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CASCADE EFFECTS IN NON EQUILIBRIUM PHASE TRANSITIONS WITH METALLURGICAL RELEVANCE

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HAL Id: jpa-00229462

https://hal.archives-ouvertes.fr/jpa-00229462

Submitted on 1 Jan 1989

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CASCADE EFFECTS IN NON EQUILIBRIUM PHASE TRANSITIONS WITH METALLURGICAL

RELEVANCE

P. Bellon, G. Martin

To cite this version:

P. Bellon, G. Martin. CASCADE EFFECTS IN NON EQUILIBRIUM PHASE TRANSITIONS

WITH METALLURGICAL RELEVANCE. Journal de Physique Colloques, 1989, 50 (C3), pp.C3-

133-C3-134. �10.1051/jphyscol:1989321�. �jpa-00229462�

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JOURNAL DE PHYSIQUE

Colloque C3, suppl6ment a u n 0 3 , Tome 50, Mars 1989

CASCADE EFFECTS IN NON EQUILIBRIUM PHASE TRANSITIONS WITH METALLURGICAL RELEVANCE

P. BELLON and G. MARTIN*

C E C M - C N R S , 1 5 r u e G. Urbain, F-94407 Vitry Cedex, France 'CENS-SRMP, F-91191 Gif-sur-Yvette Cedex, France

The order disorder transition (antiferromagnetic with conserved total spin) in the B2 structure i s studied when atomic interchanges result from two processes in parallel, a s is the case under energetic particle irradiation: thermally activated jumps and ballistic jumps. The latter favor fully disordered configurations (infinite temperature dynamics), while t h e former tend to restore some degree of order. The appropriate mean-field phase diagram is established, based on a deterministic description of the order disorder kinetics : in the latter, the thermally activated interchange frequencies have been chosen in such a way t h a t in the absence of forced interchange, the steady state value of the order parameter a s predicted by the kinetic model coincides with the equilibrium value given by a simple mean-field thermodynamic description of t h e equilibrium state of the alloy. When t h e infinite temperature dynamics is operating, a tricritical point is identified below which the non-equilibrium order disorder transition becomes first order.

Stochastic effects a r e addressed by a Master Equation, t h e transition probabilities of which are built from the atom jump frequencies entering the deterministic description. I t is shown that in the absence of forced exchanges, the steady state probability of t h e order parameter coincides with t h a t of the mean-field thermodynamics. When forced interchanges a r e operating, the free energy function is replaced by a stochastic potential which can be computed explicitly and helps comparing the respective stability of competing states. Introducing forced interchanges by bursts (replacement cascades) does not change t h e order parameter values with extremal steady state probability, but definitely affects their respective stability. The latter cannot anymore be evaluated from the Master Equation, but from a Fokker Planck equation obtained by a Taylor expansion of the former with respect to the inverse volume of the system. Below t h e tricritical temperature, cascade effects shift the phase boundary of the first order transition towards the spinodal ordering l i n e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989321

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C3-134 JOURNAL

DE

PHYSIQUE

A similar treatment i s given for the DO23 and D l a structures which are superstructures of the

FCC lattice a n d for which irradiation is known to induce inversions of respective stability (Ni4Mo). T h e full dynamical phase equilibrium diagram i s constructed following the above technique ; t h e phase boundary between the two ordered structures is very sensitive to the size of the cascades (cf. Fig.).

T h e details of this work are published in the following references:

P.Bellon a n d G.Martin:

-

i n "Non linear phenomena in materials science", edited by L.Kubin and G.Martin (Trans Tech,1988) p.109;

-

Phys. Rev. =,2570(1988);

-

Phys. R e v . B i n the press;

-

Proc. MRS Boston 1988, Symposium Q, in the press.

Fig. Dynamical equilibrium diagram for Ni4Mo under irradiation : T i s the temperature, yo t h e ratio of the forced interchange frequency to t h e prefactor of t h e thermally activated frequency.

LRO (SRO) point respectively to t h e Dl,, (DOgg) stability field,

---

i s the Dl, ordering spinodal, T p t h e tricritical point, b (1 or 100) i s t h e cascade size, i.e. t h e number of forced interchanges per u n i t ballistic event. [BUW] : existing experimental data.

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