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Parent Phase Reconstruction

Introduction

When a material undergoes a phase transformation from one crystallographic phase to another, a grain in the original microstructure may transform into several different crystallographic variants. The relationship between the parent grain orientation and the child variants is termed the orientation relationship. Consider the austenite (γ, fcc) to ferrite (α, bcc) transformation in iron, shown in Figure 1. If we assume the Nishiyama-Wasserman orientation relationship, namely {111}fcc planes parallel to {110}bcc planes and <11-2>fcc directions aligned with <110>bcc, then we would expect a parent grain to transform into as many as 12 different child variants (six in this particular example).

Methodology

Figure 1. Schematic of the parent austenite phase and six possible variants to the child ferrite phase orientations.
Figure 1. Schematic of the parent austenite phase and six possible variants to the child ferrite phase orientations.

The challenge is to reconstruct the pre-transformation microstructure from the measured post-transformation microstructure. Several different approaches have been proposed over the years. OIM Analysis™ v8.6 has adopted the procedure offered by Ranger et al. An example reconstruction for a low alloy steel is shown in Figure 2. (EBSD measurements courtesy of Matt Merwin, US Steel Research and Technology Center).

Figure 2. As-scanned and reconstructed parent grain microstructure.
Figure 2. As-scanned and reconstructed parent grain microstructure.

Figure 3. Classification of measured data into candidate parent orientations.
Figure 3. Classification of measured data into candidate parent orientations.

This method can be described in a series of steps as follows:

  1. For each domain (grain) in the as-scanned microstructure, calculate a list of all possible candidate parents based on a user prescribed orientation relationship.
  2. Determine the most probable parent for each child variant and classify as a High Confidence Parent (HCP), Ambiguous Parent (AP), or Low Confidence Parent (LCP) based on the fraction of neighboring domains having matching parents in their candidate parent lists. An example of this classification is shown in Figure 3.
  3. Group HCPs together and grow into neighboring APs.
  4. Repeat step 2 for the LCPs but extend the analysis out to the second nearest neighbors.
  5. Repeat step 3 using the 2nd order HCPs and APs.

Case Study: hcp ↔ bcc phase transformation in cobalt

Figure 4. EBSD patterns from HCP and BCC cobalt collected via in-situ heating.
Figure 4. EBSD patterns from HCP and BCC cobalt collected via in-situ heating.

The Hexagonal-Closed-Pack (HCP)/Body-Centered Cubic (BCC) transition temperature occurs at 422 °C. Figure 4 shows the orientation relationship between the two phases. When in-situ measurements are made, it is possible to capture the microstructure when it is only partially transformed, allowing the orientation relationship to be observed directly in the scan data and in the EBSD patterns themselves.

A sample was mounted on a heating stage in the scanning electron microscope, and Electron Backscatter Diffraction (EBSD) measurements were made in-situ to at a temperature above and below the transition temperature. Figure 5 shows the orientation (IPF) and phase maps at temperatures above and below the transition temperature. The in-situ measurements allow the reconstructed pre-transformation microstructure to be compared to the experimental one, confirming the reconstruction process’s quality. The differences between the two are relatively minor. Certainly, the reconstruction is of sufficient quality to capture the grain size in the pre-transformation microstructure.

Figure 5. EBSD IPF orientation maps at ambient and high temperature collected from the Co sample, and reconstructed parent Beta grains developed from ambient temperature measurements.
Figure 5. EBSD IPF orientation maps at ambient and high temperature collected from the Co sample, and reconstructed parent Beta grains developed from ambient temperature measurements.

References

  1. Humbert, M., Wagner, F., Moustahfid, H. and Esling, C. (1995) Determination of the orientation of a parent β grain from the orientations of the inherited α plates in the phase transformation from body-centred cubic to hexagonal close packed. Journal of applied crystallography 28: 571-576.
  2. Glavicic, M.G., Kobryn, P.A., Bieler, T.R. and Semiatin, S.L. (2003) An automated method to determine the orientation of the high-temperature beta phase from measured EBSD data for the low-temperature alpha-phase in Ti–6Al–4V. Materials Science and Engineering: A 351: 258-264.
  3. Cayron, C., Artaud, B. and Briottet, L. (2006) Reconstruction of parent grains from EBSD data. Materials characterization 57: 386-401.
  4. Krishna, K.M., Tripathi, P., Hiwarkar, V.D., Pant, P., Samajdar, I., Srivastava, D. and Dey, G.K. (2010) Automated reconstruction of pre-transformation microstructures in zirconium. Scripta Materialia 62: 391-394.
  5. Germain, L., Gey, N., Mercier, R., Blaineau, P. and Humbert, M. (2012) An advanced approach to reconstructing parent orientation maps in the case of approximate orientation relations: Application to steels. Acta Materialia 60: 4551-4562.
  6. Miyamoto, G., Iwata, N., Takayama, N. and Furuhara, T. (2010) Mapping the parent austenite orientation reconstructed from the orientation of martensite by EBSD and its application to ausformed martensite. Acta Materialia 58: 6393-6403.
  7. Ranger, C., Tari, V., Farjami, S., Merwin, M.J., Germain, L. and Rollett, A. (2018) Austenite Reconstruction Elucidates Prior Grain Size Dependence of Toughness in a Low Alloy Steel. Metallurgical and Materials Transactions A 49: 4521-4535.
  8. Brust, A.F., Payton, E.J., Hobbs, T.J. and Niezgoda, S.R. (2019) Application of the Maximum Flow–Minimum Cut Algorithm to Segmentation and Clustering of Materials Datasets. Microscopy and Microanalysis 25: 924-941.