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Instabilities of a Train of Steps and Growth of Step Fluctuation on Crystal Surfaces

Research Project

Project/Area Number 07640510
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 物性一般(含基礎論)
Research InstitutionNagoya University

Principal Investigator

UWAHA Makio  Department of Physics, Nagoya University Associate Professor, 大学院・理学研究科, 助教授 (30183213)

Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1996: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1995: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordsstep / morphological instability / growth exponent / bunching / wandring of a step / crystal growth / nonlinear evolution equation / パターン形成 / ゆらぎ
Research Abstract

Crystal growth of faceted surfaces is controlled by atomic steps. An array of parallel straight steps forms a vicinal surface. In sublimation or in growth of a crystal, wandering instability of a straight step and bunching instability of a step train are offten observed. In addition a straight step becomes rough when it grows as a result of accumulation of random fluctuation. Understanding these motion of steps is essential for controlling the morphology of crystals.
We generalized the standard step model of vapor growth by including the interaction between steps, the asymmetry in step kinetics and the anisotropy of step stiffness. Theoretical analysis and Monte Carlo simulation reveal the following for the motion of steps in the surface diffusion field and for the pattern formation of two-dimensional crystals.
(a) Bunching and/or wandering instability occur when an asymmetry in the diffusion field develops as a result of the asymmetry in step kinetics or of a drift due to an external field. Considering nonlinearity of the growing unstable mode we attributed the appearance of stable periodic pattern and spatiotemporal chaos in the instabilities to the symmetry of the system. Also the chaotic motion of a wandering step can be suppressed by a strong crystal anisotropy.
(b) As a result of the discretness of the lattice, several distinct stages appear in the change of the fluctuation of a step growing from a straight initial state. In the final stage a transition from the linear growth law to the nonlinear growth law has been observed in the simulation.
(c) Growth law and relaxation law of fractal aggregates are controlled not only by growth mechanism but alse by the geometrical fractal dimension of the aggregates.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (44 results)

All Other

All Publications (44 results)

