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Direct observation of chemical short-range order in a medium-entropy alloy Figure 2e is the high angle annular dark-field (HAADF) lattice image of the foc phase, and the inset is the corresponding FFT pattern ([112] zone axis. Extra diffuse reflections (one is circled in yellow) are again observed in addition to the foc diffraction spots (blue circles). Using these, inverseFFT images areobtained: the CSROregions light up inside theyellow circles in Fig. 2f, and the corresponding image for the normal fcc lattice is in Fig. 2g. Superimposing the two images leads to Fig. 2h, with details in the close up view in the inset. In this overlapped image, the CSRO stands out even more clearly because it adds intensity onto the foc columns. The red dashed rectangle gives the cell motif corresponding to the local CSRO configuration. Of special note is that the lattice planes (yellow dashed lines) characterizing the CSRO periodicity have an inter-planar spacing (dcsno) that is twice the inter-planar Fig. 1|TEMmicrostructure ofVCoNiMEA. Both images were taken with the spacing dice of the [ 3111 planes in the fcc phase (blue dashed lines), as [110] zone axis for the fec phase. a, Bright-field TEMimage showing the illustrated in the inset in Fig. 2h. Such chemical order, doubling the dlc ? equi-axed, dislocation-free fec grains, with faulted L2 plates inside, in the explains why the superlattice reflections appear at the locations coras-prepared microstructure after cold rolling followed by recrystallization responding to 21[311] in Fig. 2a,b and e. annealing at 1,173K.Left and right insets show the selected-area EDP and We next wished to determine what kind of CSRO is present and why: nano-beam EDP, respectively.b, Latticeimage of the fcesolution and the that is, the detailed arrangements of the three elemental species con: corresponding FFT pattern (inset). stituting the CSROs. To this end, we carried out energy'dispersive X-ray spectroscopy (EDS) mapping:seeFig.3aand additional maps as shown in Extended Data Fig. 2, based on HAADF imaging with the [112] zone be very small in spatial extent 225. To improve the signal-to-noise (back - axis. In Fig. 3a, each spot corresponds to an atomic column along the ground) ratio, we further carried out nano-beam (about 35nm in diam s thickness direction of the TEM foil. We mapped out each element, eter) EDP, using the same [112] zone axis. This led to much better V (red), Co (green) and Ni (blue), one by one. Theintensity (brightness) contrast (Fig. 2b): the extra reflections are easily discernible. These of the coloured spot depends on the make-up of the column, scaling disks all line up at the positions corresponding to 21[311], as marked with the content of the particular element being probed. We discover using arrows, clearly indicating the presence of CSRO. To observe the that the CSRO can be best described in terms of the Voccupancy. Spe locations and dimensions of coherently diffracting regions, Fig. 2c cifically, as seen in the EDS maps (two examples are shown, respectively, shows the dark-field TEM image (with a close-up view in the inset) taken in the left and right columns in Fig. 3b), two V-enriched (311) planes using the extra reflections; the vast majority (90\%) of these CSRO (see the map for V, under dashed yellow lines, across the red spots) regions that light up are less than 1nm in size, with an average size sandwich one V-depleted (311) plane (in either the V-Co or V-Ni map, d0.6nm; see the size distribution in Fig. 2d (and Extended Data under dashed blue line, across the intense green/blue spots but with Fig. 1a-3). The CSRO regions take up around 25\% of the total area in faint oreven vanishingred V). In other words, the V.enriched (311) planes these images. alternate with those enriched in Co and/or Ni. This alternating Fig. 2|Evidenceof CSRO in the fcc VCoNi. Thesample was deformed in [112] zone axis and the corresponding FFT pattern (inset). This pattern again tension to 18\% plastic strain. a, Selected-area EDP with the [112] zone axis. We displays the extra diffuse reflections (see, for example, inside the yellow circle) notetwoarrays of extra and diffuse disks (indicated by arrows) appearing at at 21311} positions, besides thesharper Braggs spots from the fec phase (blue 21 Ti11 positions (one example is inside the yellow circle). b, Nano-beam EDP with circles), f, g, Inverse FFT imageshowing the CSRO regions (several are circled), the [112] zone axis.Arrays of superlattice reflections at 21[311 ) positions as and the fcclattice, respectively. These two images are superimposed in hith indicated by arrows.c, Energy-filtered dark-field TEMimage takenusing the a close-up view of aCSROregion in the inset. Overlapping in this wayproduces diffuse reflections, with the inset showing aclose-up view of the dashed square bright sites that