Microstructure evolution and twinning-induced plasticity (TWIP) in hcp rare-earth high- and medium-entropy alloys (HEAs and MEAs) due to tensile deformation Open Access

High-entropy alloys (HEAs) offer exciting opportunities to develop new material systems alongside conventional alloys to meet increasing demands for high-performance materials. HEAs are defined as single-phase solid solutions with at least five alloying elements (5-35 at. % each) without a main element and a high configurational entropy ΔS_conf > 1.5 R (R: gas constant, 8.314 Jmol⁻¹ K⁻¹) that follows the Boltzmann equation.^1–5 The high entropy of the alloy should stabilize the solid solution in simple crystal structures and prevent intermetallic phases due to minimized configurational enthalpy.^5–8 Since the first results on HEAs were published by Cantor and Yeh in 2004,^9,10 a variety of advantages have been reported for HEAs, including superior mechanical, electrical, and magnetic properties or strong corrosion and wear resistance.^{1,2,5,11–13} Consequently, the field of HEAs has attracted much attention within the materials science community. With no main element, new concepts are needed to investigate and characterize the properties of HEAs. For example, the classical solute–solvent principle is not applicable.^12,13 Concerning the mechanical properties of HEA, no general strengthening due to a high-entropy effect has been observed so far.^8,14 Despite the name high-entropy alloy, multiple factors other than the calculated high configurational entropy are decisive for the microstructures and properties of HEAs.^1,3,15–17

Hexagonal-close-packed (hcp) HEAs are less investigated than cubic HEAs, and their mechanical behavior is partly unknown.^2,11,18,19 The hexagonal HEAs already described in the literature primarily consist of rare-earth elements, as these are highly similar in terms of chemical and physical properties and can, therefore, be regarded as ideal solid solutions.^18–20 The equiatomic quinary hcp alloy Ho-Dy-Y-Gd-Tb was first described by Feuerbacher et al. in 2015;¹⁹ therefore, the alloy is denoted as the Feuerbacher alloy (HEA-Fb).^8,14,18 HEA-Fb has a magnesium-type structure with point group P6₃mm/c, and the lattice parameters are reported as a = (363 ± 30) pm and c = (566 ± 20) pm.^18–20 Micropillar compression tests with HEA-Fb have been provided by Soler et al.²¹ For HEA-Fb, basal slip (0001) $[ 1 2 ¯ 10 ]$ was reported during the compression test with micropillars.

Additionally, the first set of tensile tests for HEA-Fb and a derived medium-entropy alloy (MEA) without Y at room temperature (RT) is given in Ref. 8. These results imply that HEA-Fb has no solid solution strengthening and that the configurational entropy ΔS_conf is not correlated to the tensile behavior at RT. The ductility differs significantly, which cannot be explained by solid solution strengthening or configurational entropy. Consequently, a deeper understanding of the influence of the microstructure is needed.

This work addresses the microstructure evolution due to the tensile deformation of the brittle HEA-Fb compared to the ductile 4-Y. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) analysis of HEA-Fb and 4-Y show detailed insight into microstructural changes after plastic deformation and twinning behavior. A twinning-induced plasticity (TWIP) effect was found for 4-Y opposing HEA-Fb, explaining the different ductility during tensile deformation. Additionally, twin structures are analyzed, which reveals the importance of twin boundaries as obstacles for dislocations during plastic deformation and a dynamic Hall–Petch effect. This study reveals that conventional concepts for material behavior apply to the studied HEA.

Table I lists the selected alloys used for this study. The quinary HEA-Fb is compared to the quaternary 4-Y. Both alloys were prepared with an arc melter AM 500 by Bühler in an argon atmosphere at 520 mbar after three evacuation steps. Titanium was used as an oxygen getter before melting the alloys from elemental granules. Each undeformed knob-shaped specimen weighs about 30 g, and the specimens were melted three times for homogenization. The elemental compositions were measured via micro-x-ray fluorescence (μ-XRF) analyzer Orbis PC by Ametek at 45 kV and 700 μA, and the masses of the granules were adjusted with linear interpolation to achieve equiatomic compositions (±2.3 at. %). Measured compositions are listed in Table I. From the knob-shaped specimens, small tensile specimens with a gauge length of 5 mm were wire-cut with EDM machine CUT 200 SP by Agie Charmilles. As rare-earth elements are prone to oxidation, all specimens were carefully stored in a vacuum desiccator at a pressure of about 100 mbar.

