Grain Boundary Diffusion Controlled Precipitation as a Model For thin Film Reactions

ABSTRACTIn order to arrive at a model for nucleation in the reaction of polycrystalline thin films, we have made use of a transport model that combines atom transport across interface reaction barriers with transport along grain boundaries. Through this transport model, the boundary chemical potential, μIi, and a characteristic length Li for each specie are defined. Li and the ratio of grain size to Li determine the spatial variation and the time evolution of the boundary chemical potential respectively. Nucleation of the product phase is modeled as a process whose driving force is determined by these position dependent (and time dependent) boundary chemical potentials. Thus thin film reactions become similar to precipitation from bulk homogeneous supersaturated solid solutions. Numerical calculations, however, show that boundary diffusion results in low “effective” driving forces for nucleation which can lead to heterogeneous nucleation of even the first phase. The model provides a new approach to phase selection by re-evaluation of the driving force and considers the effect of product and reactant grain structure to be fundamental to the reaction process.

Download Full-text

Transport of adsorbates in microporous solids: arbitrary isotherm

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0089 ◽

1994 ◽

Vol 446 (1926) ◽

pp. 15-37 ◽

Cited By ~ 8

Keyword(s):

Driving Force ◽

Chemical Potential ◽

Transport Model ◽

Potential Gradient ◽

Isosteric Heat ◽

Chemical Potential Gradient ◽

Equilibrium Data ◽

Random Walk Theory ◽

Microporous Solids ◽

Good Agreement

The transport of adsorbates in microporous random networks is examined in the presence of an arbitrary nonlinear local isotherm. The transport model is developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The results demonstrate more rapid increase of the transport coefficient with adsorbed concentration than straightforward use of the classical Darken equation. Application of the theory to experimental data for diffusion of carbon dioxide in carbolac, with various local isotherm choices, shows good agreement when the activation energy associated with the mobility based on a chemical potential gradient driving force is taken as the Henry’s law region isosteric heat of adsorption. Furthermore, a combination of transport and equilibrium data can discriminate better among competing isotherms than the latter data alone.

Download Full-text

A Unified Approach to Grain Boundary Diffusion and Nucleation in Thin Film Reactions

MRS Proceedings ◽

10.1557/proc-343-193 ◽

1994 ◽

Vol 343 ◽

Cited By ~ 5

Author(s):

K. R. Coffey ◽

K. Barmak

Keyword(s):

Thin Film ◽

Grain Boundary ◽

Diffusion Couple ◽

Alternative Model ◽

Boundary Diffusion ◽

Chemical Potential ◽

Grain Boundary Diffusion ◽

Boundary Phase ◽

Decay Length ◽

Product Phase

ABSTRACTAn alternative model is proposed to extend the conventional view of diffusion under a concentration gradient in a grain boundary phase of width δ. The conventional model is well developed and readily applied to the thickening kinetics of polycrystalline product phases in binary diffusion couples, however it is not readily extended to other phenomena of interest in thin films, i.e., the nucleation and growth of the product phase crystallites prior to formation of a product phase layer. In the alternative model presented here, non-equilibrium thermodynamics is used to define the chemical potentials, μi, for each atomic specie in the grain and interphase boundaries of a polycrystalline diffusion couple. The chemical potential difference for each specie between the bulk phases of the diffusion couple is partitioned between the driving force for grain boundary diffusion and that for interfacial reaction. This partition leads to a characteristic decay length that describes the spatial variation of μi. Numerical calculations of μi are used to show that boundary diffusion favors heterogeneous nucleation. Product nucleation in thin film reactions is seen to be similar to precipitation from a bulk solid solution.

