Small‑angle x-ray scattering study of α lamellae in metastable β titanium alloys
J. Šmilauerová1, P. Harcuba1, J. Stráská1, J. Stráský1, M. Janeček1, V. Holý2
1Department of Physics of Materials, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague, Czech Republic
2 Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague, Czech Republic
jana.smilauerova@matfyz.cuni.cz
Metastable β-Ti alloys contain a sufficient amount of so-called β-stabilizing elements to prevent the formation of the low-temperature α phase (hcp) in the high-temperature β matrix (bcc) during quenching. After quenching, the β phase remains in a thermodynamically metastable state and, when annealed, it can decompose into other phases and complex phase transformations can be observed [1].
Quenched metastable β-Ti alloys often contain particles of the metastable ω phase (hexagonal or trigonal lattice). These particles form by a diffusionless displacive transformation and have a size of several nm [2]. During annealing at lower temperatures, ω particles evolve by a diffusion-assisted process and their size increases to several tens of nm [3, 4]. When a metastable β-Ti alloy is aged at higher temperatures, or for a longer time, precipitates of the thermodynamically stable α phase start to nucleate either in the direct proximity of ω particles, or, in their absence, directly from the β matrix [5, 1]. α particles have a lamellar shape and the crystallographic orientation between α and β is given by the Burgers orientation relationship [6]. However, the spatial orientation of the lamellae (i.e. the orientation of their habit plane) has been under much discussion. While some research identified the habit plane as (111)β [7, 8], other studies reported the habit plane (11 11 13)β [9].
Figure 1. An example of
measured SAXS patterns; sample aged at 510 °C for 16 h. The plane of
the β matrix perpendicular to the primary beam is given in the bottom left
corner of each panel.
In the present research, we used small-angle x-ray scattering (SAXS) to investigate the spatial orientation of α lamellae with respect to the parent β phase in a metastable β-Ti alloy (Timetal LCB). Single crystals produced by the floating zone technique were used [10]. Consequently, the SAXS patterns represented a single grain, which allowed us to extract more complex information than if the scattering signal was averaged over many grain orientations. Different alloy conditions were prepared by annealing at selected temperatures below and above the ω solvus, which is approximately 500 °C for the Timetal LCB alloy [11]. More information on the annealing schemes can be found in [12].
Figure 1 shows an example of SAXS patterns measured for three orientations of the sample. Each sample was tilted to orient the planes (001)β, (110)β and (111)β perpendicular to the primary beam, see panels (a), (b) and (c) in Fig. 1, respectively. Note that the symmetry of the SAXS patterns depends on the sample orientation: four-, two- and six-fold symmetry is observed for the orientations (001)β, (110)β and (111)β, respectively. Figure 2 shows an SEM image of the sample aged at 510 °C for 16 h.
The SAXS data were fitted by a model which simplified the shape of an α lamella to a triaxial ellipsoid. We assumed that all α lamellae are similar, i.e. their axes ratios are constant, and that the size distribution of α particles follows the Gamma distribution. From the fit, we obtained the dependence of the dimensions of α lamellae on the aging condition and we determined that the habit plane is close but not equal to (111)β. The slight deviation of the habit plane from (111)β is confirmed by SEM, in which fans of similar apparent α directions can be observed; the apparent α directions resulting from the fit are represented by the red lines (Fig. 2). If the habit plane of the α lamellae was exactly (111)β, the number of apparent directions would be reduced to only four, as there are four crystallographically equivalent (111)β planes.
A Monte Carlo simulation of an SEM image was constructed using the values resulting from the fit, see Fig. 3. The comparison of figures 2 and 3 shows a good agreement between the real and simulated microstructures.
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Figure 2. SEM micrograph (back-scattered electron contrast) of the sample aged at 510 °C for 16 h. α lamellae are observed as darker regions in a lighter β matrix. The red lines indicate the apparent directions of the α lamellae resulting from the fit of SAXS data. |
Figure 3. Monte Carlo simulation of an SEM image of α lamellae using the α orientations and sizes fitted for the 510 °C/16 h sample. |
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This work was supported by a joint project of the Czech Science Foundation (GACR) project no. 22‑21151K and the Austrian Science Fund (FWF) project no. I5818-N. Single crystal growth was performed in MGML (http://mgml.eu/), which is supported by the Czech Research Infrastructures program (project No. LM2018096). This research used resources of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) by Argonne National Laboratory, supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. National Science Foundation (NSF) ChemMatCARS Sector 15 is supported by the Divisions of Chemistry (CHE) and Materials Research (DMR), NFS, under Grant No. NSF/CHE-1834750.