyzed. In order to simplify the calculations we assume both materials with the same Poisson's ratio. By using the assumption of a uniform strain field within the representative volume element and the Tresca yield criterion, the theoretical solutions are obtained for the case of two elastic phases and the case of two plastic phases, and the function of the radial displacement is presented for the case with both elastic and plastic phases. The yield criterion of functionally graded material is given in terms of the yield stresses and volume fractions of constituents rather than Young's modulus and yield stress with different unknown parameters of the whole material in the existing papers. Finally we also discuss the position where the plastic deformation first occurs and the conditions for which material first yields in the tube.     

Generation and accumulation of atomic vacancies due to dislocation movement and pair annihilation

Generation and accumulation of atomic vacancy due to pair annihilation of edge dislocations during plastic slip deformation of metallic materials are numerically evaluated by crystal plasticity analysis. Dislocation density-based models are utilised in the deformation analysis and a theoretical model for the generation of atomic vacancies is introduced. Purely uniform single- and double-slip deformations are analysed and results show that the evolution of the vacancy density depends largely on the microstructure length scale and multiplication of slip activity on different slip systems.     

Atomic mobility and strain localization in amorphous metals

Molecular dynamics simulations are employed to investigate the atomic mobility in Ni(50)Zr(50) amorphous alloys under both static conditions and shearing. Diffusion occurs under static conditions via cooperative stringlike motion involving atoms with large volumes. Atomic mobility is instead governed by rearrangements localized in shear transformation zones (STZs) under shearing. Local atomic volume plays in both cases a key role, the atomic ensembles involved in diffusion and STZ activity being strongly correlated.     

Thermal evolution of cluster assembled $\mathsf{Ni_3Al}$ materials modelled at the atomic scale

Diffusion properties of Ni₃Al cluster assembled nanostructured materials are investigated at the atomic scale. Two different model samples are considered, at equilibrium at 300 K. One is obtained by modelling cluster compaction under 2 GPa external pressure and the second by accumulating low energy deposited clusters on a Ni surface. They differ essentially by their density, the latter sample presenting an interconnected network of nanopores, which is not observed in the former. At elevated temperatures, cluster coalescence is observed in both, as well as an intense atomic diffusion at the internal surfaces and nanograin interfaces. A method is presented which allows, in a good approximation, to distinguish between the two phenomena and to estimate diffusion coefficients. At temperatures above 400 K, it is found for both samples, irrespective to their density, that the diffusion activation energy at the internal surfaces and interfaces is as low as in a liquid while the grain cores remain crystalline.Received: 20 June 2003, Published online: 16 September 2003PACS: 61.43.Bn Structural modeling: serial-addition models, computer simulation - 36.40.-c Atomic and molecular clusters - 61.46. + w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals     

Structure and dynamics in nanoionic materials

Nanomaterials, materials with particle dimensions less than 100 nm, show a range of unusual properties when compared with their bulk counterparts. Atomic transport is one of these properties and nanomaterials have been reported as having exceptionally high diffusion coefficients. In the case of ionic materials the atomic transport is important in a number of technological applications where they are used as solid electrolytes, for example in sensors, batteries and fuel cells. Hence ionic nanomaterials often referred to as nanoionics, can offer the means of producing electrolytes with improved performance. This contribution will examine the mechanisms of atomic transport in nanoionics in two model materials, zirconia and lithium niobate. Since an understanding of these mechanisms is dependent on knowledge of the microstructure of the materials consideration will also be given to the structural characterisation of the materials, with a focus on X-ray absorption spectroscopy. The use of this technique to characterise mesoporous a-Fe₂O₃ is also discussed.     

Effects of electron-hole excitations in ion-surface collisions

We investigate effects related to electron-hole pair production and atomic level shift in atom scattering at surfaces by using a recently proposed exactly soluble model. We show that electron-hole pair production weakens Stückelberg oscillations and enhances loss of memory of the initial atomic charge state for narrow bands because of the diffusion of an electron or hole captured by the band. Wide band materials tend to display memory loss at lower velocities than do narrow band materials. Allowing the atomic energy level to shift above the Fermi energy tends to reduce memory loss.     

The acoustoelastic effect on Rayleigh waves in elastic--plastic deformed layered rocks

On the basis of the acoustoelastic theory for elastic--plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic--plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect: the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic--plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.     

Normal stresses in surface shear experiments

When viscoelastic bulk phases are sheared, the deformation of the sample induces not only shear stresses, but also normal stresses. This is a well known and well understood effect, that leads to phenomena such as rod climbing, when such phases are stirred with an overhead stirrer, or to die swell in extrusion. Viscoelastic interfaces share many commonalities with viscoelastic bulk phases, with respect to their response to deformations. There is however little experimental evidence that shear deformations of interfaces can induce in-plane normal stresses (not to be confused with stresses normal to the interface). Theoretical models for the stress-deformation behavior of complex fluid-fluid interfaces subjected to shear, predict the existence of in-plane normal stresses. In this paper we suggest methods to confirm the existence of such stresses experimentally.     

Temperature and velocity dependence of the mechanical properties of intermetallic compound Ni3Al. II

This paper examines the retardation of superdislocations in LI₂ superstructure, due to the capture by superpartial dislocations (SPD) of atomic defects on the slip plane, and also resulting from diffusion of atomic defects in PD. When the jogs formed by the settling of defects on dislocations remain nondissociated, the sliding of superdislocations is accompanied by the generation of displaced rows of atoms the maximum linear energy of which in the L1₂ superstructure amounts to v/b (v is the ordering energy, b the interatomic distance). The maximum magnitude of retardation of superdislocations, dependent upon generation of displaced rows, is twice as high on cubic planes as on octahedral planes. The estimations presented indicate that the diffusion settling of atomic defects on the SPD of sliding superdislocations can be a cause of the anomalous temperature dependence of flow stresses under high temperatures. Some effects associated with the possible dissociability of jogs on SPD are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 63–67, October, 1971.The authors express their thanks to É. V. Kozlov for helpful discussion.     

Interdiffusion in vacuum-deposited dielectric thin films

The observation of interdiffusion imperfection in vacuum-deposited optical thin films is reported. We measured the diffusion lengths of interdiffusion in dielectric thin films of typical combinations of coating materials (TiO₂–SiO₂ and TiO₂–MgF₂) by analyzing the atomic concentration data along the depth obtained with X-ray photoelectron spectroscopy technique. The resultant diffusion lengths in the deposited layers of dielectric coating materials are not small, hence the effects of interdiffusion should be taken into account in the design of optical filters.