As described in Ref. 13, tensile tests at RT were carried out for the alloys, along with all pure elements and different low- and medium-entropy alloys derived from this alloy system. A universal testing machine Z 2.5/T13S (Zwick) was used at a 0.01 mm min⁻¹ truss velocity, which corresponds to a technical strain rate of $ϵ ˙≈ 10 − 3 s − 1$⁠, and elongation measurement was carried out with a video extensometer. A detailed description of tensile tests and rig can be found in Refs. 8 and 22. Immediately before testing, the oxide layers on the tensile specimens were removed by grinding with SiC paper (Grid 600).

Cross sections were metallographically prepared from the undeformed specimens and after tensile deformation. Due to the high susceptibility to oxidation, the specimen preparation of this alloy system is very challenging, and a water-free preparation routine is needed (see. 13) The cross sections, which have been microscopically analyzed in our previous work, served as the basis for TEM lamellae preparation. Thin TEM lamellae were nanofabricated using a focused ion beam (FIB) in a FEI/Thermo Fisher Scientific (TFS) Helios NanoLab 600 dual-beam system, SEM 1540EsB Cross Beam from Zeiss, and FEI Helios NanoLab 460F1 dual-beam system. The alloys bent a lot during preparation; therefore, the thinning of the TEM lamellae was limited and had to be carried out carefully, reducing the ion beam voltage to 5 kV at 1.4 nA.

Scanning electron microscopy (SEM) using a 1540EsB Cross Beam from Zeiss and Apreo FEG SEM from Thermo Scientific was applied to get an overview of the microstructures of both alloys in the undeformed state and after tensile deformation. TEM was applied in the bright-field image mode and STEM in the high-angle annular dark-field mode (HAADF) as well as the diffraction mode to analyze and compare the microstructural changes in HEA-Fb and 4-Y due to tensile deformation. Depending on the availability, various different TEM and STEM systems were used for the multi-scale characterization of the microstructure. This includes Zeiss Libra FE 200 S/TEM with omega filter in Bayreuth, FEI/TFS Tecnai G2 F30 TEM at CEMAS in Columbus, OH, FEI Titan 80-300 TEM in Jülich, and image-aberration corrected FEI/TFS Titan G2 60–300 S/TEM both at CEMAS and in Jülich. The microstructures were investigated using either 200 or 300 kV acceleration voltage. Bright-field, annular dark-field, and high-angle annular dark-field (HAADF) detectors were used in the STEM mode. The crystal structures were analyzed via selected area electron diffraction (SAED). Data processing was based on an hcp crystal structure with the space group P6₃/mmc (194) and the lattice parameters a = 361.3 nm and c = 570.4 nm. Furthermore, local chemical compositions of the TEM lamellae were analyzed with energy-dispersive x-ray spectroscopy (EDS) in FEI/TFS Titan G2 60–300 STEM and processed with TFS Velox. Along with elemental mappings, averaged line scans were measured to evaluate local changes in the elemental compositions of the alloys.

Figure 1 shows the selected stress–strain curves of HEA-Fb and 4-Y at RT for each alloy.⁸ At least two valid tensile tests were carried out, and a representative stress–strain curve is given for comparison. The tensile strength of both alloys is in the range of the pure elements, so no effect of solid solution strengthening is measurable. Furthermore, no direct correlation between ultimate tensile strength, yield strength, ductility, and ΔS_conf at RT is found, so a high-entropy effect can be ruled out as decisive for the tensile properties of HEA-Fb and 4-Y at RT.

While the tensile strengths of HEA-Fb and 4-Y are in the medium range of the constituent elements,⁸ we argue that the strengths are explainable due to the rule of mixture (ROM), which leads to 182 MPa. On the other hand, the differences in ductility are substantial. HEA-Fb behaves brittle with a strain to failure ε_f = 1 ± 0.1%, opposing the ductile 4-Y with a strain to failure ε_f = 12.3 ± 0.8%. The stress–strain curve of 4-Y reveals a pronounced yield strength with nearly constant strength up to 10% strain. As the area under the curve is larger than for HEA-Fb, this material absorbs more energy during plastic deformation before fracture. As the vast differences in the tensile ductility cannot be explained by solid solution strengthening or a high-entropy effect, the microstructure is examined in more detail.