highlight the extra CSRO lining up on [3i1) planes (yellow area, highlighting some coherently diffracting clusters corresponding to the dashed lines), dfic denotes the spacing of 3 u1] planes in the normal fec lattice, local CSROs. The size distribution of these CSRO regions is shown in d. The whereas displays the spacing corresponding to the extra chemical order. average size d is 0.60nm and 0.65nm, based on the dark-field TEM image and The red dashed box outlines this unit period for the local CSRO configuration. negative C(r). In fact, thestrength of correlation indicated by the absolute C(r) values -that is, V-V being approximately two times V-Coand V-Ni whereas V-Co is slightly larger than VNi-is also in agreement with the degree of CSRO in the upper panel of Fig. 3e, which is the theoretically predicted magnitude for the order parameter (see below). Meanwhile, negative and positive C(r) values alternate, persisting roughly (due to lattice-distortion induced displacement/uncertainty especially at large separation distances) at 2,3 and 4 times the distance r. That is, the correlation (together with concurrent anti-correlation) suggests a repeating CSRO pattern across several neighbouring atomic columns: Co(Ni)-enriched, V-enriched, Co(Ni)-enriched, V-enriched and so on, both before (upper panel in Fig. 3d) and after (lower panel in Fig.3d) tensile deformation. This alternating neighbouring-column chemical preference in the (111) planes indicates the same preference/ avoidance trend as our observations about the (311) type planes (Figs. 2h, 3b). The thermodynamic driving force leading to the CSRO is shown in the lower panel of Fig. 3e, which will be discussed later (and in Supplementary Information section 3). Next, in Extended DataFig. 4 we use schematics to help visualize the local three dimensional atomic configuration that corresponds to the CSRO identified above. The inverse FFT image (Fig. 2h and inset) and EDS mapping (Fig. 3b) suggest that V atoms have a tendency/preference to occupy the eight vertices of the unit cell, interspersed with Co/Ni-enriched positions along the [111]direction. This is idealized in the model in Extended Data Fig. 4a, viewed from the [112] zone axis. This simplified model captures the alternating |311] planes (red ball planes interspersed with blue ball planes)-the salient chemical enrich ment repeatedly featured in figures such as Fig. 2h and its inset, as well as the peak/valley undulation along [I10] scan direction in Fig. 3 . An idealized three-dimensional local configuration that corresponds to the CSRO can thus be hypothesized in Extended Data Fig. 4b (to be analysed elsewhere). The EDP corresponding with the [112] zone axis in Extended DataFig. 4c shows the extra diffuse disks at the 21[311] positions, in full agreement with direct experimental observations in Figs. 2a, b, e. Therefore, it is such an atomic configuration/arrangement that locally breaks the fcc symmetry to produce the extra reflections, while all V, Co and Ni atoms reside on the fcc lattice sites. In the following discussion, we make four important points that are of interest to the HEA/MEA community. First, we carried out density functional theory (DFT) based modelling to monitor the evolution of CSRO and understand the underlying energetics. See Methods for the methodology y2312 we adopted. The cohesive energy gradually and substantially decreases with ordering (Fig. 3e). This demonstrates the thermodynamic driving force responsible for the CSRO observed. Meanwhile, we track the CSRO using the Warren-Cowley order parameter aABs where subscript ' AB ' indicates the pair consisting of element A and element B in the sth nearest-neighbour shell (Fig. 3e, see Meth ods). We see that VCoNi is not random (AsB00 ), but instead strongly disfavours VV connection in the 1st neighbour shell, as indicated by the positive vV1, and prefers VCoa2VNi (negative VCo01 or VN1 ). aVv1 is about twice the magnitude of VC01 or VN1 and V-Co is slightly more favoured than V-Ni (Fig. 3e). These theoretical findings explain the experimentally observed CSRO reported above. Second, we explain using asimplified model why the CSRO has been difficult to detect in HEAs and MEAs. A projection of the (111) plane along the [110] beam direction is shown in Extended Data Fig. 3b. Suppose that for a given atom (take the blue C as centre), its six (1st) nearest neighbours (and none of its 2 nd nearest neighbours) residing in this plane are unlike species, and for simplicity we assume the 3rd and 4th nearest neighbours (grey spheres) have negligible effects. As illustrated, when projecting along the [110] direction (dashed lines in Fig. 3b), the centre is directly superimposed on two 1st neighbours, resulting in a mixed-species column that blurs the difference from other neighbouring columns and hence the contrast in the image and chemical mapping. Previous attempts used