Pattern formation in diffusion-limited crystal growth / Klaus Kassner.

By:

Kassner, Klaus

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9789812832023
9812832025

Subject(s): Genre/Form:

Electronic books.

Additional physical formats: Print version:: Pattern formation in diffusion-limited crystal growth.DDC classification:

548.5015118 K154p 22

LOC classification:

QD921 .K34 1996eb

Other classification:

51.12
UQ 2000

Online resources:

Click here to access online

Contents:

1. Introduction -- 2. Experiments and growth mechanisms. 2.1. Free versus directional growth. 2.2. Growth mechanisms -- 3. Semimicroscopic growth models. 3.1. Diffusion-limited aggregation. 3.2. Particle models for crystal growth -- 4. Macroscopic continuum models. 4.1. Defining equations. 4.2. Boundary integral equation. 4.3. Characteristic solutions and stability considerations -- 5. Numerical approach. 5.1. Discretization. 5.2. Dynamical code. 5.3. Stationary code -- 6. Selection problems. 6.1. Solvability theory. 6.2. Numerical evidence. 6.3. Experimental evidence and discussion -- 7. Analytic theory of morphology diagram -- 8. Lamellar eutectics. 8.1. The Jackson-Hunt theory. 8.2. Numerical results for axisymmetric growth -- comparison with the Jackson-Hunt theory. 8.3. Parity breaking. 8.4. Similarity equation. 8.5. Consequences of similarity -- scaling laws. 8.6. Anisotropy effects. 8.7. Coupling between phase dynamics and tilt angle -- 9. Liquid crystals. 9.1. Local description. 9.2. Characteristic solutions and stability considerations. 9.3. Small aspect ratio: transition to chaos. 9.4. Amplitude equations -- phase chaos. 9.5. Intermediate aspect ratios -- 10. Conclusions and outlook.

Summary: This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the theory in resolving the selection problem of dendritic growth, various new directions of research are presented in which progress has been made recently. These are the formation of nondendritic seaweed-like structures, growth of lamellar eutectics and rapid solidification. The interplay between analytic methods on the one hand (scaling arguments, asymptotic analysis, similarity equation, Sivashinsky singular expansion) and numerical calculations on the other (Newton method, dynamical schemes) is emphasized.

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Electronic-Books	OPJGU Sonepat- Campus	E-Books EBSCO			Available

Includes bibliographical references (pages 247-258).

Print version record.

This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the theory in resolving the selection problem of dendritic growth, various new directions of research are presented in which progress has been made recently. These are the formation of nondendritic seaweed-like structures, growth of lamellar eutectics and rapid solidification. The interplay between analytic methods on the one hand (scaling arguments, asymptotic analysis, similarity equation, Sivashinsky singular expansion) and numerical calculations on the other (Newton method, dynamical schemes) is emphasized.

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