Figure 2(a) shows the morphology of undeformed HEA-Fb. Additionally, the elemental mappings of oxygen (O) and Y are given in Figs. 2(b) and 2(c). The oxides found mainly follow the grain boundaries in the bulk material. From the elemental mapping of Y, no segregation or other phases are visible. Figures 2(d) and 2(e) show the cross-sectional morphology of tensile deformed HEA-Fb. An overview of the grain structure is presented in Fig. 2(d). The fracture is perpendicular to the tensile loading axis, typical for a brittle fracture. In Fig. 2(e), oxides along grain boundaries from the bulk material are shown in detail. In Fig. 2(f), the fractured surface of the specimen is shown, where the crack follows the grain boundaries. From these results, it can be concluded that the grain boundaries are weaker than the grains and are favorable sites for oxidation. Furthermore, the crack propagation along the oxidized grain boundaries leads to a brittle mechanical behavior of HEA-Fb.

TEM-related techniques assess the crystal orientation distribution, twin structures, and defects in the samples in the undeformed and tensile deformed state. HEA-Fb is compared to 4-Y. Significant differences in microstructures are apparent. A detailed analysis of the microstructure changes due to tensile deformation is given in the following.

Figure 3(a) shows the elongated features in the bright-field TEM image of undeformed HEA-Fb. SAED patterns are recorded to determine the crystal orientations of the striped features and the matrix. The indexed SAED patterns are shown in Figs. 3(b) and 3(e) for the striped feature and in Fig. 3(c) for the matrix. Additionally, Fig. 3(d) includes two sets of superimposed diffraction patterns of both the matrix and the elongated features, which are recorded at their mutual interface. Positions from which the SAED patterns were obtained are marked in the bright-filed STEM image in Fig. 3(a) by the respective letters b, c, d, and e. From the diffraction patterns, it can be interpreted that both the matrix and the elongated features have a perfect hcp structure, matching well with the structure found for HEA-Fb by Feuerbacher.¹⁹ Consequently, the elongated features are identified as twins with respect to the matrix. The twins can be indexed as $[ 2 ¯ 201 ]$ orientation in (b), (d), and (e). Interestingly, the two twins in (b) and (e) are rotated 70° to each other, while (d) and (e) are aligned. Structures are observed within the twins in the bright-field image of undeformed HEA-Fb, as shown in Fig. 3(a), which will be discussed in Sec. III C 2. The matrix [in both Figs. 3(c) and 3(d)] can be indexed as $[ 11 2 ¯ 0 ]$⁠.

Figure 4(a) shows the tensile deformed HEA-Fb in a bright-field STEM image. An overview of the lamella is given, and the direction of tensile stress is marked with horizontal arrows. The orientation of the zone axis can be indexed as $[ 20 2 ¯ 3 ]$⁠. Dark irregular structures on the material indicate the oxides (measured via EDS, not shown here), which have grown between preparation and STEM analysis despite storage in a vacuum desiccator. Like in the undeformed material, many long and aligned twins are visible in tensile deformed HEA-Fb. In Fig. 4(b), a detail of the lamella from different TEM microscope tilt angles (α₁ = 13.7°, α₂ = 11.8°; β₁ = -5.9°, β₂ = 0°) reveals that the twins have been crossed by a slip plane (marked with dotted line). The slip plane and aligned twins form an angle of about 64°. Considering twin rotation during growth (see Sec. IV A 1), this roughly reflects the sixfold (60°) symmetry of the hcp crystal.

Figures 5(a) and 5(b) show the lamella of undeformed 4-Y and its corresponding SAED pattern, respectively. The HAADF image in Fig. 5(a) demonstrates that the undeformed sample is homogeneous in the microscale range. There are no compositional variations, precipitates, or secondary phases. Elemental mappings via STEM-EDS confirm the homogenous distribution of the constituent element in the lamella (not shown here). In the bulk material, “dimple-like” features are visible, which are likely associated with the FIB preparation of the lamella. In the upper right corner of Fig. 5(a), an oxide has grown on the surface of the lamella after FIB preparation. On the top edge of the lamella, the former surface of the tensile specimen was ground before tensile tests, which induced twinning. Figure 5(b) shows a SAED from the bulk of the undeformed 4-Y. The SAED indicates a basal [0001] orientation of a perfect hexagonal structure, with some indexed examples.

