Observation of annealing twin nucleation at triple lines in nickel during grain growth
Graphical abstract
Introduction
Annealing twins, separated from parent grains by long straight grain boundaries, are one of the most common and easily recognizable features in face centered cubic (FCC) metals with stacking fault energies less than about 0.15 J/m2. Examples include metals and alloys such as Ni, Cu, Au, brass, and superalloys. Most notable in materials that have undergone recrystallization and grain growth, the twin boundary disorientation is 60° about a common 〈1 1 1〉 axis. When the boundary lies in the (1 1 1) plane of both crystals, the unique, low energy structure of these (coherent) twins [1], [2] confers improved intergranular properties; this is one of the special boundaries that are exploited in grain boundary engineering [3], [4], [5]. Twins in FCC metals have also been implicated in the strengthening of nanostructured Cu [6], the nucleation of fatigue cracks [7], and the stagnation of grain growth [8]. While methods to increase the twin boundary concentration through thermomechanical processes are known [3], [4], [5], [9], [10], we know much less about the mechanism of annealing twin formation.
The proposed mechanisms for twin formation can be classified into three categories. The first is that twins form when crystals that already have a twin relationship impinge during growth [11], [12]. The second assumes that a twin forms when growth occurs and a layer of atoms on the (1 1 1) plane is misplaced in the twin relationship; further growth on this misplaced layer leads to a twinned crystal [13], [14], [15], [16]. The third involves the replacement of higher energy grain boundaries with a combination of a twin boundary and lower energy grain boundaries [17], [18], [19], [20]. The available evidence cannot discriminate between these mechanisms for the case of grain growth because twins form within bulk metals that are opaque to visible light and electron beams. This makes it impossible to use standard probes to observe the three dimensional structure and crystal orientations before and after the twin has formed. For example, serial sectioning cannot be directly applied to this problem because the sample is destroyed during analysis [1], [21], [22] and transmission electron microscopy can only visualize the structure within very thin, nearly two-dimensional, samples. However, the recent development of near-field high-energy X-ray diffraction microscopy (nf-HEDM) [23], [24], [25], [26], [27], [28] and X-ray diffraction contrast tomography [29], [30] enables non-destructive measurements of the shapes and orientations of grains within a bulk sample at sequential stages during annealing.
In this paper, we consider the boundary replacement mechanism for twin formation during normal grain growth. Fig. 1 illustrates the most important aspects of the theory [20]. The figure depicts three grains (labeled 1, 2, and 3) meeting along a triple line. The grain boundary energies per area (γij), dihedral angles (θij), and areas (Aij), are labeled with subscripts that denote the relevant crystals. If a part of grain 2 adjacent to the triple line is replaced by a new grain with the twin disorientation, then a twin boundary is introduced and assumed to be on a (1 1 1) plane. The formation of this new grain reduces the energy if the following condition is met [20]:
Given the relatively low energy of the twin (γT = 0.06 J/m2 for Ni) and the significant anisotropy of other grain boundaries [2], there should be many combinations of grains where this condition is met. According to Herring’s [31] interfacial equilibrium condition, a decrease in the total energy should lead to observable changes in the dihedral angles such that θ′13 < θ13 and θ23 + θ12 < θ1T + θ3T.
Fullman and Fisher [17], and later Murr [20], provided strong albeit indirect evidence for the mechanism depicted in Fig. 1. With previously available techniques, it was simply not possible to observe the same triple junction before and after the event. The repetitive non-destructive three-dimensional structural characterization afforded by nf-HEDM [23], [24], [25], [26], [27], [28] makes it possible to directly observe the boundary replacement mechanism, if it occurs, and to evaluate the grain boundary crystallography and grain boundary dihedral angles. In this paper, results from high purity Ni annealed at 800 °C show that twins form at triple lines, as depicted above, and that the process decreases the total interfacial energy.
Section snippets
Methods
The three-dimensional microstructure of a Ni sample was measured in three different grain growth anneal states using nf-HEDM. The data from each anneal state was compiled as a discrete cubic grid of integers (grain identifiers) that are associated with a set of three Euler angles that describe the orientation of the crystal with respect to the external reference frame. The size of each voxel is 2 μm × 2 μm × 4 μm, in x, y and z, respectively. The x-y plane spanned a total of 600 × 600 voxels, while the z
Results
An example of the three-dimensional Ni microstructure, interpreted from the nf-HEDM data, is illustrated in Fig. 2 . The microstructure of the wire shaped specimen was established by a 2 h anneal at 750 °C that recrystallized damage from the wire drawing process. The microstructure contains many twins, which are apparent as long straight boundaries. One particular twinned grain that is visible on two perpendicular sections is indicated by the white arrows. The microstructure was measured in the
Discussion
It should be noted that the new twin-related grains observed here must have started at sizes that were initially below the threshold for detection. The voxel size in the nf-HEDM data is about 2 μm × 2 μm × 4 μm in the x, y, and z directions, respectively. Considering that the twins all grew after detection, we assume that this trajectory was the same since they first formed. As long as the energy criterion in Eq. (1) is satisfied, the growth of the twin is energetically favorable along the two
Conclusion
The present results demonstrate the utility of nondestructive three-dimensional characterization to measure changes in the grain boundary network during grain growth. The results show that during grain growth in a fully recrystallized microstructure at 800 °C, twins nucleate at triple lines in Ni. The results also show that this process reduces the total grain boundary energy. The selection criteria for the triple junctions that nucleate twins is not currently clear, but they are likely to
Acknowledgments
B.L., A.D.R., and G.S.R. were supported by the Materials World Network of the National Science Foundation (NSF – United States) under Award No. DMR-1107896. Y.J., M.B., and N.B. were supported by the French National Research Agency (Grant number ANR-11-NS09-001-01). C.M.H., S.F.L., J.L., R.M.S. were supported by NSF Grant DMR-1105173. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No.
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- 1
Current affiliation: RJ Lee Group, 350 Hochberg Rd., Monroeville, PA 15146, USA.
- 2
Current affiliation: Materials Engineering Division, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94551, USA.