Landau Theory and Martensitic Phase Transitions

Landau theory proved i t s e l f appropriate f o r descr ibing phase t r a n s i t i o n s i n systems such a s f e r r o e l e c t r i c s and ferromagnets. Primarily Landau establ ished the theory f o r second order phase t r a n s i t i o n s . Later on Devonshire generalized Landau's approach t o f i r s t order t r a n s i t i o n s . The essen t ia l point of Landau theory i s a power s e r i e s expansion of t h e f r e e energy, depending on temperature and on an order parameter describing the phase t r a n s i t i o n . In order t o deal with phase boundaries t h e theory has been generalized t o Ginzburg-Landau theory by adding a term depending on the gradient of t h e o rder parameter. I n s p i t e of t h e success of Landau and GinzburgLandau theory i n the systems mentioned above only l i t t l e work has been done concerning mar tens i t i c phase t r a n s i t i o n s . D i f f i c u l t i e s a r i s e from the f a c t t h a t the deformation of t h e u n i t c e l l does not coincide with the macroscopic s t r a i n . Considera t i o n s f o r overcoming t h i s problem a r e discussed. I t seems t h a t even in the case of mar tens i t i c phase t r a n s i t i o n s Landau theory may be used as a s t a r t i n g point t o obt a i n deeper i n s i g h t i n t o phenomena such as s o f t modes, nucleation, and the ro le of l a t t i c e d e f e c t s . 1. Introduct ion. For more than f i v e decades mar tens i t i c phase t r a n s i t i o n s have been s tudied with growing e f f o r t . In the beginning the notion of martensi te was def ined f o r ferreous a l l o y s , namely s t e e l . Later on phase t r a n s i t i o n s very s i m i l a r t o the c l a s s i c a l mar tens i t i c one were discovered i n a l o t of non-ferrous a l l o y s too. Today i t seems t h a t the t r a n s i t i o n s in non-ferreous a l loys a r e more typical and show the underlying pr inc ip les more c l e a r l y . From the very beginning mar tens i t i c phase t r a n s i t i o n s were the domain of meta l lu rg i s t s . Insp i te o f the high prac t ica l s ign i f icance in mater ials science and technology, phys ic i s t s 1 ooked upon t h i s type of phase t r a n s i t i o n s i n s t e e l s as d i r t y and unpromising. Instead phase t rans i t ions such as liquid-vapour o r ferromagnetic-paramagnetic were i n vogue. Later the evol u t i o n i n both the areas took place r a t h e r independently. In physics phase t r a n s i t i o n s were d e a l t with, i n the beginning, by phenomenolog ica l theor ies which simply describe t h e phenomena on a macroscopic s c a l e containing many atoms. The f i r s t equation of s t a t e representing a phase t r a n s i t i o n was suggested by van der Waals i n 1873. In 1937 Landau es tab l i shed h i s famous theory of second order phase t r a n s i t i o n s [ I ] which was extended by Devonshire [2,3] t o f i r s t order phase t r a n s i t i o n s i n 1949. In order t o deal with phase boundaries the phenomenological theor ies were generalized t o Ginzburg-Landau theory. Later on the microscopic foundation of the theories men t i oned above was pushed forward. From s t a t i s t i c a l mechanics the phenomenological theor ies can be drived using the mean f i e l d approximation neglecting f luc tua t ions . In s p i t e of t h i s r e s t r i c t i o n the phenomenological theor ies a r e very successful i n describing a l o t of phase t r a n s i t i o n phenomena. Nevertheless they were not appl ied t o mar tens i t i c phase t r a n s i t i o n s u n t i l recen t ly , presumably because of a lack i n col laborat ion between metallurgy and physics. The aim of t h i s paper i s t o give a survey both, o f the phenomenological theor ies of phase t r a n s i t i o n s and of t h e i r app l ica t ion t o martensi t i c phase t r a n s i t i o n s . In Chapter 2 we present the bas ic ideas of the phenomenological theor ies (Landau, Devonshire, and Ginzburg-Landau theory) . In Chapter 3 applicat ions a r e discussed. The l a s t chapter deals with mar tens i t i c t r a n s i t i o n s and t h e i r descr ip t ion using Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982401 C4-4 JOURNAL DE PHYSIQUE the theor ies mentioned above. The s p e c i f i c problems as w e l l as the poss ib le scope are ou t l i ned . 2. Phenomenological theor ies of phase t r a n s i t i o n s