Self-diffusion Of Atoms Research Articles

The measurement of self-diffusion coefficients in liquid metals with quasielastic neutron scattering

Quasielastic incoherent neutron scattering (QENS) has proven to be a versatile tool to study self diffusion of atoms in liquid metals. Here it is shown, that coherent contributions to the signal in the smallq limit appear as aflat and energy independent constant to the QENS signal in single-component liquid metals even for systems with a small incoherent scattering cross section, like aluminum. Container-less processing via electromagnetic or electrostatic levitation devices, especially designed for QENS, enables the in-situ measurement on liquid metallic droplets of sizes between 5mm to 10mm in diameter. This gives access to the study of chemically reactive, refractory metallic melts and extends the accessible temperature range to undercoolings of several hundred Kelvin below the respective melting point. Compared to experiments using a thin-walled crucible giving hollow-cylindrical sample geometry it is shown that multiple scattering on levitated droplets is negligible for the analysis of the self-diffusion coefficient. QENS results of liquid germanium and 73 germanium isotope mixtures, titanium, nickel, copper and aluminum are reviewed. The self-diffusion coefficients of these systems are best described by an Arrhenius-type temperature dependence around their respective melting points.

Insights into carbon nanotube nucleation: cap formation governed by catalyst interfacial step flow.

In order to accommodate an increasing demand for carbon nanotubes (CNTs) with desirable characteristics one has to understand the origin of helicity of their structures. Here, through in situ microscopy we demonstrate that the nucleation of a carbon nanotube is initiated by the formation of the carbon cap. Nucleation begins with the formation of a graphene embryo that is bound between opposite step-edges on the nickel catalyst surface. The embryo grows larger as the step-edges migrate along the surface, leading to the formation of a curved carbon cap when the steps flow across the edges of adjacent facets. Further motion of the steps away from the catalyst tip with attached rims of the carbon cap generates the wall of the nanotube. Density Functional Theory calculations bring further insight into the process, showing that step flow occurs by surface self diffusion of the nickel atoms via a step-edge attachment-detachment mechanism. Since the cap forms first in the sequence of stages involved in growth, we suggest that it originates the helicity of the nanotube. Therefore, the angular distribution of catalyst facets could be exploited as a new parameter for controlling the curvature of the cap and, presumably, the helicity of the nanotube.

Concentration of Vacancies and Self-Diffusion of Nodal Atoms in Binary Interstitial Solutions

Concentration of Vacancies and Self-Diffusion of Nodal Atoms in Binary Interstitial Solutions

Molecular dynamics simulation of self-diffusion processes in titanium in bulk material, on grain junctions and on surface.

The process of self-diffusion of titanium atoms in a bulk material, on grain junctions and on surface is explored numerically in a broad temperature range by means of classical molecular dynamics simulation. The analysis is carried out for a nanoscale cylindrical sample consisting of three adjacent sectors and various junctions between nanocrystals. The calculated diffusion coefficient varies by several orders of magnitude for different regions of the sample. The calculated values of the bulk diffusion coefficient correspond reasonably well to the experimental data obtained for solid and molten states of titanium. Investigation of diffusion in the nanocrystalline titanium is of a significant importance because of its numerous technological applications. This paper aims to reduce the lack of data on diffusion in titanium and describe the processes occurring in bulk, at different interfaces and on surface of the crystalline titanium.

Grain boundary grooving in thin films revisited: The role of interface diffusion

Thin nickel (Ni) films were grown on c-plane-oriented sapphire substrates by electron-beam deposition. The as-deposited films exhibited a mazed bicrystal microstructure consisting of interwoven grains of two twinned orientations. Annealing of the specimens at 700°C resulted in the thickening of the Ni film. At the same time a mass deficit in the surface regions near grain boundary thermal grooves was observed. The shape of the observed grooves was very different from that predicted by the classical Mullins model. We developed a model of thermal grooving with simultaneous film thickening due to Ni diffusion along the Ni–sapphire interphase boundary, which agreed well with the experimental results. These findings demonstrate that self-diffusion of metal atoms along the metal–ceramic interface plays an important role in mass transport in thin films. Some implications of fast interphase boundary diffusion for the thermal stability of thin films are discussed.

