A Statistical Approach to Retrieve Short-range Order Parameter in Complex Alloys from Noisy Atom-Probe Tomography Measurement

Short-range order (SRO) has been alluded to play a significant role in modulating various material properties in medium-entropy and high-entropy alloys, but a decisive characterization of SRO at nanoscale through quantifying the Warren-Cowley SRO parameter has been a challenging task. Atom-probe tomography (APT) can potentially be a useful technique to characterize SRO because in principle, APT probes both chemical and positional information of each atom in lattice. In practice, however, the limited spatial resolution of APT often leads to noisy raw data which yield a convoluted radial distribution function of atomic sites that restricts the applicability of APT in retrieving meaningful information of SRO in alloys. To address this issue, we develop a theory and a statistical approach to recover the Warren-Cowley SRO parameter from noisy APT data. The validity of our approach is verified through a large-scale benchmark GeSn alloy model which is created through our recently developed machine-learning potential¹. In particular, the benchmark tests show that our approach can accurately recover SRO parameter when the perturbation length (standard deviation of distance between the measured atomic position and its true position) is &lt; 2 Å, and can still qualitatively recover SRO even when perturbation increases to ~ 4 Å. Applying the approach to analyze real APT data in both GeSn binary alloy and SiGeSn ternary alloy, we have successfully recover the SRO parameters in these alloys, which show a qualitative agreement with both our prior theoretical modeling^2,3 and recent EXAFS measurement⁴. Importantly, the developed theoretical model and approach are generically applicable to different types of alloys, thus providing a robust framework to enable APT as an effective tool for quantitatively characterizing SRO in a wide range of compositionally complex alloys.<br/><br/>This work is supported by Department of Energy, Office of Basic Energy of Sciences under Award No. DE-SC0023412.<br/><br/>(1) Chen, S.; Jin, X.; Zhao, W.; Li, T. Intricate Short-Range Order in GeSn Alloys Revealed by Atomistic Simulations with Highly Accurate and Efficient Machine-Learning Potentials. <i>Phys. Rev. Mater.</i> <b>2024</b>, <i>8</i> (4), 043805. https://doi.org/10.1103/physrevmaterials.8.043805.<br/>(2) Cao, B.; Chen, S.; Jin, X.; Liu, J.; Li, T. Short-Range Order in GeSn Alloy. <i>ACS Appl. Mater. Interfaces</i> <b>2020</b>, <i>12</i>, 57245–57253. https://doi.org/10.1021/acsami.0c18483.<br/>(3) Jin, X.; Chen, S.; Li, T. Coexistence of Two Types of Short-Range Order in Si–Ge–Sn Medium-Entropy Alloys. <i>Commun Mater</i> <b>2022</b>, <i>3</i> (1), 66. https://doi.org/10.1038/s43246-022-00289-5.<br/>(4) Lentz, J. Z.; Woicik, J. C.; Bergschneider, M.; Davis, R.; Mehta, A.; Cho, K.; McIntyre, P. C. Local Ordering in Ge/Ge–Sn Semiconductor Alloy Core/Shell Nanowires Revealed by Extended x-Ray Absorption Fine Structure (EXAFS). <i>Appl Phys Lett</i> <b>2023</b>, <i>122</i> (6), 062103. https://doi.org/10.1063/5.0136746.