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

Format:

Book

Author/Creator:

Kassner, Klaus.

Language:

English

Subjects (All):

Crystal growth--Mathematical models.

Crystal growth.

Pattern formation (Physical sciences).

Physical Description:

1 online resource (268p. ) illustrations

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c1996.

Language Note:

English

Summary:

Reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. This work gives a pedagogical introduction to the subject, including experimental results, mathematical modelling and linear stability analysis.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 247-258).

ISBN:

981-283-202-5