Figure 6(a) shows a HAADF image of tensile deformed 4-Y, indicating twins (dark contrast) formed in the matrix (bright contrast) due to tensile stress. The direction of tensile stress is marked with horizontal arrows. Overall, extensive twinning occurs during plastic deformation, and a high concentration of twins is visible in Fig. 6(a). The cross section of twins is lenticular-shaped with a length of up to several micrometers. Along with twins, slip bands have formed due to tensile deformation, which appear perpendicular to the twins. EDS measurements were carried out to assess the chemical compositions of the twins. Figure 6(b) shows EDS of the averaged linescans of tensile deformed 4-Y from all constituent elements. As marked in the HAADF image in Fig. 6(a), the scans start in the matrix (bright contrast, higher HAADF-STEM intensity on the primary x-axis) and enter a lenticular-shaped twin (darker contrast, lower HAADF-STEM intensity) after about 0.33 μm of measurement. The elemental concentrations in at. % are given for Gd (blue), Tb (green), Dy (orange), and Ho (red). From the line scans, it is evident that the elemental composition of the matrix and twins is homogeneous and identical. The average measured composition along the line scan is Gd 22.7 at. %, Tb 27.6 at. %, Dy 25.2 at. %, and Ho 24.5 at. %.

Figure 7(a) shows a bright-field image of tensile deformed 4-Y, with positions for SAED analysis marked as (b)–(e). The diffraction patterns are provided for the matrix in Fig. 7(b), for two aligned twins in Figs. 7(d) and 7(e), and an overlap of the matrix and twins in Fig. 7(c). This overlap indicates a high density of twin structures formed during plastic deformation. The matrix can be indexed to the $[ 11 2 ¯ 0 ]$ orientation. The twins can both be indexed with $[ 2 ¯ 201 ]$ orientation, and their diffraction patterns are rotated to each other by 180° (mirrored inside the diffraction plane). From Fig. 7(a), they appear perpendicular to each other.

In Figure 8(a), the prominent examples of straight twin boundaries are depicted. It is striking that oxides (dark dots) are lined up like a string of pearls along the twin boundaries. Oxides grow on the surface of the TEM lamella inside grains during and after preparation (not shown here). In the upper part of the image, twins with different orientations, with twin boundaries forming an angle of 20° to each other, are visible; at least two twin modes are active in the undeformed material. In Fig. 8(b), an intersection of twins in undeformed HEA-Fb is shown in detail. The twin boundaries exhibit defect structures such as stacking faults and parallel dislocations. The density of defects like oxides and dislocations inside the twin is more pronounced than outside.

Figure 8(c) shows many lenticular twins in tensile deformed 4-Y. The twins are aligned parallel, so one main twin mode was activated during the tensile test. Slight deviations of their orientation are obtained. Additionally, a broad line structure that appears behind the twins is partially marked out by sharp contours. This structure indicates slip bands activated approximately perpendicular to the twinning during tensile tests. In Fig. 8(d), a twin in tensile deformed 4-Y is displayed in detail. A pileup of stacking dislocations is indicated by a dark outline of the twin boundaries. Additionally, dislocations run across the twin, perpendicular from one long side of the primary twin to the other. While HEA-Fb is already oxidized twin boundaries in the undeformed state, the twins in 4-Y are less oxidized, even after tensile deformation. Both alloys contain pileups of dislocations at the twin boundaries. Dislocations that run perpendicular inside the twins are mainly found in 4-Y.

By comparing of equiatomic HEAs, MEAs, low-entropy alloys (LEAs), and pure elements, a proposed effect of high configurational entropy on the tensile behavior at RT is ruled out for HEA-Fb.⁸ Consequently, other explanations must be found by microstructure analysis for the observed tensile behavior, as the differences in ductility are significant.

