Morphological stability study in binary alloys II. Stability of coherent concentration modulations

Abstract

The stability of a precipitated two phase structure is analysed with respect to changes in number and size of the precipitated domains, using the equilibrium interfacial concentration profile and width of part I of this paper, and keeping the precipitate volume fraction at a constant value. Thereby the total system energy may show an absolute minimum at a finite precipitate size, if the ratio η out of the interfacial self energy component and of the pair potential strength stays below a certain value in the case of ordering alloys. This is caused by an increase of the absolute value of the negative pair interaction energy component during coarsening, leading to a drop of the interface energy density. η is fitted to parts of the FeAl and the CuAl phase diagrams, leading to a transition region between classical one and two phase zones of the phase diagram, that is characterized by an unorthodox kinetic behaviour of the microstructure. This microstructure might interpret several experiments.

Short‐Range Order and Atomic Displacements in Ni–20 at% Cr Single Crystals

“…The K-state hasamong other explanationsbeen associated with long-range order and short-range order. For the long-range ordered case, highly ordered particles in a partially ordered matrix ("disperse order" [9]) have been suggested, e.g. by [lOj, for anexplanationof the anomaly in the specific heat (see [2, 111 for a critical discussion) and by [8] who observed "small homogeneous coherent precipitates by matrix strain contrast" in a transmission-electron microscope, that were unable t o coarsen.…”

Ordered domain characterization in α-Cu-Al alloys from dissolution kinetics studies

“…In agreement with the present computations, it was concluded that de-coarsening together with a decrease of the number of regions -Are with increasing Ta will take place. The decrease of Are with increasing Ta was also predicted for Cu-15AI by Aubauer's theory [48] for the stability of coherent concentration modulations.…”

“…The consideration of concentration fluctuations in addition to the statistical concept of SRO can account for the onset of disperse-order formation. Such a consideration was used recently by Trattner and Pfeilner [53] and by Pfeiler et al [54] for explaining relaxation behaviour in alloys which do not follow a single exponential process [34,48,55].…”

Morphological stability study in binary alloys. I. Discrete lattice theory and application to interfacial zone

“…This is connected with a decrease of the interfacial energy density. All of this stands in contrast to the clustering case and is analysed in more detail in the second part [22]. Moreover, as a difference to plane interfaces an asymmetric concentration profile appears in case of a finite value of the precipitate size.…”

“…The constants yo and yl originate from pure-metal properties and are irrelevant for interface features, while y ( T ) , c,, and cB are derivable from the concerned phase diagram (as done in [22]). The density g(c) can be found by combining f ( c ) of (11) with the elastic energy, as it is performed in (3).…”