Self-diffusion dynamics processes relevant to 2D homoepitaxy growth of Ni adatom on Ni(111) surface

Using molecular dynamics and modified analytic embedded atom methods, the atomic self-diffusion dynamics behaviors relevant to 2D crystal growth on Ni(111) surface have been studied between 150 and 600K. On perfect Ni(111) surface, the activation energy and prefactor are 0.058±0.001eV and 4.2×10−4cm2/s between 150 and 350K, and 0.082±0.003eV and 7.8×10−4cm2/s from 400 to 600K. Ni adatom just hops along the directions of close-packed steps on stepped Ni(111) surface, the corresponding activation energies and prefactors are 0.188±0.002eV and (3.8–4.4)×10−3cm2/s along the direction of A-type step, 0.140±0.001eV and (1.1–1.2)×10−3cm2/s along the direction of B-type step, and both fitting lines of Arrhenius law intersect at Tc=420–440K. Our results show that the atomic growth dynamics under nonequilibrium conditions is gradually dominated by the prefactor with increasing temperature. In addition, the shape-change of the 2D nanometer-size island has been discussed on stepped Ni(111) surface in different temperature range.

Self-diffusion and ‘order–order’ kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation

Self-diffusion of component atoms and ‘order–order’ relaxations in a B2-ordering binary system AB showing a tendency for triple-defect formation were consistently simulated by means of two Monte Carlo techniques. In view of a strict correlation between antisite-defect and vacancy concentrations the Kinetic Monte Carlo (KMC) simulations were implemented with a temperature-dependent vacancy concentration determined by means of Semi-Grand Canonical Monte Carlo (SGCMC) simulations. The Ising model of the system was completed with local-configuration-dependent saddle-point energy parameters related to vacancy mediated atomic jumps. The simulations elucidated the atomistic origin of the experimentally observed low rate of ‘order–order’ relaxations in NiAl, as well as reproduced the experimental relation between the activation energies for ‘order–order’ kinetics and Ni self-diffusion in NiAl. Higher value of the deduced activation energy for atomic migration with respect to the effective energy barriers related to individual atomic jumps indicated their high correlation.

Hydrogenation-induced microstructure evolution in as cast and severely deformed Mg-10 wt.% Ni alloy

We determined the kinetics of hydrogen absorption of the hypoeutectic Mg-10 wt.% Ni alloy in the as-cast state and after processing by four passes of equal channel angular pressing (ECAP). While during the first hydrogenation cycle the ECAP-modified alloy exhibited faster absorption than its as-cast counterpart, this advantage was lost after the second hydrogenation cycle; parity was regained after six cycles. We attributed these differences in the hydrogen absorption kinetics to the formation of large (tens of micrometers) faceted Mg crystals observed during the first hydrogenation cycle. These crystals were significantly larger in the ECAP-modified alloy than in its as-cast counterpart. We discussed the growth of large Mg crystals during hydrogenation in terms of self-diffusion of Mg atoms driven by the metal-hydride transformation stress. The larger size of these crystals in the ECAP-processed alloy was attributed to the acceleration of diffusion by ECAP. Our metallographic studies revealed a number of microstructural changes in the alloys upon hydrogenation, such as cracking, accumulation of plastic strain in large Mg crystals, and re-distribution of the dispersed particles of Mg2Ni phase in the partly hydrogenated alloys.

UV-induced blue thermoluminescence of annealed Na-rich aluminosilicates

The luminescence properties of gemstones (silicates, carbonates, phosphates, etc.), are of interest since could be potentially employed as personal dosimeters not only in case of radiation accident or radiological terrorism where conventional monitoring was not established, but also as a UV personal dosimeter. We, herein, report on preliminary results of the UV-induced 480 nm-thermoluminescence (TL) response of a well-characterised natural albite (NaAlSi3O8) from Minas Gerais (Brazil) that, due to its high transparency, is used as gemstone. Different annealing on several aliquots (from 480 to 960 °C) induces several changes in the sensitivity of the sample probably associated with (i) dehydration and dehydroxylation processes and (ii) changes in the lattice structure increasing the Al/Si disorder giving rise to ionic self-diffusion of alkali atoms, thermal stress into atomic positions and variation in the concentration of alkali ions in planar defects. The complex structure of albite has several planar defects (twinning and exsolution interphases which contain hydroxyl groups, water molecules, etc.) that can act as luminescence centres. When the thermal preannealed samples are exposed to 1 h at 254.7 nm under lab conditions one can appreciate changes in the TL behaviour that allows us to think in the albite as a potential UV dosimeter. ©2006 Elsevier Ltd. All rights reserved.

