Elsevier

Acta Materialia

Volume 49, Issue 14, 16 August 2001, Pages 2661-2669
Acta Materialia

Atomistic study of the coherency loss during the B.C.C.–9R transformation of small copper precipitates in ferritic steels

https://doi.org/10.1016/S1359-6454(01)00178-1Get rights and content

Abstract

Using 3D atomistic static simulations, we first investigate the atomic coherency between a small twinned 9R embryo (less than 6 nm in diameter) and the b.c.c. Fe matrix. We show that the (114̄)9R planes of the precipitate are aligned with the (11̄0)b.c.c. planes of the matrix, and that the coherency loss of the precipitate/matrix interface is due to the formation of dislocation loops inside the precipitate. Then, we use 3D atomistic simulations to study the structure changes of an initially b.c.c. copper precipitate and show that the structure evolves towards a 9R structure. Finally, we use the above results to propose a simple geometric mechanism which may be relevant for the b.c.c./9R transformation at low temperature and when the influence of vacancies can be neglected.

Introduction

Due to the very low solubility of copper in iron, thermal aging of irradiated steels containing residual levels of copper leads to the formation and growth of Cu-rich clusters in the Fe matrix. It is now well known that irradiation hardening and related embrittlement of pressure vessel steels are at least partially due to the precipitation of copper [1], [2], [3], [4]. Recent investigations on model alloys using HREM [5], [6], [7], [8] have shown that the growing precipitates undergo a transformation from the b.c.c. structure to a twinned 9R. (The 9R structure may be considered as a close-packed structure with stacking faults every third close-packed plane. Thus, the stacking sequence of the close packed planes is ABC/BCA/CAB/….) The Cu content inside the precipitates was shown to be higher than 95% [9], [10]. Upon further aging, the Cu precipitates grow and transform to a 3R structure, and finally reach the expected f.c.c. structure. Up to now, the microscopic mechanism of this complex series of structural transformations has not been well understood.

A hard sphere model of the b.c.c. to 9R martensitic transformation in bulk Cu-based alloys was first proposed by Ahlers [11], based upon the mechanism suggested by Bogers and Burgers [12]. The model agrees well with experimental observations of the transformation in Cu-based alloys and has the advantage over other transformation models (e.g. [13], [14]) of providing a description of the atomic displacements during the transformation. However, there is a good agreement between the various models on the correspondence between planes in the parent and product structures. In particular, the (114̄)9R and (001)9R martensite planes are both reported to be inherited from {011}b.c.c. planes.

These models, developed for the b.c.c.–9R martensitic transformation in bulk Cu-based alloys, lead to orientation relationships which agree very well with the observations of the 9R copper precipitates following transformation from a b.c.c. structure coherent with the ferritic matrix [6]. Furthermore, the smallest 9R embryos of Cu precipitates always consist of two twin-related variants separated by a (114̄)9R type plane. These embryos are very similar to the morphology observed in the initial stages of bulk transformation from b.c.c. to 9R in Cu–Zn alloys [14]. Thus, it has been suggested [6] that the model developed by Ahlers for the b.c.c.–9R martensitic transformation in bulk Cu-based alloys would also apply for the transformation in Cu precipitates.

However, the first step of the Ahlers model is a very large shear along the (110)b.c.c. plane in the [1̄10]9R direction which transforms the (011)b.c.c. planes into closed packed planes. The amplitude of the shear is γ=0.25. Such a large shear would significantly change the shape of the spherical precipitates. To maintain the coherency observed at the interface by HREM, the Fe matrix has to follow the shape change of the precipitate, implying displacements too large to be reached by elastic distortions only, and topological defects would form in the matrix which have never been observed. In other words, Ahlers' model, developed for the b.c.c.–9R transition in bulk samples, does not take into account the influence of the surrounding Fe matrix. Therefore, its validity can be questioned when studying precipitates smaller than a few nanometers.