To our knowledge, this study is the first analysis of twin evolution due to tensile deformation at RT for the quinary HEA-Fb and quaternary 4-Y. The results provide a key contribution to the understanding of plastic deformation of high-entropy alloys from the example of a hexagonal rare-earth-based alloy system with no solid solution strengthening. Lenticular-shaped structures have already been reported for HEA-Fb, which were considered cubic precipitates.²⁰ Rod-like cubic close-packed precipitates, slightly enriched in Y (<3 at. %), were reported for HEA-Fb and other rare-earth-based HEAs.⁸ New findings in this study with TEM diffraction analysis give clear evidence that these structures are twins, proving the HEA-Fb single-phase.

As polycrystalline hexagonal-close-packed metals, like Mg, do not fulfill the von Mises–Taylor criterion, twinning and nonbasal slip occur when stress along the c-axis is applied.^2,23–27 As all constitutional elements and HEA-Fb and 4-Y exhibit a Mg-type structure, twinning during plastic deformation is expected. For the two alloys analyzed in this work, the c/a ratios can be calculated as 1.579 for HEA-Fb¹⁹ and 1.578 for 4-Y, which is lower than in an ideal hcp crystal. A low c/a ratio indicates the activation of non-basal slip and twinning during plastic deformation.

It is important to note that tensile twinning modes and slip systems may be distinct from each other.^25,28 Depending on the c/a ratio, various slip and twinning modes are activated first.^11,29 For hexagonal metals like Mg, the tensile twinning mode $[ 10 1 ¯ 2 ]$ is often observed.^24,28,30 There are only a few reports on twinning in pure rare earths. For Gd, there is an early report of $[ 10 1 ¯ 2 ]$ twins.³¹ In a study on cold-rolled Dy, the deformation twins were characterized as $[ 10 1 ¯ 2 ]$ and $[ 11 2 ¯ 1 ]$⁠.³² The $[ 10 1 ¯ 2 ]$ twinning mode occurs easily and commonly, as it accommodates tension strain along the c-axis during plastic deformation.^25,33

Figure 9(a) shows a schematic of a three-dimensional twin and its lenticular-shaped projection in the plane of a TEM lamella, visible for tensile deformed 4-Y in Fig. 8(c).³⁴ When twinning, the introduction of twin boundaries alters the local stress states of the lattice, and the twin will reorientate by rotation to achieve the lowest energetical state.²⁹ Reorientation of grains during deformation is common in metals with low stacking fault energies. A stacking fault is formed when a dislocation dissociates into partials, so the mobility of dislocations also depends on the stacking fault energy.^35,36 Mg with a low stacking fault energy of 18 mJ/m²³⁷ and a lattice rotation of about 3.8° was reported for $[ 11 1 ¯ 2 ]$ twins during their growth.²³ In Fig. 9(b), a twin rotation of 3.8° is shown. The lattice rotation increases the strain of the alloy.² Rotation during growth explains deviations in the alignment of the observed lenticular-shaped twins in tensile deformed 4-Y.

Figures 9(c) and 9(d) show the schematic drawings of the superimposed crystal lattices found in undeformed HEA-Fb. Through careful TEM diffraction analysis, geometric relationships between twins and their parental grains are identified. Interestingly, HEA-Fb contains twins already in the undeformed state. While the zone axis of the matrix is identified as $[ 11 2 ¯ 0 ]$⁠, the twins are on the perpendicular zone axis $[ 2 ¯ 201 ]$⁠, as can be seen in Fig. 7(a) and illustrated in Fig. 9(c). The two neighboring twins share the same zone axis $[ 2 ¯201]$ but are rotated by 70° to each other. As the diffraction pattern is symmetrical for this zone axis, this rotation of 70° corresponds geometrically to a horizontal mirror image and an additional rotation of −15°. Either way, at least two different twinning modes were activated here. Their twin boundaries observed in the imaging mode form an angle of around 15°–20°, as depicted in Fig. 8(a). After tensile tests of this very brittle alloy, the twinning morphologies in the tensile deformed HEA-Fb are comparable to undeformed HEA-Fb; straight, long twins are observed. Consequently, little twinning during plastic deformation was activated, resulting in the observed brittle behavior with strain at a failure of less than 1%. Comparing HEA-Fb in the undeformed state and after tensile tests, the main difference is the activation of slip. After tensile deformation, slip bands are visible through the whole lamella. The slip bands form an angle of about 63°–64° to the observed twins. Considering twin rotation in the order of 3°–4° as reported for Mg, this angle reflects the sixfold symmetry of the hexagonal lattice. It implies that the slip and twin systems in HEA-Fb are identical.

