Mechanically derived short-range order and its impact on the multi-principal-element alloys

Abstract

Chemical short-range order in disordered solid solutions often emerges with specific heat treatments. Unlike thermally activated ordering, mechanically derived short-range order (MSRO) in a multi-principal-element Fe₄₀Mn₄₀Cr₁₀Co₁₀ (at%) alloy originates from tensile deformation at 77 K, and its degree/extent can be tailored by adjusting the loading rates under quasistatic conditions. The mechanical response and multi-length-scale characterisation pointed to the minor contribution of MSRO formation to yield strength, mechanical twinning, and deformation-induced displacive transformation. Scanning and high-resolution transmission electron microscopy and the anlaysis of electron diffraction patterns revealed the microstructural features responsible for MSRO and the dependence of the ordering degree/extent on the applied strain rates. Here, we show that underpinned by molecular dynamics, MSRO in the alloys with low stacking-fault energies forms when loaded at 77 K, and these systems that offer different perspectives on the process of strain-induced ordering transition are driven by crystalline lattice defects (dislocations and stacking faults).

Fig. 1. Atomistic MC simulations for CSRO domains in fcc-structured Fe₄₀Mn₄₀Co₁₀Cr₁₀ (at%) HEA system.

a Near-random distribution of four principal elements obtained after the MC simulations at 1373 K. A cell with 216000 atoms (15.7 nm × 13.6 nm × 12.8 nm) was used for the simulation. b, c Non-random distribution of principal elements showing thermally activated Cr-enriched like pairs and Fe–Co unlike pairs at 873 and 750 K, respectively, based on the MC simulations. The captured slices of configurations with a thickness of ~2 nm are shown for clear visualisation. d, e, f Corresponding radial distribution function g(r) profiles from the MC simulations, revealing that when the temperature is lowered, both Cr–Cr like pairs (red curves) and Fe-Co unlike pairs (blue curves) are strongly favoured at the first nearest-neighbour distances for producing CSROs in the HEA before straining.

Fig. 2. Tensile stress–strain curves of the B-doped Fe₄₀Mn₄₀Co₁₀Cr₁₀ (at%) HEA at 77 K for different strain rates.

The material was finally aged at 773 K for 360 min followed by furnace cooling to room temperature. This fcc single-phase sample was tensile-tested at 77 K, with strain rate έ = 2.8 × 10⁻⁵ s⁻¹ (black curve; low rate; labelled as HEA-L) and έ = 1.1 × 10⁻⁴ s⁻¹ (blue curve; moderate rate; labelled as HEA-M), under uniaxial quasistatic conditions. In addition, the tensile curve of the same alloy composition subjected to recrystallising at 1073 K for 60 min followed by water quenching to room temperature is included, along with the uniaxial quasistatic 77 K-straining curve at έ = 1.2 × 10⁻³ (red curve; high rate; labelled as HEA-H) for comparison. All samples exhibited similar grain sizes ranging from ~3.5–5.1 μm. σ_YS represents the 0.2% offset yield strength; ε_f, the total elongation; and σ_UTS, the maximum tensile strength. Inset: the magnified curves.

Fig. 3. Microstructure of the tensile-tested samples.

a Typical EBSD orientation (left column) and phase identification (middle column) maps, where the tensile loading direction was normal to the plane of view, obtained from the fracture surfaces of HEA-L. Micro-voids were formed at the internal grain and along grain boundaries. Right column top panel: sketch of the sample orientation showing the geometry of normal direction (ND), transverse direction (TD), rolling direction (RD), and the tensile loading direction. fcc: face-centred cubic; hcp: hexagonal closed pack. Middle panel: Representative misorientation angle profile of mechanical twinning boundaries and hcp boundaries. b Conventional bright-field TEM image of HEA-L, projected along the [011] zone axis, showing plentiful slip bands and mechanical twins. In the corresponding EDP, extra spots caused by mechanical twins are indicated by ‘Tw’. c Lamellar twin thickness distribution with respect to the applied strain rates, determined from the TEM images for HEA-M and HEA-L. Inset: a representative STEM image of nano-twin with a mirror-symmetry at an angle of ~70° with respect to the twinning plane. d TEM image along [$\overline{1}$12] zone axis for HEA-M. Clear extra diffuse discs at the ½{311} locations in the corresponding EDP (right panel) are indicated by green arrows. e HRTEM image (left panel) of slip band passing with mechanical twins in d and corresponding FFT patterns (right panel) from specific regions of the slip-band-free matrix (grey box), slip band (red box), and mechanical twins (blue box), based on the [$\overline{1}$12] zone axis. The considerable overlap of slip bands and twins (schematic in the top right corner) resulted in double diffraction in the FFT pattern and Moiré-fringed lattices in the TEM image.