Download Full-text

Principles of Microstructural Design in Two-Phase Systems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.558-559.827 ◽

2007 ◽

Vol 558-559 ◽

pp. 827-834 ◽

Cited By ~ 7

Author(s):

Suk Joong L. Kang ◽

Yang Il Jung ◽

Kyoung Seok Moon

Keyword(s):

Growth Rate ◽

Grain Growth ◽

Driving Force ◽

Driving Forces ◽

Interface Reaction ◽

Processing Parameters ◽

Microstructural Development ◽

Two Phase ◽

Interface Mobility ◽

Microstructural Design

When a polycrystal is in chemical equilibrium, the microstructure evolves as a result of grain growth under the capillary driving force arising from the interface curvature. As the growth rate of an individual grain is the product of the interface mobility and the driving force, the growth of the grain can be controlled by changing these two parameters. According to crystal growth theories, the growth of a crystal with a rough interface is governed by diffusion and its interface mobility is constant. In-contrast, the growth of a crystal with faceted interfaces is governed by the interface reaction and diffusion for driving forces below and above a critical value, respectively. As the growth rate is nonlinear for the regime of interface reaction control, the grain growth is nonstationary with annealing time. Calculations reveal that the types of nonstationary growth behavior including pseudo-normal, abnormal, and stationary are governed by the relative value of the maximum driving force, gmax, to the critical driving force for appreciable growth, gc. Recent experimental observations showing the effects of critical processing parameters on microstructural development also support the theoretical prediction. The principles of microstructural design are deduced in terms of the coupling effects of gmax and gc.

Download Full-text

Restless motion

10.1093/oso/9780192846839.003.0003 ◽

2021 ◽

pp. 30-39

Author(s):

Adrian P Sutton

Keyword(s):

Driving Force ◽

Chemical Potential ◽

Driving Forces ◽

Random Motion ◽

Atomic Motion ◽

Einstein Relation ◽

Free Energy Barrier ◽

Thermally Activated ◽

Fluctuation Dissipation ◽

Activated Processes

Atoms in solids are in constant random motion. Their kinetic energy is heat. Heat associated with local regions may fluctuate. The size of the fluctuations increases with decreasing size of the region. Such fluctuations enable thermally activated processes to occur. At equilibrium interstitials and vacancies undergo random walks in solids, which gives rise to diffusion in crystals and reptation in polymers. The activation energy is the free energy barrier these defects have to overcome to jump between sites. Diffusion is biased by driving forces resulting from gradients of chemical potential. The mobility relates the drift velocity of defects to the driving force on them. The Einstein relation relates the mobility to the diffusivity. It is an example of the fluctuation-dissipation theorem. Atomic motion enables diffusion and limits mobility. Thermal expansion is also a consequence of atomic motion, resulting from a fundamental asymmetry in all interatomic forces.

Download Full-text

Differences Between the Growth Kinetics of Thin Film and Bulk Diffusion Couples

MRS Proceedings ◽

10.1557/proc-10-283 ◽

1981 ◽

Vol 10 ◽

Author(s):

U. Gösele ◽

K. N. Tu

Keyword(s):

Thin Film ◽

Equilibrium Phase ◽

Interface Reaction ◽

Bulk Diffusion ◽

Equilibrium Phase Diagram ◽

Specific Reference ◽

Second Phase ◽

Diffusion Couples ◽

Reaction Barriers ◽

Equilibrium Phases

It is proposed that interface reaction barriers in binary A/B diffusion couples lead to the absence of phases predicted by the equilibrium phase diagram, provided that the diffusion zones are sufficiently thin (“thin film case”). With increasing thickness of the diffusion zones the influence of interface reaction barriers decreases and the simultaneous existence of diffusion-controlled growth of all equilibrium phases is expected (“bulk case”). First-phase and different modes of second-phase formation in the diffusion zones as well as the influence of impurities are discussed with specific reference to silicide formation. For this discussion the concept of a critical thickness of the first forming phase is introduced, below which a second compound phase cannot grow simultaneously with the first one.

Download Full-text

Phase Formation and Microstructural Development During Solid-State Reactions in Ti-Al Multilayer Films

MRS Proceedings ◽

10.1557/proc-343-205 ◽

1994 ◽

Vol 343 ◽

Cited By ~ 19

Author(s):

Carsten Michaelsen ◽

Stefan Wöhlert ◽

RÜdiger Bormann

Keyword(s):

Solid State ◽

Phase Formation ◽

Boundary Diffusion ◽

Driving Forces ◽

Multilayer Films ◽

Solid State Reactions ◽

Microstructural Development ◽

Second Phase ◽

Equilibrium Conditions ◽

Phase Selection

ABSTRACTThe phase selection which is generally observed in the early stages of solid-state reactions was studied using Ti-Al multilayer films as a model system.Although all Ti-Al intermetallic phases have similar driving forces of about 30 kJ/g-atom, TiAl3 is the only phase which is formed as long as the reactants are not consumed. The critical thickness beyond which a second phase is formed is larger than 100 μm. We found that the formation of TiAl3 takes place by nucleation and growth, demonstrating that the driving force available for first-phase formation is considerably reduced by a preceding formation of solid solutions. Furthermore, we observed that nucleation continues at later stages, indicating that non-equilibrium conditions are maintained which are possibly influenced by grain-boundary diffusion. However, the phase selection is determined by the different growth velocities, being much higher for TiAl3 than for all other phases.