Solid-state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion

The initial stages of solid-state dewetting of 25nm-thick Fe films on basal plane-oriented sapphire substrates were found to occur via nucleation and growth of through-thickness craters within the film. The rims along these voids were not elevated, in contrast to commonly observed void growth mechanisms. Instead, the material that was consumed during the crater expansion was absorbed by several isolated grains in its vicinity but not adjacent to it. These grains transformed into faceted hillocks that protruded above the original film surface at later stages. A thin film dewetting model is proposed, in which the self-diffusion of Fe atoms along the grain boundaries transports the mass from the expanding cavities to the hillocks and determines the kinetics of this dilation. The grain boundary self-diffusion coefficients of Fe that were estimated based on the experimentally determined crater expansion rates and the proposed model agreed well with the literature.

The effect of evaporation on size and shape evolution of faceted gold nanoparticles on sapphire

We studied the size and shape evolution of about 180 faceted gold nanoparticles attached to a sapphire substrate during annealing at 950 °C in air. We employed the scanning force microscopy and interrupted annealing techniques to track the changes in size and shape of individual nanoparticles. The height of all single-crystalline nanoparticles was constant up to the longest cumulative annealing time of 65 h. The lateral dimensions of ∼20% of all nanoparticles shrunk during anneals, while all three dimensions of the remaining 80% of nanoparticles remained constant. Only the nanoparticles with the height below the average (for all particles) were laterally shrinking. We formulated a kinetic model relating the lateral shrinkage of the nanoparticles to the evaporation of Au atoms adsorbed on sapphire. We also assumed that the process controlling particles shrinkage is the slow self-diffusion of Au atoms along the lateral facets of the nanoparticles toward the substrate. The model predicted a power law dependence of the shrinkage rate on the particle height, with the exponent n = 3. The corresponding exponent determined from the experimental data was n = −2.9 ± 0.3, in excellent agreement with the theory. The low value of the effective self-diffusion coefficient along the lateral facets determined with the aid of our model (3.2 ± 0.2 × 10 −17 m 2 s −1) was attributed to the difficulties of step nucleation on atomically flat facets.

Particle rearrangement during sintering of heterogeneous powder mixtures: A combined experimental and theoretical study

We studied the morphology evolution of individual three-particle W–Cu–W agglomerates during sintering anneals at 1000 °C. The angle between the lines connecting the centers of W and Cu particles decreased during annealing, provided its initial value was different from 180°. While the W particles retained their spherical shape during sintering, the shape of Cu particles changed significantly after long sintering times. Both the rate of the particles’ rearrangement and the linear shrinkage of the particle pairs determined in the experiments increased with decreasing initial angle between the particles. We proposed an analytical model of sintering of cylindrical three-wire agglomerates controlled by self-diffusion of Cu atoms along the surface of Cu wire and along the W–Cu interphase boundary. The proposed model incorporates a thermodynamic method for calculating the distribution of chemical potential of metal atoms moving along the rigid cylindrical interphase boundary. The predictions of the model were in good agreement with the experimental data, underlying an important role played by capillary-driven diffusion in rearrangement of particles during sintering.

Universality in Self-Diffusion of Atoms among Distinctly Different Glass-Forming Liquids

The long-time self-diffusion coefficients D(S)(L) in distinctly different glass-forming liquids are analyzed from a unified point of view recently proposed by the present author. It is shown that as long as the systems are in equilibrium, they are all described by the following two types of master curves, depending on whether the control parameter is intensive or extensive: D(S)(L)(x) = d(0)x(-1)(1 - x)(2+η) exp[cx(3+η)(1 - x)(2+η)] for a reduced intensive control parameter x, such as a reduced inverse temperature, and D(S)(L)(x) = d(0)x(-1)(1 - x)(2) for a reduced extensive control parameter x, such as a reduced volume fraction, where d(0) and c are constant. Here, the exponent η (≠0) results from many-body correlations in a supercooled liquid state. The constants η and c depend on the systems and are given by (η,c) = (4/3,62) for fragile liquids, (5/3, 62) for strong liquids, and (0,0) for other glass-forming systems in which the peak heights of their non-Gaussian parameters are always much less than 1.0. It is also shown that all of the data for the diffusion coefficient start to deviate from the master curves at lower temperatures (or higher volume fraction), where the systems become out of equilibrium, leading to a glass state.

Mechanisms of bulk diffusion at “high” and “low” temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T D) and low (T < T D) temperatures (where T D is Debye temperature). It has been shown that the mechanisms of diffusion at high and low temperatures differ significantly. In the high-temperature range, the diffusion is provided by fluctuations, which can be described in terms of local melting, i.e., the formation of a “liquid diffusion channel.” In the low-temperature range, when melting for some reasons is hindered, the diffusion is due to the fluctuation formation of a “hollow diffusion channel.” The calculation of the activation energies of these processes in the case of self-diffusion agrees well with the experiment in the temperature range T > T D and has demonstrated that the activation energy increases significantly at T < T D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.

