Evaluation of classical precipitation descriptions for gamma ^{prime prime } ,(hbox {Ni}_{3}hbox {Nb}{-}hbox {D0}_{22}) in Ni-base superalloys

I J Moore,N T Nuhfer,E J Palmiere,M G Burke

doi:10.1007/s10853-017-1091-9

Abstract

The growth/coarsening kinetics of gamma ^{prime prime }, (hbox {Ni}_{3}hbox {Nb}{-}hbox {D0}_{22}) precipitates have been found by numerous researchers to show an apparent correspondence with the classical (Ostwald ripening) equation outlined by Lifshitz, Slyozov and (separately) Wagner for a diffusion controlled regime. Nevertheless, a significant disparity between the actual precipitate size distribution shape and that predicted by LSW is frequently observed in the interpretation of these results, the origin of which is unclear. Analysis of the literature indicates one likely cause for this deviation from LSW for gamma ^{prime prime } precipitates is the “encounter” phenomenon described by Davies et al. (Acta Metall 28(2):179–189, 1980) that is associated with secondary phases comprising a high volume fraction. Consequently, the distributions of both gamma ^{prime prime } precipitates described in the literature (Alloy 718) and measured in this research in Alloy 625 are analysed through employing the Lifshitz–Slyozov-Encounter-Modified (LSEM) formulation (created by Davies et al.). The results of the LSEM analysis show good far better agreement than LSW with experimental distributions after the application of a necessary correction for what is termed in this research as “directional encounter”. Moreover, the activation energy for gamma ^{prime prime } coarsening in Alloy 625 shows conformity with literature data once the effect of heterogeneous (on dislocations) precipitate nucleation at higher temperatures is accounted for.

Highlights

Since its inception in 1961, the cube root law developed on either side of the iron curtain by Lifshitz, Slyozov [13] and Wagner [29] (LSW) to quantitatively describe the phenomenon of spherical particle coarsening (Ostwald ripening), has been successfully applied to several systems [9]
‘‘directional encounter’’ yields a much closer agreement with the both the LSEM and LSW curves; the level and particular type of correspondence varies between studies and ageing conditions: all of the precipitate size distribution (PSD) published by Han et al [11] (Fig. 7a) display a consistent and strikingly good conformity with the constructed LSEM distribution except those measured from precipitates in samples aged at 998 K for durations ! 200 h as both retain a noticeable skew
The PSDs measured by Sundararaman et al [28] show a generally good agreement with LSEM compared to LSW but the specific the shape and level of agreement changes between curves

Summary

Introduction

Since its inception in 1961, the cube root law developed on either side of the iron curtain by Lifshitz, Slyozov [13] and Wagner [29] (LSW) to quantitatively describe the phenomenon of spherical particle coarsening (Ostwald ripening), has been successfully applied to several systems [9]. Using an adaptation defined by Boyd et al [2] a decade later, the LSW approach has been shown to yield an apparently good agreement with experimental measurements of the change in size of non-spherical particles such as c00 (Ni3Nb–D022) in Ni-base alloys [4, 7, 8, 11, 23, 28, 30, 31] Despite this apparent success, closer scrutiny of the results to which the latter formalism has been applied (such a coarsening of h00 precipitates in Al–Cu alloys by Boyd et al [2] in the derivation paper) reveals a marked discrepancy between the real and calculated precipitate size distributions. Such behaviour has been observed for c00 precipitates in a number of studies [11, 23, 26]

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Conclusion