Download Full-text

High-resolution scanning electron microscopy of thin-film magnetic media of magnetic recording disk

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100131309 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1334-1335

Author(s):

K. Ogura ◽

H. Nishioka ◽

N. Ikeo ◽

T. Kanazawa ◽

J. Teshima

Keyword(s):

Thin Film ◽

Fine Structure ◽

High Resolution ◽

Magnetic Recording ◽

High Performance ◽

Magnetic Hysteresis ◽

Grain Structure ◽

Magnetic Media ◽

Cross Sectional ◽

Resolution Observation

Structural appraisal of thin film magnetic media is very important because their magnetic characters such as magnetic hysteresis and recording behaviors are drastically altered by the grain structure of the film. However, in general, the surface of thin film magnetic media of magnetic recording disk which is process completed is protected by several-nm thick sputtered carbon. Therefore, high-resolution observation of a cross-sectional plane of a disk is strongly required to see the fine structure of the thin film magnetic media. Additionally, observation of the top protection film is also very important in this field.Recently, several different process-completed magnetic disks were examined with a UHR-SEM, the JEOL JSM 890, which consisted of a field emission gun and a high-performance immerse lens. The disks were cut into approximately 10-mm squares, the bottom of these pieces were carved into more than half of the total thickness of the disks, and they were bent. There were many cracks on the bent disks. When these disks were observed with the UHR-SEM, it was very difficult to observe the fine structure of thin film magnetic media which appeared on the cracks, because of a very heavy contamination on the observing area.

Download Full-text

Driving forces on dislocations: finite element analysis in the context of the non-singular dislocation theory

Archive of Applied Mechanics ◽

10.1007/s00419-021-02017-w ◽

2021 ◽

Author(s):

Xiandong Zhou ◽

Christoph Reimuth ◽

Peter Stein ◽

Bai-Xiang Xu

Keyword(s):

Finite Element ◽

Dislocation Loop ◽

Driving Force ◽

Complex Geometry ◽

Driving Forces ◽

Singular Solutions ◽

Dislocation Model ◽

Configurational Force ◽

Element Analysis ◽

Dislocation Configuration

AbstractThis work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.

Download Full-text

Interface Behavior of Brazing between Zr-Cu Filler Metal and SiC Ceramic

Crystals ◽

10.3390/cryst11070727 ◽

2021 ◽

Vol 11 (7) ◽

pp. 727

Author(s):

Bofang Zhou ◽

Taohua Li ◽

Hongxia Zhang ◽

Junliang Hou

Keyword(s):

Interfacial Reaction ◽

Reaction Layer ◽

Chemical Potential ◽

Filler Metal ◽

Diffusion Constant ◽

Interface Reaction ◽

Diffusion Path ◽

Interface Behavior ◽

Interfacial Reaction Layer ◽

Sic Ceramic

The interface behavior of brazing between Zr-Cu filler metal and SiC ceramic was investigated. Based on the brazing experiment, the formation of brazing interface products was analyzed using OM, SEM, XRD and other methods. The stable chemical potential phase diagram was established to analyze the possible diffusion path of interface elements, and then the growth behavior of the interface reaction layer was studied by establishing relevant models. The results show that the interface reaction between the active element Zr and SiC ceramic is the main reason in the brazing process the interface products are mainly ZrC and Zr2Si and the possible diffusion path of elements in the product formation process is explained. The kinetic equation of interfacial reaction layer growth is established, and the diffusion constant (2.1479 μm·s1/2) and activation energy (42.65 kJ·mol−1) are obtained. The growth kinetics equation of interfacial reaction layer thickness with holding time at different brazing temperatures is obtained.

Download Full-text