Tetragonal fcc-Fe induced by $\kappa$-carbide precipitates: Atomic scale insights from correlative electron microscopy, atom probe tomography, and density functional theory

Correlative scanning transmission electron microscopy, atom probe tomography, and density functional theory calculations resolve the correlation between elastic strain fields and local impurity concentrations on the atomic scale. The correlative approach is applied to coherent interfaces in a $\kappa$-carbide strengthened low-density steel and establishes a tetragonal distortion of fcc-Fe. An interfacial roughness of $\sim 1\mathrm{nm}$ and a localized carbon concentration gradient extending over $\sim 2–3\mathrm{nm}$ is revealed, which originates from the mechano-chemical coupling between local strain and composition.

Figure 1

STEM images of a needle-shaped specimen taken under (a) ABF, (b) HAADF conditions, and corresponding APT reconstruction illustrated in (c). Pronounced contributions from diffraction contrast are present in the ABF image of (a), as seen in the contrast modulations indicating the location of $\gamma /\kappa$ interfaces. The perimeter of the APT reconstruction is highlighted in (a). In (b) and (c), the location of direct 1:1 correlation of STEM and APT is indicated.

Figure 2

(a) Two-dimensional detector hit-density histogram for the first 2 million ions acquired during the analysis of the dataset shown in Fig. 4. (b) Atomic planes imaged within the tomographic reconstruction; the color code is similar to that used in Figs. 1 and 4. (c) Spatial distribution map performed during the tomographic reconstruction process enabling the measurement of the average spacing between the (002) planes.

Figure 3

(a) Fourier-filtered HAADF-STEM image of a narrow $\gamma -\mathrm{Fe}$ matrix channel in between two $\kappa$-carbide precipitates. (b) Color coded image of (a) based on the nearest-neighbor intensity difference of atomic columns. A value of 0 indicates the disordered $\gamma -\mathrm{Fe}$ matrix, and values of $>2$ represent the chemically ordered $\kappa$ phase. In-plane strains (c) ${\varepsilon }_{xx}$ and (d) ${\varepsilon }_{yy}$ and shear strain (e) ${\varepsilon }_{xy}$ with respect to a reference region defined in the left $\kappa$ precipitate. The reference region (ref) for strain determination is indicated in (a).

Figure 4

Direct 1:1 correlation of atomic resolution STEM and APT. The APT reconstruction was refined on the corresponding subvolume using crystallographic information from the detector map and the corresponding structural information from STEM. (a) Superimposed HAADF-STEM image (gray) and APT reconstruction of a 1.5 nm thick slice projected along [001] $\gamma /\kappa$. (b) APT concentration profile extracted across the horizontal $\gamma /\kappa$ interface highlighted by the arrow in (a). STEM-deduced in-plane strains (c) ${\varepsilon }_{xx}$ and (d) ${\varepsilon }_{yy}$ and shear strain (e) ${\varepsilon }_{xy}$ with respect to the reference region (ref) defined in the wide $\gamma -\mathrm{Fe}$ matrix channel indicated by the white square.

Figure 5

(a) Solution enthalpy for two C concentrations in $\gamma -\mathrm{Fe}$ computed at fixed volumes as a function of imposed tetragonal strain for AFMD (double-layer antiferromagnetic) and PM (paramagnetic) states. The tetragonal strain present in the experiment, for AFMD and PM $\gamma -\mathrm{Fe}$, is indicated by vertical arrows. (b) C concentration in $\gamma -\mathrm{Fe}$ as a function of tetragonal strain at 298 and 873 K. Here, the $\gamma -\mathrm{Fe}$ matrix is treated in the AFMD state. The pluses and crosses indicate values resembling the broad, cubic $\gamma$ channels. $v_{\kappa }:v_{\gamma }$ is the volume fraction ratio of $\kappa$ and $\gamma$.