only the [100] and [110] Direct observation of chemical short-range order in a medium-entropy alloy Figure 2e is the high angle annular dark-field (HAADF) lattice image of the foc phase, and the inset is the corresponding FFT pattern ([112] zone axis. Extra diffuse reflections (one is circled in yellow) are again observed in addition to the foc diffraction spots (blue circles). Using these, inverseFFT images areobtained: the CSROregions light up inside theyellow circles in Fig. 2f, and the corresponding image for the normal fcc lattice is in Fig. 2g. Superimposing the two images leads to Fig. 2h, with details in the close up view in the inset. In this overlapped image, the CSRO stands out even more clearly because it adds intensity onto the foc columns. The red dashed rectangle gives the cell motif corresponding to the local CSRO configuration. Of special note is that the lattice planes (yellow dashed lines) characterizing the CSRO periodicity have an inter-planar spacing (dcsno) that is twice the inter-planar Fig. 1|TEMmicrostructure ofVCoNiMEA. Both images were taken with the spacing dice of the [ 3111 planes in the fcc phase (blue dashed lines), as [110] zone axis for the fec phase. a, Bright-field TEMimage showing the illustrated in the inset in Fig. 2h. Such chemical order, doubling the dlc ? equi-axed, dislocation-free fec grains, with faulted L2 plates inside, in the explains why the superlattice reflections appear at the locations coras-prepared microstructure after cold rolling followed by recrystallization responding to 21[311] in Fig. 2a,b and e. annealing at 1,173K.Left and right insets show the selected-area EDP and We next wished to determine what kind of CSRO is present and why: nano-beam EDP, respectively.b, Latticeimage of the fcesolution and the that is, the detailed arrangements of the three elemental species con: corresponding FFT pattern (inset). stituting the CSROs. To this end, we carried out energy'dispersive X-ray spectroscopy (EDS) mapping:seeFig.3aand additional maps as shown in Extended Data Fig. 2, based on HAADF imaging with the [112] zone be very small in spatial extent 225. To improve the signal-to-noise (back - axis. In Fig. 3a, each spot corresponds to an atomic column along the ground) ratio, we further carried out nano-beam (about 35nm in diam s thickness direction of the TEM foil. We mapped out each element, eter) EDP, using the same [112] zone axis. This led to much better V (red), Co (green) and Ni (blue), one by one. Theintensity (brightness) contrast (Fig. 2b): the extra reflections are easily discernible. These of the coloured spot depends on the make-up of the column, scaling disks all line up at the positions corresponding to 21[311], as marked with the content of the particular element being probed. We discover using arrows, clearly indicating the presence of CSRO. To observe the that the CSRO can be best described in terms of the Voccupancy. Spe locations and dimensions of coherently diffracting regions, Fig. 2c cifically, as seen in the EDS maps (two examples are shown, respectively, shows the dark-field TEM image (with a close-up view in the inset) taken in the left and right columns in Fig. 3b), two V-enriched (311) planes using the extra reflections; the vast majority (90\%) of these CSRO (see the map for V, under dashed yellow lines, across the red spots) regions that light up are less than 1nm in size, with an average size sandwich one V-depleted (311) plane (in either the V-Co or V-Ni map, d0.6nm; see the size distribution in Fig. 2d (and Extended Data under dashed blue line, across the intense green/blue spots but with Fig. 1a-3). The CSRO regions take up around 25\% of the total area in faint oreven vanishingred V). In other words, the V.enriched (311) planes these images. alternate with those enriched in Co and/or Ni. This alternating Fig. 2|Evidenceof CSRO in the fcc VCoNi. Thesample was deformed in [112] zone axis and the corresponding FFT pattern (inset). This pattern again tension to 18\% plastic strain. a, Selected-area EDP with the [112] zone axis. We displays the extra diffuse reflections (see, for example, inside the yellow circle) notetwoarrays of extra and diffuse disks (indicated by arrows) appearing at at 21311} positions, besides thesharper Braggs spots from the fec phase (blue 21 Ti11 positions (one example is inside the yellow circle). b, Nano-beam EDP with circles), f, g, Inverse FFT imageshowing the CSRO regions (several are circled), the [112] zone axis.Arrays of superlattice reflections at 21[311 ) positions as and the fcclattice, respectively. These two images are superimposed in hith indicated by arrows.c, Energy-filtered dark-field TEMimage takenusing the a close-up view of aCSROregion in the inset. Overlapping in this wayproduces diffuse reflections, with the inset showing aclose-up view of the dashed square bright sites that highlight the extra CSRO lining