  • [Publications] M. Uwaha et al.: "Fluctuations and Instabilities of Steps in the Growth and Sublimation of Crystals" Journal of Crystal Growth. 146・1〜4. 164-170 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Sato and M. Uwaha: "Morphological Instability Caused by Asymmetry in Step Kinetics" Physical Review B. 51・16. 11172-11175 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Irisawa et al.: "Scaling Laws in Thermal Relaxation of Fractal Aggregates" Europhysics Letters. 30・3. 139-144 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. sato and M. Uwaha: "Sep Bunching as Formation of Soliton-Like Pulses in Benney Equation" Europhysics Letters. 32・8. 639-644 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Sato and M. Uwaha: "Nonlinear Effect in Step Bunching Caused by Electric Current" Journal of the Physical Society of Japan. 65・6. 1515-1518 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Sato and M. Uwaha: "Wandering Instability of an Isolated Step with Direct Electric Current" Journal of the Physical Society of Japan. 65・7. 2146-2151 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Irisawa et al.: "Power Law Relaxation of Perimeter Length of Fractal Aggregates" Fractals. 4・3. 251-256 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y. Saito and M. Uwaha: "Anisotropy Effect on Step Morphology Described by Kuramoto-Sivashinsky Equation" Journal of the Physical Society of Japan. 65・11. 3576-3581 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K. Nishino et al.: "Power Law Behavior of the Step Roughening with Surface Diffusion" Surface Science. 372(印刷中). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 佐藤正英,上羽牧夫: "表面拡散場中での原子ステップの不安定化" 日本結晶成長学会誌. 24・1(印刷中). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Sato and M. Uwaha: "Kinematical Bound States of Steps Caused by Asymmetry in Step Kinetics" Journal of the Physical Society of Japan. 66・4(印刷中). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S. Miyashita et al.: "Experimental Evidence of Dynamical Scaling in a Two-Dimensional Fractal Growth" Journal of the Physical Society of Japan. 66・4(印刷中). (1977)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Nishinaga et al.: "Advances in the Understanding of Crystal Growth Mechanisms" Elsevier, Amsterdam(印刷中), (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Uwaha Y.Saito and M.Sato: "Fluctuations and Instabilities of Steps in the Growth and Sublimation of Crystals" J.Cryst.Growth. 146 nos. 1-4. 164-170 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Morphological Instability Caused by Asymmetry in Step Kinetics" Phys.Rev.B. 51 no.16. 11172-11175 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Irisawa, M.Uwaha and Y.Saito: "Sealing Laws in Thermal Relaxation of Fractal Aggregates" Europhys.Lett.30 no.3. 139-144 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Sep Bunching as Formation of Soliton-Like Pulses in Benney Equation" Europhys.Lett.32 no.8. 639-644 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Nonlinear Effect in Step Bunching Caused by Electric Current" J.Phys.Sic.Jpn.65 no.6. 1515-1518 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Wandering Instability of an Isoated Step with Direct Electric Current" J.Phys.Soc.Jpn.65 no.7. 2146-2151 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Irisawa, M.Uwaha and Y.Saito: "Power Law Relaxation of Perimeter Length of Fractal Aggregates" Fractals. 4 no.3. 251-256 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Saito and M.Uwaha: "Anisotropy Effect on Step Morphology Described by Kuramoto-Sivashinsky Equation" J.Phys.Soc.Jpn.65 no.11. 3576-3581 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Nishino, M.Uwaha and Y.Saito: "Power Law Behavior of the Step Roughening with Surface Diffusion" Surf.Sci.(in press). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Instabilities of Atomic Steps in the Surface Diffusion Field" J.Jpn.Assoc.Cyrst.Growth. 24 no.1 (in press) (in Japanese). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Kinematical Bound States of Steps Caused by Asymmetry in Step Kinetics" J.Phys.Soc.Jpn.66 no.4 (in press). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Miyashita: "Experimental Evidence of Dynamical Scaling in a Two-Dimensional Fractal Growth" J.Phys.Soc.Jpn.66 no.4 (in press). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Nishinaga et al.: Fluctuation and Morphological Instability of Steps in a Surface Diffusion Field Advances in the Understanding of Crystal Growth Mechanisms ed.Elsevier (in press), (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Sato and M.Uwaha: "Nonlinear Effect in Step Bunching Caused by Electric Current" Journal of the Physical Society of Japan. 65・6. 1515-1518 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Sato and M.Uwaha: "Wandering Instability of an Isolated Step with Direct Electric Current" Journal of the Physical Society of Japan. 65・7. 2146-2151 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Irisawa et al.: "Power Law Relaxation of Perimeter Length of Fractal Aggregates" Fractals. 4・3. 251-256 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Saito and M.Uwaha: "Anisotropy Effect on Step Morophology Described by Kuramoto-Sivashinsky" Journal of the Physical Society of Japan. 65・11. 3576-3581 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Nishino et al.: "Power Law Behavior of the Step Roughening with Surface Diffusion" Surface Science. 372(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 佐藤正英,上羽牧夫: "表面拡散場中での原子ステップの不安定化" 日本結晶成長学会誌. 24・1(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Irisawa et al.: "Power Law Relaxation of Perimeter Length of Fractal Aggregates" Fractals. 4・3. 251-256 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Saito and M.Uwaha: "Anisotropy Effect on Step Morphology Described by Kuramoto-Sivashinsky" Journal of the Physical Society of Japan. 65・11. 3576-3581 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Nishino et al.: "Power Law Behavior of the Step Roughening with Surface Diffusion" Surface Science. 372(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 佐藤正英,上羽牧夫: "表面拡散場中での原子ステップの不安定化" 日本結晶成長学会誌. 24・1(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Sato and M.Uwaha: "Kinematical Bound States of Steps Caused by Asymmetry in Step Kinetics" Journal of the Physical Society of Japan. 66・4(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] S.Miyashita et al.: "Experimental Evidence of Dynamical Scaling in a Two-Dimensional Fractal Growth" Journal of the Physical Society of Japan. 66・4(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Nishinaga et al.: "Advances in the Understanding of Crystal Growth Mechanisms" Elsevier,Amsterdam (印刷中), (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Makio Uwaha: "Fluctuations and Instabilities of Steps in the Growth and Sublimation of Crystals" Journal of Crystal Growth. 146. 164-170 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Masahide Sato: "Morphological Instability Caused by Asymmetry in Step Kinetics" Physical Review B. 51. 11172-1175 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Toshiharu Irisawa: "Scaling Laws in Thermal Relayation of Fractal Aggregates" Europhysics Letters. 30. 139-144 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Masahide Sato: "Step Bundring as Formation of Soliton-like Pulses" Europhysics Letters. 32. 639-644 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Toshiharu Irisawa: "Power Law Relaxation of Perimeter Length of Fractal Aggregates" Fractals. (出版予定).

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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