Abstract
In phase transformations, metastability is associated with a transformation temperature on heating which differs from the transformation temperature on cooling. The phenomenon is especially prevalent in solids. From an intuitive point of view, the failure of the body to be “absolutely stable” is a consequence of the observation that at a given temperature and pressure, which would ordinarily cause the body to adopt a well-determined configuration, more than one configuration is observed. If we compare this behavior with, say, a minimum free energy calculation in the spirit of Gibbs, we find that only one configuration minimizes what is thought to be the appropriate free energy.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.W. Gibbs, “On the equilibrium of heterogeneous substances”, Trans. Conn. Acad. Ill (1875–1878), p. 108 and p.343.
G. van Tendeloo, J. van Landuyt and S. Amelinckx, “The a-ß phase transition in quartz and AIPO4, as studied by electron microscopy and diffraction”, Phys. Stat. Sol. a 33 (1976), p. 723.
R.S. Coe and M.S. Paterson, “The a-ß inversion in quartz: a coherent phase transition under nonhydrostatic stress”, J. Geophys. Res. 74 (1976), p. 921.
L.A. Thomas and W.A. Wooster, “Piezocrescence — the growth of Dauphine twinning under stress”, Proc R. Soc. A2Q8 (1951), p. 43.
R.S. Rivlin, “Some thoughts on material stability” in Finite Elasticity (ed. D.E. Carlson and R.T. Shield), Martinus Nijhoff (1982).
J.L. Ericksen, “Multi-valued strain energy functions for crystals”, Int. J. Solids Struct. 18, (1982), p. 913.
R.O. James, “Displacive phase transformations in solids”, to appear.
M. Pitteri, “On (v+ 1)-lattices”, J. Elasticity 15 (1985), p. 3.
J.L. Ericksen, “Nonlinear elasticity of diatomic crystals”, Int. J. Solids Struct. 6 (1970), p. 951.
G.P. Parry, “On phase transitions involving internal strain”, Int. J. Solids Struct. 17 (1981), p. 361.
C. Berger, L. Eyraud, M. Richard and R. Rivière, “Étude radiocristallograpique de variation de volume pour quelques matériaux subissant des transformations de phase solide-solide”, Bull. Soc. Chim. France (1966), p. 628.
C. Berger, M. Richard and L. Eyraud, “Applications de la microcalorimetrie a la determination precise des variations d’enthalpie de quelques transformations solide-solide”, Bull. Soc. Chim. France (1965), p. 1491.
W.A. Wooster and N. Wooster, Nature 157 (1946), p. 405.
P. Vigoureux, Quartz Resonators and Oscillators, H.M. Stationery Office (1931).
J.M. Bail, “Constitutive inequalities and existence theorems in nonlinear elastostatics”, in Nonlinear Analysis and Mechanics, Vol. 1 (ed. R.J. Knops), Pitman (1977).
M.E. Gurtin, An Introduction to Continuum Mechanics, Academic Press (1981).
R. Pego, “Phase Transitions in one Dimensional Nonlinear Viscoelasticity: Admissibility and Stability”, to appear in IMA Volumes and its Applications, Dynamical Problems in Continuum Physics, Springer Verlag.
L.D. Landau and E.M. Lifshits, Statistical Physics, 3rd edition, (Trans. J.B. Stykes and M.J. Kearsley), Pergamon (1980).
M. Achenbach and I. Müller, “Creep and yield in martensitic transformations”, Ingenieur Archiv (in press).
J.H. Wiener, Statistical Mechanics of Elasticity, John Wiley and Sons (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
James, R.D. (1987). The Stability and Metastability of Quartz. In: Antman, S.S., Ericksen, J.L., Kinderlehrer, D., Müller, I. (eds) Metastability and Incompletely Posed Problems. The IMA Volumes in Mathematics and Its Applications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8704-6_10
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8704-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8706-0
Online ISBN: 978-1-4613-8704-6
eBook Packages: Springer Book Archive