The Nature of Lattice Distortion and Strengthening in High Entropy Alloy

: High entropy alloys (HEAs) belong to a new class of materials with multiple principal components that are chemically concentrated in less explored phase spaces. Since the initial discovery 1,2 , HEAs have attracted tremendous interest for their remarkable structural diversity and associated properties, including high strength and high ductility 3,4,5 . Underlining the structural diversity is the metastability of HEAs 6,7 , to which a key contributor is the lattice distortion effect that emerges as a direct consequence of interplay between atomic size misfits and chemical disorder. Lattice distortion also directly contributes to alloy strengthening 8 and ductility 9 . Despite the recognized significance, however, the critical knowledge of lattice distortion is still missing in the study of HEAs 10 . Here, we first report on the nature of lattice and chemical disorder in a single-phase HEA and determine its local atomic structure. Our results uncover the manifestation of disorder at three different length scales, namely, the lattice distortion at the atomic scale, the

2 chemical disorder at the nm scale, and the emergence of nanoscopic shear at the mesoscopic scale. The multiscale disorder leads to hierarchical strengthening, unlike anything that we know before about metals 11 . This finding provides the structural basis for theoretical understanding of structure-property relationships in HEAs, and demonstrates the randomness of disorder as a new dimension for designing future strong and ductile alloys 12 .

Main
To determine the nature of lattice distortion and strengthening in a HEA, we study the single-phase solid solution (SPSS) AlxCoCrFeNi (x=0.1) (Suppl. Note 1). The facecentered-cubic (FCC) structure of this alloy is evidenced by X-ray diffraction 13 . The addition of Al to the random solution of CoCrFeNi 14 strengthens the alloy. Al also acts as a destabilizer with the secondary body-centered-cubic (BCC) phases starting to form at x≥0.3 15 . Beyond what we know, however, significant challenges remain on the characterization of local structure in Al0.1CoCrFeNi and other SPSS HEAs 10,16 , particularly on quantifying local lattice distortion and relating local structure to materials properties 17 .
Previous investigations of lattice distortion have largely relied on X-ray/Neutron scattering for the bulk averaged pair distribution function information 18 . However, such analyses often show small, or no significant, differences between HEAs and conventional alloys 19,20 .
This study is based on coherent electron nanodiffraction, which was previously used for analyzing disorder in amorphous materials 21 . We report on how the observation and 3 analysis of spatial fluctuations in diffuse scattering from a small volume of crystal, recorded using scanning electron nanodiffraction (SEND) [22][23][24] , can be applied for quantitative analysis and imaging of lattice distortion. For a wholistic insight from atomic mechanisms to the underlining nature of chemical disorder, we augment the diffraction study with aberration-corrected high-resolution electron microscopy (HREM) analysis and analytical transmission electron microscopy (TEM) determination of chemical inhomogeneity.

Local crystal structure
The Al0.1CoCrFeNi sample studied here was homogenized at 1100 °C under hot isostatic pressure (Methods). After TEM sample preparation, we used a variety of analytical microscopy techniques to examine its local crystal structure. Results from these analyses are presented in Fig. 1. Bright-field (BF) TEM imaging (Fig. 1a) reveals the Moiré fringe contrast caused by overlapping lattices in the HEA. Energy-filtered selected area electron diffraction (SAED) pattern ( Fig. 1b) from the sample shows two types of diffuse scattering (Type-1 and 2) close to the FCC Bragg reflections. The arc-shaped diffuse scattering (Type-1) falls on a ring, whose corresponding d-spacing (1.461 Å) is in between the d-spacing of {200} reflections of the FCC crystal (d200 = 1.79 Å) and {220} reflections (d220 = 1.27 Å).
Weak diffuse scattering is also observed at the position of the FCC forbidden {110} reflections (Type-2). An examination by high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) found the inhomogeneous atomic column 4 contrast in localized (nm-sized) regions, where elongations along <100> and <110> directions are seen (Fig. 1c). The local atomic displacements and the resulted symmetry breaking are further evidenced by convergent beam electron diffraction (CBED) (Fig. 1d), where the rocking curve information reflects the local symmetry of the crystal volume illuminated by the sub-nm electron probe 22 . Interestingly, the area averaged CBED pattern has the 4mm symmetry, which matches with the diffraction simulation from the ideal FCC structure model. Together, the above results demonstrate the multi-faceted nature of the HEA crystal structure that cannot be described in a traditional way based on the concept of crystals with defects, such as the presence of secondary phases or short-range ordering 16,25 . For reference, we also plotted the ACF of randomly generated maps in the background (Suppl. Note 2). Among the five elements, Cr map shows a stronger correlation between neighboring pixels (1 nm apart) greater than the 3 R  bounds ( Fe. Additionally, we found a tendency of Al to alloy with transition metals (TMs), while 5 TMs tend to repel each other within the 1 nm distance (Extended Data Fig. 2). Thus, fluctuations in elemental distribution are observed in Al0.1CoCrFeNi, with a significant amount of Cr segregation at the nm scale (Extended Data Fig. 3). This trend is consistent with the high Cr concentration measured inside the BCC phase in Al0.5CoCrFeNi 15 .

Fluctuations in electron diffuse scattering
To determine the origin of electron diffuse scattering in  Fig. 2b with notable diffraction spots within the marked dashed circles, which demonstrates the fluctuations in local electron diffuse scattering. By forming a dark field images using the 4D-DD, we found that the distribution of Type-1 diffuse scattering is highly inhomogeneous (Extended Data Fig. 4), while Type-2 diffuse scattering comes from the well-separated, nm-sized, BCC clusters (Extended Data Fig. 5). This shows that the HEA investigated here is largely single phase with a minute fraction of the BCC phase, which is consistent with the phase diagram prediction 26 .    (Fig. 2i, inset). The cluster sizes are at the order of a few nm.

The spatial and angular distribution of lattice distortion
Thus, the atomic displacements induced by lattice distortion in the HEA are neither spatially homogeneous nor random in displacement directions. This non-randomness, contrary to the prevailing assumption that lattice distortion is caused by random atomic displacements at each lattice site 8,18 , offers a new dimension for the design of HEAs 12 .

Nanoscopic shear
To further elucidate the concept of correlated lattice distortion, we focus on regions of a thin sample where Moiré fringes are observed (Fig. 1a). A spherical aberration (Cs)corrected TEM was used for this purpose. respectively, where gs and hs denote the two shear vectors. By comparing these ORs with the directly recorded diffraction pattern (Fig. 3e) Figure 3f schematically illustrates the real space lattices associated with ORs A and B and their variants in a square lattice. In the HEA, these types of distortions can form clusters of several nm is sizes as seen in Fig. 1a,   Fig. 2i, Fig. 3a and b, giving rise to nanoscopic shear.
In metals, shear is generally associated with martensitic transformation 29 . The shear with preferred orientation relationships in the HEA resembles the shear in the martensite, but without the fully formed second phase. In a sense, nanoscopic shear can be regarded as embryonic martensite stabilized by chemical disorder.

Nanoscopic shear interaction with dislocations
Next, we investigate the role of nanoscopic shear during deformation through the analysis of the compressed HEA nanopillars (for details of the compression experiment, (111) lattice planes (Fig. 4d).The parallel Moiré fringes are predominately observed in front of the dislocation band (Fig. 4b), as well as in the slightly deformed samples (Fig.   4a). The perpendicular Moiré fringes seen in Fig. 4c tend to