Contrasting the undeformed HEA-Fb, the undeformed 4-Y alloy does not contain twins. The microstructure is homogeneous, containing no variants in composition or precipitates. The microstructure changes dramatically due to tensile deformation. Extensive twinning is activated during plastic deformation, and many aligned twins form in the parental grain. The hcp crystal structure is confirmed by employing SAED, whereas the local chemical composition was analyzed via EDS in TEM. These in-depth methods ensure that the found structures are twins that formed during the tensile deformation. Compared to HEA-Fb, the grain’s twin density is higher. The twins in tensile deformed 4-Y occur in clusters, and they are all oriented in two directions perpendicular to each other. While the matrix is on the $[ 11 2 ¯ 0 ]$ zone axis, the indexed twins are on the $[ 2 ¯ 201 ]$ zone axis. In between twins on this same zone axis, a rotation of 180° is found. These zone axes are the same as obtained in HEA-Fb, so essentially, the same twinning modes have been activated in both alloys.

In HEA-Fb, straight and parallel twins are observed in the undeformed state and after plastic deformation in the tensile test. They are very homogeneous in size and shape and are apparently aligned. The twins are activated with at least two significant orientations, which are rotated by 70° to each other. The twins in HEA-Fb are, on average, 350 nm thick and extend partially through the entire TEM lamella, exceeding a length of 10 μm.

Compared to twins in HEA-Fb, the twins formed in tensile deformed 4-Y differ significantly in their shapes. These twins are lenticular, considerably shorter, have rounder twin boundaries and are irregularly shaped. While twins typically appear as straight lines,² but lenticular shapes have been reported as well.^23,34,38 As grains are split into non-interacting domains by twinning, an asymmetric movement of twin boundaries and, hence, an asymmetric twin growth are the result.³⁹ Due to the misalignment of twins and parental grains, the formation of interface defects is facilitated.^29,33 This explains the uneven twin shapes in tensile deformed Y-4. The thickness (15–200 nm) and the length of the twins vary to a greater extent than those of HEA-Fb. Consequently, the irregular twin shapes in tensile deformed 4-Y indicate the gradual twin growth during plastic deformation, opposing the straight twins in HEA-Fb, which occur during or immediately after casting.

The tips of the twins can be blunted or sharp, whereby the types of dislocations attached provide an explanation for this observation.^29,33 When the twins in tensile deformed 4-Y are regarded, it is striking that they mostly end in sharp tips [see Fig. 8(c)]. In hexagonal Mg and Ti alloys, parallel basal-prismatic (PB/BP) serrations at the twin boundaries accommodate deviations from the perfect habit planes. External stresses induce local inhomogeneous shear during plastic deformation, forming PB/BP serrations.^29,33 For Ti, the formation of short fragments of coherent PB interfaces between the twin and parental grain is reported to cause faceting at the twin.³³ In the AZ 31 Mg alloy, the formation of sharp twin tips is attributed to the formation of such PB/BP serrations at the ends of twins. In contrast, blunt twin tips are formed when the twin ends at the interface of the twin and parental grain, whereby PB/BP serrations may also be present. Overall, the formation of sharp or blunt twin tips is determined by the glide of twinning dislocations on the interfaces of the twinning plane, the interface, and PB/BP serrations.²⁹ 

Plasticity requires the movement of dislocations through the metal. Strengthening occurs when dislocation movement is successfully hindered by obstacles in the alloy, e.g., twin boundaries, which are strong obstacles.^40–42 When dislocations pileup at twin boundaries, the local stress is increased.² Here, the competitive role of twinning against cracking is relevant. Suppose the critical stress for twinning is lower than that for cracking. In that case, the accumulation of dislocations at the twin interfaces leads to secondary twinning and, thus, to the strengthening of the microstructure by reduction in the local stress.⁴³ The possible strengthening effect of obstacles depends inversely on their spacings, so close-spaced obstacles have a significant strengthening effect.¹ 