Elementary Process of Electromigration at Metal Nanojunctions and Its Application to Fabrication of Single Molecule Transistors

We have investigated electromigration process at metal nanojunctions by introducing a novel spectroscopic approach. When the junction voltage exceeded certain critical values, conductance showed successive drops by one quantum conductance, corresponding to one-by-one removal of metal atoms. The observed critical voltages agree with the activation energies for surface diffusion of metal atoms. This fact clearly indicates that the elementary process of electromigration is the self-diffusion of metal atoms driven by microscopic kinetic energy transfer from a single conduction electron to a single metal atom. This new finding can be applied to reproducible formation of atomic-spacing gaps for single molecule junctions and also to the failure-tolerant interconnects for VLSIs.

Liquid-like structure and self-diffusion channels on Al surfaces

Molecular dynamics simulation with embedded atom method potentials is performed to study the atomic structure and self-diffusion on three aluminum surfaces: (001), (110) and (111). Using mean-square displacement, structure ordering parameter, radial-distribution function and z-direction density, we find that their atoms on the first layer present obvious self-diffusion then change into liquid-like structure under melting points: Al(110) at 700±10 K, Al(001) at 860±10 K, and Al(111) at 930±10 K. In the liquid-like structure, self-diffusions always take place on the first layer of the original surface along the direction parallel rather than vertical to the surface: some of the diffusions occur on the outermost layer and more diffusions occur outside the original surface. The main diffusion channels of the three surfaces are different: along [001] on Al(110), [110] and [110] on Al(001), and [110], [101] and [011] on Al(111). No inter-layer diffusion takes place in liquid-like structure, which is different from in the liquid structure of melted surface.

Single master curve for self-diffusion coefficients in distinctly different glass-forming liquids

An existence of a single master curve for the long-time self-diffusion coefficients D(S)(L)(T) in diversely different glass-forming liquids is predicted over wide temperature T ranges above the glass transition point T(g) by analyzing various experimental and simulation data consistently from a unified point of view based on the mean-field theory recently developed. In order to scale those data appropriately, the power-law dependence of the α- and the β-relaxation times on D(S)(L) is used. Then, it is shown that any equilibrium data for self-diffusion of atom in different systems are all collapsed onto a singular function f(T(f)((α))/T) , where T(f)((α)) is a fictive singular temperature of atom α. Thus, we emphasize that any equilibrium self-diffusion data can be described by a single master curve f(x) above T(g)(>T(f)), while the data out of equilibrium start to deviate from f(x) around T(g).

One master curve for self-diffusion of one atom in different glass-forming liquids

Self-diffusion of a single atom α in glass-forming liquids, A x B y C z ⋯, is studied from a unified point of view based on the mean-field theory (MFT) proposed recently by the present author, where α ∈ { A, B, C,...} and x + y + z + cdots = 100. Several experimental data and simulation results available at present are then analyzed consistently with the aid of MFT. Thus, it is shown that there exists a master curve for the long-time self-diffusion coefficient D S L( α) of α atom, even though atom α belongs to any different multicomponent glass-forming liquids. This suggests that if a whole data set for D S L( α) in a simple glass-forming liquid is once found, only one data point for α atom in any other complex glass-forming liquids is enough to predict a whole control parameter dependence of D S L( α) for each α atom belonging to those liquids.

Crack propagation of single crystal -Sn during in situ TEM straining

In situ tensile process of single-crystal Sn was investigated by transmission electron microscopy (TEM). Despite the traditional wedge microcrack, a new tetragonal microcrack was observed during crack propagation in the single-crystal Sn. During in situ tensile straining, the dislocation dipoles formed at the front of the wedge microcrack tip, the coalescence of which is the source of microvoids at the crack tip, and then the wedge microcrack propagated deeply by aggregation of discontinuous microvoids. The tetragonal microcrack propagated by the intersection along two vertical slip planes. Moreover, the series of high-resolution images showed that Sn islands formed at the center of the frontier crack plane due to the anisotropic self-diffusion of Sn atoms along different crystallographic planes.

Mechanisms of bulk diffusion at high and low temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T D) and low (T T D and has demonstrated that the activation energy increases significantly at T < T D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.