*2.1. Types of Rafting*

Rafting is an important phenomenon of the microstructure evolution in L12 hardened superalloys, such as nickel- and cobalt-based superalloys [21–23]. There are extensive studies on the formation mechanism in single crystal superalloys, which are also applicable to individual grains in polycrystalline superalloys [24]. Here, we are mainly focused on the rafting behavior in single crystals.

Under mechanical loading in <001> direction, raft structures can form in single crystals in the direction either parallel (P-type) or normal (N-type) to the direction of external loading. The factors controlling the rafting orientation mainly include the sign of applied stress, σ*<sup>A</sup>* (positive for tensile loading and negative for compressive loading), the γ/γ' lattice misfit, δ, and the difference in the mechanical behavior between γ and γ' phase, Δ*G* [25,26]. Here, δ = 2 - *a*γ − *a*<sup>γ</sup> / - *a*γ + *a*<sup>γ</sup> , with *a*γ and *a*<sup>γ</sup> being the lattice constants of γ' phase and γ phase, respectively. Δ*G* is usually used to represent the hardness ratio of the γ' precipitate to the γ matrix with Δ*G* > 1 for hard precipitates and Δ*G* < 1 for soft precipitates. The P-type raft structures form under σ*A*δ(1 − Δ*G*) <sup>&</sup>lt; 0, and the N-type raft structures form under σ*A*δ(1 − Δ*G*) <sup>&</sup>gt; 0, as shown in Figure 3. Schmidt and Gross [25] summarized several cases for the raft structures presented in regions (1–7) in Figure 3, in which regions (5–7) represent extreme cases. Note that the raft structures presented in region (5) are only observed in very soft precipitates under compressive loading, and the raft structures presented in regions (6) and (7) are observed in two-phase materials with different Poisson's ratio and/or Zener anisotropy parameter [26].

**Figure 3.** Types of raft structures under mechanical loading in <001> orientation of single crystals and positive lattice misfit. Δ*G* represents the hardness ratio of the γ' precipitate to the γ matrix. Seven different cases are summarized and marked with corresponding numbers in the figure. 1—N-type structure under compression for Δ*G* > 1; 2—P-type structure under tension for Δ*G* > 1; 3—P-type structure under compression for Δ*G* < 1; 4—N-type structure under tension for Δ*G* < 1; 5—N-type structure under compression for Δ*G* < 1; 6—N-type structure under tension for Δ*G* > 1; 7—P-type structure under tension for Δ*G* < 1. Adapted from [25].

The rafting direction plays an important role in determining the mechanical behavior of superalloys. In most cases, the N-type raft structures can reduce the low-cycle fatigue strength of materials and the P-type raft structures generally possess high creep resistance and low-cycle fatigue strength [27–29]. Note that the N-type raft structures can also increase the creep resistance by effectively hindering the motions of dislocations at high temperature under the action of small stress [28] in comparison to the corresponding alloys with cubic γ' precipitates. Mughrabi and Tetzlaff [28] reported that the prerafting to form the P-type raft structures in superalloys with negative γ/γ' lattice misfit also resulted in the improvement in fatigue strength at elevated temperature. Compromise needs to be made in controlling the rafting behavior of superalloys with negative γ/γ' lattice misfit.

Commercial nickel-based superalloys possess negative lattice misfit at room temperature, whose magnitude decreases with the increase of environmental temperature [30,31]. To better describe the effect of lattice misfit on the rafting behavior, cobalt-based superalloys are taken as an example for comparison. Cobalt-based superalloys possess positive lattice misfit at room temperature, whose magnitude also decreases with the increase of environmental temperature, but the lattice misfit remains positive even at temperature of 1000 ◦C [22,31]. Negative lattice misfit in nickel-based superalloys and positive lattice misfit in cobalt-based superalloys at such a high temperature result in the formation of N-type and P-type raft structures under tension, respectively. The opposite behavior is observed under compression.

It is known that a superalloy of single crystal exhibits different mechanical behavior from the corresponding superalloy of polycrystal, and its creep and fatigue properties are extremely sensitive to crystal orientation [32,33]. The complex geometry of single-crystal turbine blades and the multiaxial stress state under service necessitate careful characterization and analyses of the mechanical behavior and γ/γ' microstructure evolution of single crystal superalloys in typical crystal orientations, including <011> and <111>. Under a tensile loading in <011> direction, directional coarsening of γ' phases was found parallel to (010) plane, while equiaxed coarsening behavior was observed in (100) plane, which exhibits a 45-degree rafting [34,35]. Under a tensile loading in <011> direction, no rafting behavior was present [34,36]. However, there always exists a slight misorientation between actual loading direction and <011> or <111> crystal orientation, which can lead to the formation of raft structures different from theoretical results. If the loading direction slightly deviates from <011> direction, see Figure 4 as an example, directional coarsening of γ' phases is still found parallel to (010) plane, but the coarsening behavior in (100) plane is not equiaxed, tending to align along [010] or [001] direction. In the case of loading direction slightly deviating from <111> direction, rafting behavior along one main direction is also observed (Figure 5). These unexpected phenomena were also reported in some works [37–39], which is believed to be related to asymmetric stress distribution in γ/γ' microstructures, caused by a slight misorientation from the loading direction and microdefects randomly distributed in the material. Therefore, the rafting in a superalloy of single crystal is sensitive to the effective loading direction.

**Figure 4.** Microstructures of a nickel-based single crystal superalloy under a tensile loading of 250 MPa at 1253 K, with a 5◦ misorientation from [011] direction. (**a**) Loading diagram of a cubical cell, (**b**) initial microstructure in (100) plane, (**c**) micrograph in (100) plane for 150 h, (**d**) micrograph in (011) plane for 20 h, and (**e**) micrograph in (011) plane for 100 h.

**Figure 5.** Microstructures of a nickel-based single crystal superalloy under a tensile loading of 250 MPa at 1253 K with a 5◦ misorientation from [111] direction. (**a**) Loading diagram of a cubical cell, (**b**) micrograph of initial microstructure in (121) plane, (**c**) micrograph in (121) plane for 300 h, (**d**) micrograph in (111) plane for 20 h, and (**e**) micrograph in (111) plane for 200 h.