Fig. 4. STEM analysis of the origin of mechanically driven SRO in the deformation structure.

a STEM image (top) of HEA-M along the [$\overline{1}$12] zone axis and the corresponding enlarged annular dark-field image (bottom), showing the glide of mobile dislocations across the pre-existing single slip lines and slip bands that are inclined to the <011> directions on the {111} planes. b STEM image of one slip band. c [$\overline{1}$12] STEM-FFT pattern (top column) and corresponding inverse FFT lattice fringes (bottom column), obtained from the undistorted area (blue box) in b, showing neither extra diffuse scattering nor SFs. d [$\overline{1}$12] STEM-FFT pattern obtained from the distorted zone of the local lattice in the red box in b showing the mechanically driven SRO (MSRO)-derived extra discs at the ½{311} locations (green circles). e Inverse FFT image produced by superimposing one single MSRO domain (green dotted circle) with fcc lattice fringes. Corresponding magnified lattice fringes showed the sublattice structure of the domain core, where the {311} atomic planes alternate with normal fcc (white lines) and MSRO (green dotted lines). f, g Inverse FFT images from different fcc normal spots, obtained from the interface between MSRO and fcc phase: examples revealing that the structural features attributable to the MSRO-derived diffuse discs at the ½{311} locations in the FFT patterns are associated directly with the synergy of SFs (red lines) on {111} planes and edge dislocations with Burgers vector b = 1/3 < 111 > (marked by ‘T’).

Fig. 5. TEM diffraction patterns, intensity of MSRO-derived extra diffuse discs, and the associated STEM images for different strain rates.

Selected-area [$\overline{1}$12] TEM-EDPs taken from individual HEA grains: a before and b after tensile straining at different strain rates. These EDPs were acquired from the region of slip bands in each deformed specimen. Green arrows indicate periodic diffuse scattering along the {311} directions caused by MSRO. c Logarithmically scaled diffraction intensity along the red lines in a, b: that is, the diagonal lines across normal fcc {311} spots in the EDPs from HEA-L (black) and HEA-M (blue). The hump owing to MSRO-generated diffuse scattering in b is outlined by green arrows in the profiles. The measured diffraction intensity for the same alloy composition subjected to 77 K-tensile straining at έ = 10⁻³ (red; HEA-H) is also included. d Inverse STEM-FFT (left panel) and annular dark-field (right panels) images formed with the MSRO-introduced extra diffuse discs in the FFT or diffraction patterns (yellow dashed circles) in b. The bright contrast in the real microstructure shows the MSRO domains (green dashed circles) in the slip bands that form during straining. The magnified region (yellow box) of the STEM image revealed no shearing of the MSROs in the slip bands inclined to the <110> directions. e Histograms of identified MSROs diameters for HEA-L (grey) and HEA-M (blue) samples, showing the mean value d.

Fig. 6. MD simulations for the origin of MSRO-generated extra scattering in non-equiatomic Fe₄₀Mn₄₀Cr₁₀Co₁₀ (at%) HEA and non-equiatomic NiCrCo MEAs upon loading at 77 K.

a MD-EDPs for the interstitial-free FeMnCrCo structure before and after straining. The [$\overline{1}$12] diffraction patterns for the structure before straining show MSRO-derived faint diffuse diffraction scattering at the ½{311} locations, while the relative intensity of MSRO-derived diffuse scattering increased with a higher strain rate. The colour scale (bottom right) defines the relative intensity of diffraction spots in arbitrary units (blue: low intensity; red: high intensity). b Corresponding cell structures strained at 77 K under conditions of different strain rates, showing the distribution of deformation-induced SFs (stacking faults: top panel) and dislocations with different Burgers vectors (bottom panel). The dislocation distribution reveals that strong slip planarity was achieved at higher strain rates. There were no LRO precipitates in all cell structures. This affirms that spot-like scattering at the ½{311} locations in the MD-EDPs directly correlates with SFs and dislocations, but not with LRO structure. The strained cell structures at slow and moderate έ were included in this work for comparison, as the highest έ (2 × 10⁹s^–1) caused severe amorphisation of the system and restricted the observation of the έ effect under equivalent conditions. c Volume fraction of the SFs and dislocations as a function of the strain rate for the non-equiatomic HEA. d MD-EDPs for the strained Ni₆₀Cr₂₀Co₂₀ (at%) MEA, confirming that the relative intensity of MSRO-derived diffuse scattering increased with increasing strain rate. In the MD-EDP for the MEA system before straining, there were no diffuse discs. The strained cell structures, showing the distribution of mechanical SFs and dislocations, are shown in Supplementary Fig. 11. e Volume fraction of the mechanical SFs and dislocations as a function of έ for the MEA. f Increased SF volume fraction with a higher έ for other NiCrCo-based non-equiatomic MEAs with different SFEs. The corresponding strained cell structures and MD-EDPs are shown in Supplementary Fig. 12. The SFEs were determined from the current molecular static simulations at 0 K (see Supplementary Table 1).