| Description |
1 online resource (348 pages) |
| Contents |
Intro -- Preface -- Contents -- Chapter 1: Diffusion in Continuum -- 1.1 Introduction -- 1.2 Fickś First Law -- 1.2.1 Definition of Diffusion and Fickś First Law -- 1.2.2 Mathematical Interlude: Gradient Operator -- 1.2.3 Similar Linear Rate Laws -- 1.2.4 Limitations to Fickś First Law -- 1.2.5 Unit and Magnitudes of D -- 1.2.6 Application of the First Law -- 1.3 Fickś Second Law -- 1.3.1 Mass Conservation and Continuity Equation -- 1.3.2 Mathematical Interlude: Divergence Operator -- 1.3.3 Fickś Second Law -- 1.3.4 Evolution of c(x,t) with Time |
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1.3.5 Mathematical Similarity to Fourierś Law -- 1.4 Solutions to Fickś Second Law -- 1.4.1 Steady-State Solutions -- 1.4.2 Transient-State Solutions -- 1.5 Diffusion from an Instantaneous Planar Source or Thin-Film Source Solution -- 1.5.1 Solution of Fickś Second Law -- 1.5.2 Salient Features of the Solution -- 1.5.3 Leak Test -- 1.5.4 Mathematical Interlude: Error Function -- 1.5.5 Back to the Leak Test -- 1.5.6 Variations of the Thin-Film Source Solution -- 1.5.7 Reflection and Superposition Method -- 1.5.8 Application of the Thin-Film Source Solution -- 1.6 Semi-infinite Source Solution |
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1.6.1 Solution of Fickś Second Law -- 1.6.2 Salient Features of the Solution -- 1.6.3 Variations of the Error-Functional Solution -- 1.6.4 Generalization of Error-Functional Solutions -- 1.6.5 Mathematical Interlude: Properties of erf(z) -- 1.7 Trigonometric Infinite Series Solution -- 1.7.1 Statement of the Problem -- 1.7.2 Solution of Fickś Second Law by Separation-of-Variables Method -- 1.7.3 Mathematical Interlude: Orthogonality Theorem -- 1.7.4 Evaluation of the Last Constant by the Orthogonality Theorem -- 1.7.5 Application to the Trivial Initial-Condition Case |
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1.7.6 Salient Features of the Series Solution -- 1.7.7 First-Term Approximation or Long-Time Solution -- 1.7.8 Average Concentration and the First-Term Approximation -- 1.7.9 Homogenization Time -- 1.8 Method of Laplace Transform -- 1.8.1 Definition of Laplace Transform -- 1.8.2 Application to Diffusion Problems -- 1.9 Solutions When D Is Not Constant -- 1.9.1 When D = D(t) -- 1.9.2 When D = D(c): Boltzmann-Matano Analysis -- 1.10 Diffusion in Higher Dimensions -- 1.11 Moving Boundary Problem -- Problems -- References -- Chapter 2: Atomic Theory of Diffusion -- 2.1 Introduction |
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2.2 A Naïve View of Diffusion -- 2.3 Random Walk Theory -- 2.4 Diffusion Mechanisms -- 2.5 A Few General Relations -- 2.6 Derivation of Self-Diffusion Coefficient -- 2.7 Defect (Vacancy) Diffusion Coefficient -- 2.8 Thermodynamic Variables Dependence of DA -- 2.9 Correlation Effect -- 2.10 Quantitative Treatment of the Correlation Factor -- 2.11 Various Diffusivities So Far -- Problems -- References -- Chapter 3: Chemical Reaction Kinetics -- 3.1 Introduction -- 3.2 Chemical Reaction and Rate Law -- 3.2.1 Reaction System -- 3.2.2 Chemical Reaction Rate -- 3.2.3 Concentration Change in General |
| Summary |
This book provides beginning graduate or senior-level undergraduate students in materials disciplines with a primer of the fundamental and quantitative ideas on kinetic processes in solid materials. Kinetics is concerned with the rate of change of the state of existence of a material system under thermodynamic driving forces. Kinetic processes in materials typically involve chemical reactions and solid state diffusion in parallel or in tandem. Thus, mathematics of diffusion in continuum is first dealt with in some depth, followed by the atomic theory of diffusion and a brief review of chemical reaction kinetics. Chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions are examined. Through this course of learning, a student will become able to predict quantitatively how fast a kinetic process takes place, to understand the inner workings of the process, and to design the optimal process of material state change. Provides students with the tools to predict quantitatively how fast a kinetic process takes place and solve other diffusion related problems; Learns fundamental and quantitative ideas on kinetic processes in solid materials; Examines chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions, among others; Contains end-of chapter exercise problems to help reinforce students' grasp of the concepts presented within each chapter |
| Notes |
3.2.4 Reaction Rate Law |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Materials -- Mechanical properties.
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Statistical physics.
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Mathematical modelling.
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Maths for scientists.
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Testing of materials.
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Science -- Mathematical Physics.
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Mathematics -- Applied.
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Science -- Chemistry -- General.
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Technology & Engineering -- Material Science.
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Materials -- Mechanical properties
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| Form |
Electronic book
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| ISBN |
9783030259501 |
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3030259501 |
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