Many steels rely on dispersion hardening with transition metal carbides or carbonitrides. Ti_xV_(1-x)C_yN_z precipitates are used in the high-Mn steels investigated in a recent project [1]. Consequently, the quantitative characterization of such precipitates is essential to understand the interdependency of alloy composition, thermomechanical treatment and final mechanical properties. 

In an earlier paper, the extraction of a precipitate spectrum image (SI) by the subtraction of matrix contribution was demonstrated using the capabilities of DualEELS [2]. The combination of closely spaced edges, weak edges and strong ELNES makes absolute quantification of such a precipitate SI challenging.

Thus absolute experimental cross-sections, derived from ceramic standards of TiC_0.98. TiN_0.88, VC_0.83 and VN_0.97, are used. A wedge shaped lamella of the standard is prepared by focused ion beam milling and an SI is recorded over a region where t/λ varies from 0.2 to 0.8. Using the procedures in [1], the low loss and high loss regions are spliced and the result Fourier logarithmically deconvolved to give a single scattering distribution.   At each energy loss, the resulting spectral intensities per unit energy, normalized by the zero loss intensity, are plotted against the product of the metal atoms per volume in the standard multiplied by the local thicknesses. The slope of this line is the absolute differential cross-section appropriate to the probe and collection angles used. An absolute value of λ is required to convert the t/λ map to a t map. This is measured using a needle shaped specimen.  Its t/λ is measured at one orientation and its t is measured from the image width after rotation through 90^o, giving a direct measurement of λ.   The cross-sections for the individual edges can be separated out by fitting a suitable background before the non-metal edge and using its Hartree-Slater calculated cross-section to extrapolate it under the metal edge. The non-metal edge can then be corrected for the sub-stoichiometry.

The precipitate has the same rocksalt structure as the standards but is a quaternary. With the four standards, two cross-sections are obtained from each edge. In principle, a cross-section appropriate to the precipitate composition can be made for each edge using an appropriately weighted average. However, because the N and Ti edges are so close, the edges from TiN_0.88 are difficult to separate and are not used here.  Thus the Ti cross-section from TiC_0.98 and the N cross-section from VN_0.97 are always used. Fortunately, the Ti metal fraction and the N non-metal fraction are only ~0.3 and so this causes no issues. To complete the standards for a multiple linear least squares (MLLS) fit to the precipitate SI, shapes for the background and the residual carbon and oxygen edges left after the matrix subtraction are required. The latter can be extracted from the average matrix spectrum.

Figure 1 shows the result of such an MLLS fit and the residuals are extremely low. The maps of the fitting coefficients for the four elements are shown in Figure 2. When normalized by the zero loss intensity, they give the number of each atom type per unit area. Using the volume of the unit cell appropriate to the composition, the “thickness” occupied by each atom type can be found. The sum of the Ti and V “thicknesses” is the precipitate thickness and a profile of this is shown in the lower part of Figure 3. Outside the precipitate, the values are essentially zero, as expected, and have low noise, indicating the sensitivity of the technique. The values of x, y and z can also be found and profiles of them are shown in the upper part of Figure 3.   The region outside the precipitate has been zeroed. The values are essentially constant across the precipitate and become noisy at the edge where the signals themselves are low and hence noisy.

References:

[1] G. Paul et al Erste Erkenntnisse zum Ausscheidungsverhalten von Mikrolegierungselementen in Hoch-Mangan Stählen; Ed. G. Petzow, (2012) Sonderbände der praktischen Metallographie, vol. 44

[2] J. Bobynko et al Ultramicroscopy 149 (2015) 9-20.

Acknowledgements:

EEC Funding from the RFCS Fund for PrecHiMn (RFSR-CT-2010-00018) and PreTiControl (RFSR-CT-2015-00013); Prof W. Lengauer (TU-Wien) for the provision of carbide and nitride standards; Dr G. Paul (thyssenkrupp Steel Europe AG) for the provision of the vanadium steel sample.

Figures:

Figure 1. Spectra from a 10 x 9 pixel region in the precipitate centre are summed and compared to the corresponding MLLS fit and residuals. Absolute experimental cross-sections for C, N, Ti and V, derived from TiC0.98, VC0.83, TiN0.88 and VN0.97 standards, are used for the fit, together with a background shape and the shapes of the C and O K-edges from the matrix. The C cross-section is the average of those from TiC0.98 and VC0.83 weighted by the metal fraction and the V cross-section is the average of those from VC0.83 and VN0.97 weighted by the non-metal fraction. The N and Ti cross-sections are those from VN0.97 and TiC0.98 respectively.

Figure 2. The maps of the MLLS fit coefficients for the four elements in the precipitate. The width of the maps is 19 nm. In all cases zero is black. White is 0.171, 0.061, 0.094 and 0.211 for C, N, Ti and V respectively.

Figure 3. The lower plot is the thickness through the centre of the precipitate averaged over two rows. It is obtained from the sum of the Ti and V atoms. Note that the thickness where there is matrix is close to zero and has low noise indicating the sensitivity of the method. The upper plots are the values of x, y, z in TixV(1-x)CyNz. The matrix region has been forced to zero.

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