Ubiquitous short-range order in multi-principal element alloys

Abstract

Recent research in multi-principal element alloys (MPEAs) has increasingly focused on the role of short-range order (SRO) on material performance. However, the mechanisms of SRO formation and its precise control remain elusive, limiting the progress of SRO engineering. Here, leveraging advanced additive manufacturing techniques that produce samples with a wide range of cooling rates (up to 10⁷ K s^-1) and an enhanced semi-quantitative electron microscopy method, we characterize SRO in three CoCrNi-based face-centered-cubic (FCC) MPEAs. Surprisingly, irrespective of the processing and thermal treatment history, all samples exhibit similar levels of SRO. Atomistic simulations reveal that during solidification, prevalent local chemical order arises in the liquid-solid interface (solidification front) even under the extreme cooling rate of 10¹¹ K s^-1. This phenomenon stems from the swift atomic diffusion in the supercooled liquid, which matches or even surpasses the rate of solidification. Therefore, SRO is an inherent characteristic of most FCC MPEAs, insensitive to variations in cooling rates and even annealing treatments typically available in experiments.

Fig. 1. Qualitative characterization of SRO in MPEAs with various thermal processing routes.

a Schematic of the as-cast, LDED, and LPBF sample preparation method. b Bright-field TEM images of the selected area and SAED patterns under the same conditions for ten samples. The white arrows and circles indicate the diffused spots related to SRO. c, Schematic of the TTT diagram of SRO, showing the difference in SRO is limited even with a wide range of cooling rates. Scale bars for bright-field TEM images, 100 nm. Scale bars for SAED patterns, 5 nm⁻¹.

Fig. 2. ESQ-SAED characterization of SRO in MPEAs with various thermal processing routes.

a–f Illustration of the ESQ-SAED data processing procedure to enable a more precise analysis of the degree of SRO. Each Bragg peak in the SAED pattern (a) will be detected and labeled by the red dots in (b). The Braggs peaks will be further classified to create two sets of image tiles, one for the SRO and one for the matrix (c). The SNR of the SRO peak is significantly improved by averaging the same type of image tiles, as shown in (d). Further, the fitting of the peaks (e) and the radial-integral (f) facilitate the determination of the peak intensity. The relative SRO intensity is calculated by normalizing the averaged SRO intensity with the averaged matrix intensity. g Comparison of the relative SRO intensity of the ten CoCrNi-based MPEAs with different processing methods. h Comparison of the relative SRO intensity in four FCC MPEAs with different compositions. The error bar shows the standard deviation.

Fig. 3. Modeling the evolution of chemical distribution during solidification and after annealing in an equiatomic CoCrNi MEA.

a, b Snapshots showing the solidification process. Green represents the FCC crystal structure, red represents the solidification front, and purple represents the liquid. c, d Atomic slices of the structure (in the x-z plane) showing the distribution of atoms (c) and the pairwise order parameters ∆α_Ni-Ni and ∆α_Co-Cr (d) after solidification, respectively. A threshold of 2 has been applied on the colorbar of the pairwise order parameters to show the contrast. Thus, the atoms with order parameters smaller than 2 are colored by dark blue. The original result without threshold is included in Supplementary Fig. 16. e, f Atomic slices of the structure (in the x-z plane) showing the distribution of atoms (e) and the pairwise order parameters ∆α_Ni-Ni and ∆α_Co-Cr (f) after annealing, respectively. g The probability distribution of ∆α_Ni-Ni and ∆α_Co-Cr order parameters in the RSS, as-solidified and as-annealed samples. h Line profiles showing the variation of ∆α_Ni-Ni and ∆α_Co-Cr as a function of solid growth distance in the solidifying direction (z-axis) in the as-solidified sample.

Fig. 4. Atomistic insights into the formation mechanism of CSRO at the solidification front.

a, b Snapshots of the solidification front evolution. The top and bottom rows highlight the structural and chemical evolutions, respectively. c The net movement distance (in the growth direction, i.e., the z-direction) of the solidification front for t = 4 ps, 8 ps and 12 ps. The horizontal axis (Width) is equivalent to the x-axis, as defined in the coordinate system in (a). d The solidification front’s growth distance as a function of time. The average growth velocity is 9.45 nm ns⁻¹. e Mean square displacements of elements in the supercooled liquid as a function of time. The diffusivities for the three elements are labeled. f Illustration of the diffusion distance of elements in the liquid (left) and the average distance traveled by the solidification front (right) after the same duration of 37 ps. g–j, Schematic illustration of the CSRO formation mechanism and the suppression of long-range chemical order during solidification.

Fig. 5. In-situ nano-mechanical testing to understand the evolution of SRO during cyclic loading.

a Schematic drawing of the push-to-pull (PTP) device used for cyclic loading. b SEM image of the PTP setup. c TEM image showing the boxed region in (b). d The mechanical loading curve. e Evolution of the relative SRO intensity as a function of loading cycles, underscoring the impact of dislocations on SRO during cyclic loading. The error bar shows the standard deviation.