Introduction:
The X-ray Laue diffraction is a general method to determine the periodicities of crystalline solids. When the ultra brilliant synchrotron X-ray source and the state-of-art X-ray optics are integrated to generate intense white-beam with submicron spatial resolution, it enables the Laue microdiffraction mode that scans and instantly collect the Laue diffraction pattern at the each point of a region [1]. This enables surface morphological characterization as well as the precise structural determination simultaneously. The Laue microdiffraction has been successfully applied for obtaining the orientation mapping for polycrystalline solids [1, 2], measuring the local lattice distortion [3], and mapping the heterogeneity for large deformation [4].
Fig. 1
Basic principles of Laue diffraction by white-beam is illustrated in Fig. 1.
Here we illustrate a new approach for characterizing phase transformation using Synchrotron Laue microdiffraction, particularly for highly coherent reversible transformation like martensitic transformation. Due to the change of symmetry between the austenite phase and martensite phase, twinned martensite forms and results in complex interface morphologies. The formation of these interfaces relies on the conditions of compatibility. When the lattice parameters of austenite and martensite phase satisfy: 1) middle eigenvalue of the transformation stretch tensor is unity; 2) at least one of the 2-fold axes of the austenite lattice is inextensible, the austenite/martensite fits together perfectly without any distortion at the interface. These conditions are also known as the Cofactor Conditions. The satisfaction of the Cofactor Condition implies the tremendous improvement of reversibility in phase-transforming materials and shows unusual mosaic of microstructure containing stress-free triple junctions. To quantitatively study these unusual interface morphologies, we use synchrotron X-ray Laue microdiffraction to characterize the orientation mapping of a stabilized austenite/twinned martensite interface in spatial domain.
Experiment:
The Laue microdiffraction was conducted on beamline 12.3.2 of the Advanced Light Source, Lawrence Berkeley National Laboratory. Details of the experimental setup can be found in [1]. The Laue patterns were analyzed and indexed using the XMAS software [2].
The specimen used for characterization is 30at%Au-25at%Cu-45at%Zn with dimension ~5mmx5mmx0.5mm. It undergoes L21 (cubic) to M18R (monoclinic) reversible phase transformation at ~-40C. The lattice parameters of both austenite and martensite can be found in [5], which satisfy closely the Cofactor Conditions. To drive the phase transformation at such temperature and stabilize the austenite/martensite interface, we designed a thermal stage providing large temperature gradient field (-60C to 5C within 1mm gap) across the specimen.
Results and discussion:
By scanning an area of 200 microns x 200 microns, we obtained the orientation mapping for both phases with different crystal structures. The uniform region on the left in Fig. 2(a) and (b) corresponds to the austenite phase. The color regions on the right in Fig. 2(a) and (b) are the different martensite variants with various orientations. From such a mapping, the “ZERO” indexed regions are closely related to the morphological properties of the elastic transition layer from austenite to martensite. For example, the dark blue region in Fig. 2(a) and its corresponding yellow region in Fig. 2(b). The width of the transition layer is at most 10 microns.
Fig. 2 Orientation mapping: (a) angle between the c-axis of unit cell and the Z-axis of the stage; (b) angle of the c-axis of unit cell in XY plane of the stage.
Since this material has been tuned to satisfy the aforementioned Cofactor Conditions for both Type I and Type II twin systems, half of the solutions of the crystallographic equations of martensite in such a material predict the absence of elastic transition layer. This theory agree well with the quantitative measurement of the interface by synchrotron X-ray Laue microdiffraction.
Reference:
[1] M. Kunz, N. Tamura, K. Chen, A. A. MacDowell, R. Celestre, M. Church, S. Fakra, E. Domning, J. Glossinger, J. Kirschman, G. Morrison, D. Plate, B. Smith, T. Warwick, V. Yashchuk, H. Padmore, and E. Ustundag, Review of Scientific Instruments 80, 035108 (2009).
[2] N. Tamura, XMAS: a versatile tool for analyzing synchrotron x-ray microdiffraction data, edited by R. Barabash and G. Ice (Imperial College Press (London), 2014).
[3] R. Barabash, G. E. Ice, B. C. Larson, G. M. Pharr, K. S. Chung, and W. Yang, White microbeam diffraction from distorted crystals. Appl. Phys. Lett. vol. 79(2001).
[4] A. Mehta, XY. Gong, V. Imbeni, A. R. Pelton, and R. O. Ritchie, Understanding the deformation and fracture of Nitinol endovascular stents using in situ Synchrotron X-rya microdiffraction. Adv. Mater., 19 (2007)
[5] Y. Song, X. Chen, V. Dabada, T. Shield and R. D. James, Enhanced reversibility and unusual microstructure of phase-transforming material. Nature, 502, 85 (2013).