Being generally interested in twinning phenomena in crystals, the author became curious to know what can be done with available continuum theory, to better analyze growth twins in minerals. The most common mineral is quartz, a very useful material, and a variety of different kinds of growth twins occur in quartz crystals. So, he picked this material for his first attempt to analyze growth twins. The author is encouraged to find that, even at the elementary level, this does add something to our understanding of them. His aim is to elaborate this, using thermoelasticity theory and the X-ray theory described below.
[1] Zanzotto, G.: On the material symmetry group of elastic crystals and the Born rule. Archivefor Rational Mechanics and Analysis, 121, 1-36 (1992).
2.
[2] Zanzotto, G.: Geobarothermometric properties of growth twins and mathematical analysis of quartz data for a broad range of temperatures and pressures. Physics and Chemistry of Minerals, 16, 783-789 (1989).
3.
[3] Zanzotto, G.: Thermoelastic stability of multiple growth twins in quartz and general barothermometric implications. Journal of Elasticity, 23, 253-287 (1990).
4.
[4] Thomas, L. A. and Wooster, W A.: Piezocrescence The growth of Dauphine twinning in quartz under stress. Proceedings of the Royal Society of London, A208, 43-62 (1951).
5.
[5] Dana, J. D. and Dana, E. S.: The System of Mineralogy, 7th ed., Vol. 3 (rewritten and enlarged by C. Frondell), John Wiley, New York, 1962.
6.
[6] Ericksen, J. L.: Equilibrium theory for X-ray observations of crystals. Arhivefor Rational Mechanics and Analysis, 139, 181-200 (1997).
7.
[7] Ericksen, J. L.: Twinning analyses in the X-ray theory. International Journal of Solids and Structures, 38, 967-995 (2001).
8.
[8] Ericksen, J. L.: On correlating two theories of twinning. Archivefor Rational Mechanics and Analysis, forthcoming.
9.
[9] James, R. D.: Displacive phase transformations in solids. Journal of Mechanics and Physics of Solids, 34, 359-394 (1986).
10.
[10] James, R. D.: The stability and metastability of quartz, in Metastability and Incompletely Posed Problems, ed. S. Antman, J. L. Ericksen, D. Kinderlehrer, & I. Muller, IMA Volumes in Mathematics and its Applications, 3, 147-175 (1987).
11.
[11] Balzer, R. and Sigvaldson, H.: Equilibrium vacancy concentrations measurements on zinc single crystals. Journal of Physics F: Metal Physics, 9, 171-178 (1979).
12.
[12] Jay, A. H.: The thermal expansion of quartz. Proceedings of the Royal Society of London, A142, 237-247 (1933).
13.
[13] Pitteri, M. and Zanzotto, G.: Continuum Modelsfor Phase Transitions and Twinning in Crystals, CRC/Chapman and Hall, London, 2000.
14.
[14] Ericksen, J. L.: Notes on the X-ray theory. Journal of Elasticity, 55, 201-218 (1999).
15.
[15] Pitteri, M.: On lattices. Journal of Elasticity, 15, 3-25 (1985).
16.
[16] Truesdell, C.: A First Course in Rational Continuum Mechanics, Academic Press, New York, 1977.
17.
[17] Cahn, R. W.: Twinned crystals. Advances in Physics, 3, 363-345 (1954).
18.
[18] Friedel, G.: Sur les macles du quartz. Bulletin Societi Francais Miniralogie, 46, 79-95 (1923).
19.
[19] Cady, W G.: Piezoelectricity, Dover, New York, 1946.
20.
[20] Wooster, W A. and Wooster, N.: Control of electrical twinning in quartz. Nature, 157, 405-406 (1946).
21.
[21] Dana, E. S.: A Textbook in Mineralogy, 4th ed. (revised and enlarged by W E. Ford), John Wiley, New York, 1932.
