On Certain Weak Phase Transformations in Multilattices

Journal of Elasticity

Volumn 72, Issue 1-3, 2003, Pages 241-261

  Pitteri, Mario ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

crystalline solids; phase transformations; physical possibility; quartz; thermoelasticity

Indexed keywords

CRYSTALLINE MATERIALS; EMPLOYMENT;

CLIFFORD; CRYSTALLINE SOLIDS; JOHN HOPKINS UNIVERSITY; MULTILATTICE; PHASES TRANSFORMATION; PHYSICAL POSSIBILITY; THERMO-MECHANICS;

PHASE TRANSITIONS;

EID: 78651284590     PISSN: 03743535     EISSN: 15732681     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000018779.45974.97     Document Type: Article

References (22)

1. A. Bressan, Metodo di assiomatizzazione in senso stretto della meccanica classica. Applicazione di esso ad alcuni problemi di assiomatizzazione non ancora completamente risolti. Rend. Sem. Mat. Univ. Padova 32 (1962) 55–212.
2. A. Bressan, A General Interpreted Modal Calculus. Yale Univ. Press, New Haven/London (1972). Foreword by N.D. Belnap, Jr., 327 pages.
3. A. Bressan, (a) On physical possibility and (b) Supplement: A much used notion of physical possibility and Gödel's undecidability theorem. In: M. Dalla Chiara Scabbia (ed.), Italian Studies in Philosophy of Science. North-Holland, Amsterdam (1981) pp. 197–210 and 211–214.
4. B. Budiansky and L. Truskinovsky, On the mechanics of stress-induced phase transformations in zirconia. J. Mech. Phys. Solids 41 (1993) 1445–1459. DOI: 10.1016/0022-5096(93)90034-D
5. J.L. Ericksen, Local bifurcation theory for thermoelastic Bravais lattices. In: J.L. Ericksen, R.D. James, D. Kinderlehrer and M. Luskin (eds), Microstructure and Phase Transition, IMA Volumes in Mathematics and its Applications, Vol. 54. Springer, New York (1993).
6. J.L. Ericksen, On the theory of the α-β phase transition in quartz. J. Elasticity 63 (2001) 61–86. DOI: 10.1023/A:1013047100380
7. G. Fadda, L. Truskinovsky and G. Zanzotto, Unified Landau description of the tetragonal, orthorhombic, and monoclinic phases of zirconia. Phys. Rev. B 66 (2002) 174107 1–10. DOI: 10.1103/PhysRevB.66.174107
8. M. Golubitsky, D. Schaeffer and I. Stewart, Singularities and Groups in Bifurcation Theory, Vol. II. Applied Mathematical Sciences, Vol. 69. Springer, New York (1988).
9. G. Hamel, Ñber die Grundlagen der Mechanik. Math. Annalen 66 (1908) 350–397. DOI: 10.1007/BF01450694
10. G. Hamel, Die Axiome der Mechanik, Handbuch der Physik, Vol. 5. Springer, Berlin (1927) pp. 1–42.
11. T. Hahn (ed.), International Tables for X-ray Crystallography, Vol. A. Reidel, Dordrecht/ Boston (1996).
12. R.D. James, The stability and metastability of quartz. In: S.S.Antman, J.L. Ericksen, D. Kinderlehrer and I. Müller (eds), Metastability and Incompletely Posed Problems, IMA Volumes in Mathematics and its Applications, Vol. 3. Springer, New York (1987).
13. P. Painlevé, Les Axiomes de la Mécanique. Gauthier-Villars, Paris (1922).
14. M. Pitteri, On the axiomatic foundations of temperature. In: C. Truesdell's Rational Thermodynamics, 2nd edn. Springer, New York (1984) Appendix G6, pp. 522–544.
15. M. Pitteri, On bifurcations in multilattices. In: R. Monaco, M. Pandolfi and S. Rionero (eds), Proc. of WASCOM 2001, Porto Ercole, Italy. World Scientific, Singapore (2002).
16. M. Pitteri, On certain weak phase transformations in multilattices. TMR Network "Phase Transitions in Crystalline Solids" Preprint Series, No. 100 (2002). Also Rapporto Tecnico DMMMSA No. 88, 2/12/2002. Available at http://www.dmsa.unipd.it/tmr/publichtml/PreprintDMMMSA.pdf.
17. M. Pitteri and G. Zanzotto, Continuum Models for Phase Transitions and Twinning in Crystals. CRC/Chapman & Hall, Boca Raton/London (2002).
18. N.K. Simha and L. Truskinovsky, Phase diagram of zirconia in stress space. In: R. Batra and M. Beatty (eds), Contemporary Research in the Mechanics and Mathematics of Materials. CIMNE, Barcelona (1996).
19. P. Tolédano and V. Dmitriev, Reconstructive Phase Transformations: In Crystals and Quasicrystals. World Scientific, Singapore (1996).
20. C.A. Truesdell, An Idiot's Fugitive Essays on Science: Methods, Criticism, Training, Circumstances. Springer, New York (1984).
21. C.A. Truesdell, Rational Thermodynamics, 2nd edn. Springer, New York (1984).
22. C.A. Truesdell and R.G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics. Academic Press, New York (1980).