Sum-Rule Relations among Phenomenological Coefficients: Application to Segregation and Chemical Diffusion in Multicomponent Alloys and Mixed Ceramic Oxides

In this overview, we discuss the sum-rule relating phenomenological coefficients in randomly mixed systems and consider several applications to collective diffusion problems. These applications include intrinsic diffusion multicomponent alloys, chemical diffusion in strongly ionic mixed cation crystals and demixing of cations in randomly mixed quaternary transition metal oxides. In each case a substantial simplification is possible as a result of the sum-rule.

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Consequences on Chemical Diffusion in Materials of Sum-Rule Relations between Phenomenological Coefficients

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.237-240.789 ◽

2005 ◽

Vol 237-240 ◽

pp. 789-800

Author(s):

Irina V. Belova ◽

Graeme E. Murch

Keyword(s):

Chemical Diffusion ◽

Sum Rule ◽

Phenomenological Coefficients

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Sum-rule relationships among phenomenological coefficients: Simplifications for the analysis of segregation and chemical diffusion

Journal of Phase Equilibria and Diffusion ◽

10.1007/s11669-005-0042-3 ◽

2005 ◽

Vol 26 (5) ◽

pp. 503-509

Author(s):

I. V. Belova ◽

G. E. Murch

Keyword(s):

Chemical Diffusion ◽

Sum Rule ◽

Phenomenological Coefficients

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A Formalism to Describe Demixing of Mixed Oxides of Large and Small Grain Size in an Electric Field

MRS Proceedings ◽

10.1557/proc-822-s6.14 ◽

2004 ◽

Vol 822 ◽

Author(s):

Irina V. Belova ◽

Mandy J. Brown ◽

Graeme E. Murch

Keyword(s):

Steady State ◽

Electric Field ◽

Random Distribution ◽

Mixed Oxides ◽

Transport Coefficients ◽

Atomic Composition ◽

Ceramic Oxides ◽

Sum Rule ◽

Composition Profiles ◽

Mixed Ceramic

AbstractIn this paper, we address the theory of electric field demixing of the cations in semi-conducting and initially homogeneous mixed ceramic oxides. We include the off-diagonal phenomenological transport coefficients by assuming a random distribution of cations and making use of an exact sum-rule expression. The steady state atomic composition profiles are shown to be quite different when different assumptions are made about vacancy equilibration. We show that in the case of large grained material (where vacancies in the interior do not equilibrate easily to the external oxygen partial pressure), a maximum develops in the steady state vacancy composition profiles. This behaviour is verified by independent Monte Carlo simulations.

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Sum-Rule Relationships among Phenomenological Coefficients: Simplifications for the Analysis of Segregation and Chemical Diffusion

Journal of Phase Equilibria and Diffusion ◽

10.1361/154770305x66637 ◽

2005 ◽

Vol 26 (5) ◽

pp. 503-509

Author(s):

I.V. Belova ◽

G.E. Murch

Keyword(s):

Chemical Diffusion ◽

Sum Rule ◽

Phenomenological Coefficients

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Interdiffusion Data in Multicomponent Alloys as a Source of Quantitative Fundamental Diffusion Information

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.263.1 ◽

2007 ◽

Vol 263 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Irina V. Belova ◽

Graeme E. Murch

Keyword(s):

Diffusion Processes ◽

Chemical Diffusion ◽

Tracer Diffusion ◽

Ternary Alloys ◽

Diffusion Data ◽

Fundamental Information ◽

Random Alloy ◽

Phenomenological Coefficients ◽

Correlation Factors ◽

Alloy Systems

Tracer diffusion experiments have historically furnished much of the information about fundamental diffusion processes as embodied in such quantities as tracer correlation factors and vacancy-atom exchange frequencies. As tracer diffusion experiments using radiotracers are rather less often performed nowadays, it is important to be able to process other diffusion data to provide similar fundamental information. New procedures that are primarily based around the random alloy model have been established recently for analyzing chemical diffusion data in binary and ternary alloy systems. These procedures are reviewed here. First, we review the random alloy model, the Sum-rule relating the phenomenological coefficients and three diffusion kinetics formalisms making use of the random alloy. Next, we show how atom-vacancy exchange frequency ratios and then component tracer correlation factors can be extracted from chemical diffusion data in alloy systems. Examples are taken from intrinsic diffusion and interdiffusion data in a number of binary and ternary alloys.

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