Direct Measurement of Microstructural Avalanches during the Martensitic Transition of Cobalt Using Coherent X-Ray Scattering

Heterogeneous microscale dynamics in the martensitic phase transition of cobalt is investigated with real-time x-ray scattering. During the transformation of the high-temperature face-centered cubic phase to the low-temperature hexagonal close-packed phase, the structure factor evolution suggests that an initial rapid local transformation is followed by a slower period during which strain relaxes. Coherent x-ray scattering measurements performed during the latter part of the transformation show that the kinetics is dominated by discontinuous sudden changes—avalanches. The spatial size of observed avalanches varies widely, from 100 nm to $10\mu \mathrm{m}$, the size of the x-ray beam. An empirical avalanche amplitude quantifies this behavior, exhibiting a power-law distribution. The avalanche rate decreases with inverse time since the onset of the transformation.

Figure 1

(a) The $(00.2{)}_{\mathrm{hcp}}$ and $(111{)}_{\mathrm{fcc}}$ Bragg peaks for three times during the fcc-hcp transformation during a quench to $T_q=-10\mathrm{K}$. The ○ symbols represent data immediately following the quench (scaled down to 25% of their original value); $\times$ and $+$ symbols represent data collected starting 3050 and 6344 s following quench onset, respectively. From Lorentzian fits of the data (shown as solid curves), the complete evolution of (b) integrated intensity, (c) width at half maximum, and (d) location for both Bragg peaks was determined. The integrated intensity sum from both Bragg peaks is also shown in (b). Growth and strain redistribution stages of the transition are separated by the vertical gray lines in (b)–(d).

Figure 2

A waterfall plot showing the evolution of a 100 pixel cross section of a speckle pattern near the $(00.2{)}_{\mathrm{hcp}}$ peak during a phase transformation. Abrupt changes in pixel intensity such as the one at approximately 10 min indicate the occurrence of avalanches. A smaller avalanche occurs at approximately 7 min.

Figure 3

(a) The two-time difference values for a quench to $T_q=-5\mathrm{K}$. (b) Avalanche amplitudes calculated from the data in (a). (c) The cumulative number of avalanches over time $N(t)$ near the $(01.3{)}_{\mathrm{hcp}}$ peak for various $T_q$. The line is a fit of the logarithmic function to the $T_q=-5\mathrm{K}$ data. (d) A typical distribution of avalanche amplitudes during a phase transformation with a power-law fit of the data.