Skip to main content

A Mechanical Theory for Crystallization of a Rigid Solid in a Liquid Melt; Melting-Freezing Waves

  • Chapter
Mechanics and Thermodynamics of Continua
  • 355 Accesses

Abstract

Crystals of solid helium in their melt exhibit a phenomenon generally not found in other materials: oscillations of the solid-liquid interface in which atoms of the solid move only when they melt and enter the liquid. Such melting-freezing waves were predicted by Andreev & Parshin [AP] in 1978 and exhibited experimentally1 by Keshishev, Parshin, & Babkin [KPB] in 1979.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angenent, S., & M. E. Gurtin, Multiphase thermomechanics with interfacial structure. 2. Evolution of an isothermal interface. Arch. Rational Mech. Anal. 108, 323–391 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Andreev, A. F., & A. Y. Parshin, Equilibrium shape and oscillations of the surface of quantum crystals, Sov. Phys. JETP 48, 763–766 (1978).

    ADS  Google Scholar 

  3. Castaing, B., Balibar, S., & C. Laroche, Mobilité à 1 MHz du font de fusion de 4He, J. Physique 41, 897–903 (1980).

    Article  Google Scholar 

  4. Cahn, J. W., & D. W. Hoffmann, A vector thermodynamics for anisotropic surfaces. 2. Curved and faceted surfaces, Act. Metall. 22, 1205–1214 (1974).

    Article  Google Scholar 

  5. Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Gjostein, N. A., Adsorption and surface energy. 2. Thermal faceting from minimization of surface energy, Act. Metall. 11, 969–978 (1963).

    Article  Google Scholar 

  7. Gurtin, M. E., Multiphase thermomechanics with interfacial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal. 104 195–221 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241 (1986).

    MathSciNet  ADS  MATH  Google Scholar 

  9. Gurtin, M. E., Toward a nonequilibrium thermodynamics of two phase materials, Arch. Rational Mech. Anal. 100, 275–312 (1988).

    MathSciNet  ADS  MATH  Google Scholar 

  10. Gurtin, M. E.. An Introduction to Continuum Mechanics, Academic Press (1981).

    Google Scholar 

  11. Gurtin, M. E., & P. Podio Guidugli, A hyperbolic theory for the evolution of plane curves, Forthcoming.

    Google Scholar 

  12. Gurtin, M. E., & A. Struthers, Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. Forthcoming.

    Google Scholar 

  13. Keshishev, K. O., Parshin, A. Y., & A. V. Babkin, Experimental detection of crystallization waves in He4, JETP Lett. 30, 56–59 (1979).

    ADS  Google Scholar 

  14. Maris, J. H., & A. F. Andreev, The surface of crystalline helium 4, Phys. Today, 25–30 (Feb. 1987).

    Google Scholar 

  15. Rogers, R. C., Notes on a linear model of mechanical phase transitions, Forthcoming.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Bernard Coleman on his sixtieth birthday

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gurtin, M.E. (1991). A Mechanical Theory for Crystallization of a Rigid Solid in a Liquid Melt; Melting-Freezing Waves. In: Markovitz, H., Mizel, V.J., Owen, D.R. (eds) Mechanics and Thermodynamics of Continua. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75975-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-75975-8_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52999-6

  • Online ISBN: 978-3-642-75975-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics