Ferritic Alloys with Extreme Creep Resistance via Coherent Hierarchical Precipitates

There have been numerous efforts to develop creep-resistant materials strengthened by incoherent particles at high temperatures and stresses in response to future energy needs for steam turbines in thermal-power plants. However, the microstructural instability of the incoherent-particle-strengthened ferritic steels limits their application to temperatures below 900 K. Here, we report a novel ferritic alloy with the excellent creep resistance enhanced by coherent hierarchical precipitates, using the integrated experimental (transmission-electron microscopy/scanning-transmission-electron microscopy, in-situ neutron diffraction, and atom-probe tomography) and theoretical (crystal-plasticity finite-element modeling) approaches. This alloy is strengthened by nano-scaled L21-Ni2TiAl (Heusler phase)-based precipitates, which themselves contain coherent nano-scaled B2 zones. These coherent hierarchical precipitates are uniformly distributed within the Fe matrix. Our hierarchical structure material exhibits the superior creep resistance at 973 K in terms of the minimal creep rate, which is four orders of magnitude lower than that of conventional ferritic steels. These results provide a new alloy-design strategy using the novel concept of hierarchical precipitates and the fundamental science for developing creep-resistant ferritic alloys. The present research will broaden the applications of ferritic alloys to higher temperatures.

Figure S1b is a DF-TEM image acquired, using the <111> reflection, and exhibits the narrow dark zones within the L2 1 precipitate. The DF-TEM image in Figure S1c, using the <020> reflection, reveals narrow zones within the parent L2 1 phase, showing a higher intensity than the surrounding L2 1 -precipitate phase. The DF-TEM image, using the <111> reflection in Figure S1b, which is unique to the L2 1 structure, exhibits the possible presence of anti-phase boundaries (APBs) or a second phase (B2-NiAl) within the L2 1 phases. Moreover, the DF-TEM image, using the <020> reflection in Figure S1c, which is common to both phases, presents the same narrow zones, but brighter contrast than those originating from the L2 1 precipitates. Since APBs should be invisible, when imaged using the <020> or <222> reflections 1 , and the B2-NiAl has a higher structure factor, relative to the L2 1 structure 2 , the bright contrast zones in Figure S1c are considered as the B2 phases.
 ND Experiment Figure S2 shows the representative ND patterns of (a) and ( (Figures 1b, 1c, and Figure S1), the superlattice reflections are believed to originate from the parent L2 1 phase, although ND cannot detect the superlattice reflections (e.g., 111 and 311 peaks, which are unique to the L2 1 structure) due to the limited intensity of neutrons.
Moreover, the ND with the limited resolution appeared to be incapable of detecting the B2 phase. Thus, the Rietveld refinement 3 was conducted with an assumption of the presence of the Fe matrix and L2 1 phases for both HPSFA and SPSFA.
The averaged phase strain represents the volume-averaged lattice strain of the individual phase (Fe or L2 1 ), which depends on the elastic and plastic anisotropy of the individual phases. In order to obtain the averaged phase strain, a whole-pattern Rietveld refinement was performed to fit the entire ND spectrum, employing the GSAS Program developed at the Los Alamos National Laboratory 3 . The average phase strain is calculated, using the following formula where is the lattice parameter of a given phase measured during heating and/or loading, and 0 is the corresponding lattice parameter before loading (5 MPa at 973 K). The lattice parameters extracted from the Rietveld-refinement approach were utilized for the misfit calculations, which is defined as where is the lattice misfit, and and 2 1 are the lattice parameters of Fe and L2 1 phases, respectively. 4 Lattice parameters of the precipitate and matrix were determined at room temperature, using the Rietveld refinement 3 . Note that the lattice parameter of the L2 1 structure phase is about 2 times larger than that of the BCC Fe structure, since a L2 1 structure consists of eight sub-lattices of a BCC structure 4  

Finite-Element Crystal-Plasticity Model
The crystal-plasticity constitutive relationship and the lattice-strain evolution defined in the present simulation are discussed below. The kinematics is described, using the multiplicative decomposition: In this case, F ik e represents the elastic portion, and F kj p stands for the plastic portion of the total deformation gradient, F ij . The elastic-constitutive behavior is described, using the following relationship, In this case, E kl e is the Lagrange-Green strain, and T ij represents the material-stress tensor, which is related to the Cauchy stress, σ ij , through the following relationship, As for the plastic portion, F kj p , the following relationship was considered, where NSLIP is the total number of slip systems, γ̇( α) is the strain rate of slip, and s i (α) and m j (α) represent the slip direction and slip plane normal, respectively, of the α-th system.
The hardening law employed in this model is expressed in terms of, However, for the self-hardening model, we use, where h 0 is the initial hardening modulus, τ 0 is the initial slip strength, and τ s is the saturated slip strength. γ̇0 (α) is the characteristic strain rate, n is the stress component, and h αβ is the latent hardening moduli. The terms, τ (α) and τ flow (α) , are the resolved shear stress and flow strength of the α-th slip system, respectively, is the stress exponent, and q is the latent-hardening coefficient in the same set of slip systems.
The orientations of each Fe grain were set to be random within the setup of the model. In order to simulate the lattice-strain behavior and compare that to the experimental results obtained from the ND results, a certain set of grains, which have the orientation, <hkl>, whose degree angles are within a certain range of error margins from the diffraction vector, Q, was selected. This set of grains is normally about 2 % of the total grains, and the orientation error margin is normally set to be ± 5°, compared to the vector, Q 5 .

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The thermal-residual simulation includes a thermally-heating model from room temperature up to 1,023 K, followed by applying a uniaxial stress of 650 MPa. The preexisting thermal stress will generate a residual stress within the model, therefore resulting in a differentiated starting point for the lattice strain in the stress versus lattice-strain diagram (e.g., Figure 3e). The beginning points were, then, adjusted to be starting at the origin again     Note that the HPSFA specimens were aged at 973 K for 100 hours, followed by creep tests, and the precipitate sizes of HPSFA were derived from the grip sections of the crept samples at 973 K (no stress). The FBB8 specimens were aged at 973 K as a function of time 6 . Since the precipitate of HPSFA is of an elongated shape, as observed in Figures 1b, 1c, 5b, and Figures S1b, and S1c, the width and length of the precipitate were separately determined. In contrast, since the precipitate of FBB8 has a spherical morphology, as observed in Figure 1a, the diameter of the precipitate was employed.  Correspondences and requests for materials should be addressed to the corresponding and