up on [3i1) planes (yellow area, highlighting some coherently diffracting clusters corresponding to the dashed lines), dfic denotes the spacing of 3 u1] planes in the normal fec lattice, local CSROs. The size distribution of these CSRO regions is shown in d. The whereas displays the spacing corresponding to the extra chemical order. average size d is 0.60nm and 0.65nm, based on the dark-field TEM image and The red dashed box outlines this unit period for the local CSRO configuration. negative C(r). In fact, thestrength of correlation indicated by the absolute C(r) values -that is, V-V being approximately two times V-Coand V-Ni whereas V-Co is slightly larger than VNi-is also in agreement with the degree of CSRO in the upper panel of Fig. 3e, which is the theoretically predicted magnitude for the order parameter (see below). Meanwhile, negative and positive C(r) values alternate, persisting roughly (due to lattice-distortion induced displacement/uncertainty especially at large separation distances) at 2,3 and 4 times the distance r. That is, the correlation (together with concurrent anti-correlation) suggests a repeating CSRO pattern across several neighbouring atomic columns: Co(Ni)-enriched, V-enriched, Co(Ni)-enriched, V-enriched and so on, both before (upper panel in Fig. 3d) and after (lower panel in Fig.3d) tensile deformation. This alternating neighbouring-column chemical preference in the (111) planes indicates the same preference/ avoidance trend as our observations about the (311) type planes (Figs. 2h, 3b). The thermodynamic driving force leading to the CSRO is shown in the lower panel of Fig. 3e, which will be discussed later (and in Supplementary Information section 3). Next, in Extended DataFig. 4 we use schematics to help visualize the local three dimensional atomic configuration that corresponds to the CSRO identified above. The inverse FFT image (Fig. 2h and inset) and EDS mapping (Fig. 3b) suggest that V atoms have a tendency/preference to occupy the eight vertices of the unit cell, interspersed with Co/Ni-enriched positions along the [111]direction. This is idealized in the model in Extended Data Fig. 4a, viewed from the [112] zone axis. This simplified model captures the alternating |311] planes (red ball planes interspersed with blue ball planes)-the salient chemical enrich ment repeatedly featured in figures such as Fig. 2h and its inset, as well as the peak/valley undulation along [I10] scan direction in Fig. 3 . An idealized three-dimensional local configuration that corresponds to the CSRO can thus be hypothesized in Extended Data Fig. 4b (to be analysed elsewhere). The EDP corresponding with the [112] zone axis in Extended DataFig. 4c shows the extra diffuse disks at the 21[311] positions, in full agreement with direct experimental observations in Figs. 2a, b, e. Therefore, it is such an atomic configuration/arrangement that locally breaks the fcc symmetry to produce the extra reflections, while all V, Co and Ni atoms reside on the fcc lattice sites. In the following discussion, we make four important points that are of interest to the HEA/MEA community. First, we carried out density functional theory (DFT) based modelling to monitor the evolution of CSRO and understand the underlying energetics. See Methods for the methodology y2312 we adopted. The cohesive energy gradually and substantially decreases with ordering (Fig. 3e). This demonstrates the thermodynamic driving force responsible for the CSRO observed. Meanwhile, we track the CSRO using the Warren-Cowley order parameter aABs where subscript ' AB ' indicates the pair consisting of element A and element B in the sth nearest-neighbour shell (Fig. 3e, see Meth ods). We see that VCoNi is not random (AsB00 ), but instead strongly disfavours VV connection in the 1st neighbour shell, as indicated by the positive vV1, and prefers VCoa2VNi (negative VCo01 or VN1 ). aVv1 is about twice the magnitude of VC01 or VN1 and V-Co is slightly more favoured than V-Ni (Fig. 3e). These theoretical findings explain the experimentally observed CSRO reported above. Second, we explain using asimplified model why the CSRO has been difficult to detect in HEAs and MEAs. A projection of the (111) plane along the [110] beam direction is shown in Extended Data Fig. 3b. Suppose that for a given atom (take the blue C as centre), its six (1st) nearest neighbours (and none of its 2 nd nearest neighbours) residing in this plane are unlike species, and for simplicity we assume the 3rd and 4th nearest neighbours (grey spheres) have negligible effects. As illustrated, when projecting along the [110] direction (dashed lines in Fig. 3b), the centre is directly superimposed on two 1st neighbours, resulting in a mixed-species column that blurs the difference from other neighbouring columns and hence the contrast in the image and chemical mapping. Previous attempts used only the [100] and [110]