Abstract
The α–β phase transition in quartz has features which workers have long found puzzling. My purpose is to explore using a theory for this that is rather different conceptually from those used by other workers. It does suggest different kinds of experiments, likely to shed light on aspects of the transition, and a possible modification of theory which might be helpful in understanding some subtleties.
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REFERENCES
J.L. Ericksen, Equilibrium theory for X-ray observations of crystals. Arch. Rational Mech. Anal. 139(1997) 181–200.
R.D. James, Displacive phase transformations in solids. J. Mech. Phys. Solids 34(1986) 359–394.
R.D. James, The stability and metastability of quartz. In: S. Antman, J.L. Ericksen, D. Kinderlehrer and I. Müller (eds), Metastability and Incompletely Posed Problems, IMA Volumes in Mathematics and its Applications 3. Springer, New York (1987) pp. 147–175.
J.L. Ericksen, On the theory of growth twins in quartz, to appear in Math. Mech. Solids.
R. Balzer and H. Sigvaldson, Equilibrium vacancy concentrations measurements on zinc single crystals. J. Phys. F: Metal Physics 9(1979) 171–178.
A.H. Jay, The thermal expansion of quartz. Proc. Roy. Soc. London A 142(1933) 237–247.
M. Pitteri and G. Zanzotto, Continuum Models for Phase Transitions and Twinning in Crystals. CRC/Chapman and Hall, London (2000).
J.L. Ericksen, Notes on the X-ray theory. J. Elasticity 55(1999) 201–218.
M. Pitteri, On (υ+ 1)lattices. J. Elasticity 15(1985) 3–25.
J.L. Ericksen, A minimization problem in the X-ray theory. In: Contributions to Continuum Theories, Anniversary Volume for Krzystof Wilmanski, (collected by B. Albers). Weierstrass Institut für Angewandte Analysis und Stochastic, Report No. 18 (2000).
L.A. Thomas and W.A. Wooster, Piezocrescence – the growth of Dauphiné twins in quartz under stress. Proc. Roy. Soc. London A 208(1951) 43–62.
A.B. Pippard, The Elements of Classical Thermodynamics. Cambridge Univ. Press, Cambridge (1957).
K.R. Hosieni, R.A. Howald and M.W. Scanlon, Thermodynamics of the lambda transition and the equation of state of quartz. Amer. Mineral. 70(1985) 782–793.
G. Dolino, The incommensurate phase of quartz. In: R. Bline and A.P. Levanyuk (eds), Incommensurate Phases in Dielectrics 2. Elsevier Scientific, Amsterdam (1986) pp. 207–230.
M.A. Carpenter, E.K.H. Salje, A. Graeme-Barber, B. Wruck, M.T. Dove and K.S. Knight, Calibration of excess thermodynamic properties and elastic constant variations associated with the α↔β phase transition in quartz. Amer. Mineral. 83(1998) 2–22.
R. Coe and M.S. Paterson, The α–β inversion in quartz: a coherent phase transition under stress. J. Geophys. Research 74(1969) 4921–4948.
M.B. Walker, Dauphiné-twin domain configurations in quartz and aluminum phosphate. In: J.F. Scott and N.A. Clark (eds), Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals. Plenum Press, New York (1986) pp. 9–18.
R.J. Ackermann and C.A. Sorrell, Thermal expansion and the high-low transformation in quartz. J. Appl. Cryst. 7(1974) 461–467.
G. Van Tendeloo, J. Van Landuyt and S. Amelincx, The α–β phase transition in quartz and AlPO4as studied by electron microscopy and diffraction. Phys. Status Solidi A 33(1976) 723–735.
P. Tolédano and V. Dmitriev, Reconstructive Phase Transitions in Crystals and Quasicrystals. World Scientific, Singapore (1996).
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Ericksen, J. On the Theory of the α–β Phase Transition in Quartz. Journal of Elasticity 63, 61–86 (2001). https://doi.org/10.1023/A:1013047100380
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DOI: https://doi.org/10.1023/A:1013047100380