A simple way to better understand the structural transformations in copper precipitates is to perform atomistic simulations. Using static relaxation of an embedded atom method (EAM) potential, Ludwig et al. [15] have studied the instability of b.c.c. copper precipitates embedded in an α-Fe matrix. When the diameter of the precipitate is 4 nm, the authors observe that the b.c.c. structure of the precipitates is stabilized by the interface with the matrix. When the diameter of the precipitate is larger than 6 nm, the simulations predict the development of an instability within the copper precipitates. However, this instability was not studied in detail. As it will be shown later, the details of this instability are important to better understand the atomic mechanism of the b.c.c.–9R structural transformation in the copper precipitates.

Vacancy concentration and distribution have been shown to influence the stability of the b.c.c. copper precipitates [16], [17], and thus the critical size for the b.c.c.–9R transformation of the copper precipitates. In the present paper, we focus on the b.c.c.–9R transformation mechanism in the limit of small vacancy concentration.

We only consider here the b.c.c.–9R transformation in small copper precipitates, i.e. in precipitates with a diameter less than 6 nm. In that case, the b.c.c. precipitates directly transform into a 9R embryo containing two twin domains [5], [6], [7], [8], because a single 9R domain formation would cost a prohibitive elastic energy. The b.c.c.–9R transformation in larger precipitates, where we expect the formation of a large number of twin domains, has been recently studied using molecular dynamics simulations [16]. When the diameter is larger than 8 nm, the authors show that the b.c.c.–9R transformation starts simultaneously in several parts of the precipitate. However, this heterogeneous nucleation makes the structure analysis more difficult, and sometimes hides the simple geometric arguments that we will point out with our study of the small 9R embryos.

In this work, the structure of the copper precipitates is studied using 3D atomistic static simulations. The first part of this paper is a detailed geometric study of a 9R copper embryo embedded in the α-Fe matrix. Particular attention is paid to the interface coherency at the atomic level. In the second part the evolution of an initially b.c.c. copper precipitate as predicted by energy minimization using EAM potentials is presented. Finally, the last part summarizes the microscopic b.c.c.–9R transformation pointed out by the simulations.

Section snippets

Geometrical description

Several potentials have been developed for Fe–Cu alloys [15], [17], [18]. Since these potentials are fitted on properties of the most stable phase (b.c.c. for iron, f.c.c. for copper), the predictions for the b.c.c. and 9R structure of copper have to be checked before using a particular potential. We have chosen the EAM potential developed for Fe–Cu alloys by Ludwig et al. [15], based on the potentials developed by Simonelli et al. [19] for iron and by Voter [20] for copper. This potential has

Mechanism of the b.c.c.–9R transformation in copper precipitates

After the structural description of the copper precipitates given in Section 2, this section deals with the b.c.c.–9R transition mechanism of the copper precipitates. First, the simulation predictions obtained by minimization of a EAM energy are carefully analyzed. Then, the microscopic model of the b.c.c. to 9R transition, suggested by the simulations, is presented. Finally, the energy and stability of the 9R precipitates are discussed.

Summary and conclusion

In the first part of the paper, the atomic structure of a small twinned 9R Cu precipitate (less than 6 nm in diameter) embedded in the α-Fe matrix, has been studied by a geometrical approach and using a static relaxation technique. The analysis of the 3D structure of the precipitates shows that:

    (i)

    The (114̄)9R planes of the precipitates are aligned with the (1̄10)b.c.c. planes of the matrix.

    (ii)

    The structure of the (114̄)9R and (1̄10)b.c.c. planes is very similar: both planes can be generated

Acknowledgements

The author would like to thank Dr A. Barbu for providing the HREM images. Many helpful and insightful discussions with Dr D. Rodney and G. Martin are gratefully acknowledged.

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    Now at Laboratoire d'Etude des Microstructures, CNRS/ONERA, 29 av. de la Division Leclerc, B.P. 72, 92322 Châtillon Cedex, France.

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