Depending on the local stress state and the type of dislocation, they can dissociate into partials.⁴² If partial dislocations can glide along twin boundaries, local stresses are relieved, which increases the ductility.¹ For face-centered-cubic (FCC) metals, the Basinski mechanism describes the transformation from glissile to sessile dislocations when attached to twin boundaries, which may lead to work hardening.^24,44 The Basinski mechanism is discussed for hexagonal metals as well.⁴⁵ However, Morrow et al. argue that it is not applicable for hexagonal metals, as they observe dislocations at twin boundaries that remain mobile.⁴⁶ Nonetheless, a pileup of dislocations will lead to a hardening effect.

On the contrary, twinning nucleation, growth, and rotation lowers the local stress, which induces a softening effect during plastic deformation. The softening effect is also confirmed by decreasing stress–strain curves during tensile tests.⁴⁰ As evident for 4-Y in Fig. 1, the stress level remains relatively constant during most plastic deformation, so twinning growth and pileup of dislocations are balanced out in this phase. Before the fracture of the specimen, the stress–strain curve of 4-Y declines. Necking of the specimen is a possible explanation for the decrease in stress, but stress relaxation can also be observed when twins intersect other interfaces.²⁴ 

Twinning during plastic deformation causes a dynamic Hall–Petch effect because it reduces the grain size and, therefore, the main mean free path of dislocations.^15,35,41,47 For coarser grains and low temperatures, the predisposition for twinning is enhanced compared to the predisposition of slip.⁴⁸ Furthermore, a dynamic Hall–Petch effect was reported for hexagonal metals.⁴⁵ To what extent the dynamic Hall–Petch effect contributes to the strengthening of metals is still debatable. Regardless, it is claimed to be the main cause of the twinning-induced plasticity (TWIP) effect.^15,47 The TWIP effect is utilized to overcome the strength-ductility trade-off with the sequential activation of deformation mechanisms in so-called TWIP steels.⁴⁹ 

TWIP steels are austenitic and contain high Mn (20 wt. %) contents along with small additions of C/Si/Al, which leads to very low stacking fault energies in the range of 20–40 mJ/m² at RT.^35,47,50 When FCC metals have a low stacking fault energies, dislocations have an overall higher mobility, stacking faults are wider, and the material is more prone to twinning, which is the main prerequisite for a TWIP effect.^35,41,50 Additionally, the formation of thin nanometric deformation twins contributes to the TWIP effect, because it accommodates local stresses in the matrix and twins.⁴¹ In TWIP steels, double twin systems are also activated.⁵¹ Considering the competitive role of twinning against cracking, the activation of more than one twin system increases the ductility of the alloys.⁴³ Overall, the TWIP effect is based on the dynamic Hall–Petch effect due to twins' division of the parental grains, the blocking of dislocation movement at the twin boundaries, and reduced movement of grain edges when twins are present.³⁵ 

TWIP effects are not limited to TWIP steels, e.g., it was documented for a carbon-doped FCC HEA.⁴² The quaternary 4-Y also fulfills all the criteria that lead to a TWIP effect. An essential prerequisite for a TWIP effect is a low stacking fault energy, which is given for hcp metals. Furthermore, excessive twinning of 4-Y occurs due to plastic deformation at RT, including the formation of double twin systems. Twinning during tensile deformation leads to a dynamic Hall–Petch effect. 4-Y is significantly more ductile than HEA-Fb, where little twinning occurs due to tensile deformation. Consequently, the ductile tensile behavior of 4-Y at RT can be attributed to a TWIP effect.

Figure 10 summarizes the microstructures of HEA-Fb and 4-Y in the undeformed state and after tensile deformation. In contrast to undeformed 4-Y, twins have already formed in undeformed HEA-Fb [see Fig. 10(a)], so their formation does not contribute to the plastic response of this alloy. Figure 2 shows that crack propagation in HEA-Fb follows the grain boundaries, as depicted in Fig. 10(b). As the grain boundaries and already formed twin boundaries are heavily oxidized, they do not serve as obstacles that strengthen the metal but, on the contrary, represent weaknesses in the material structure. The oxidation of grain boundaries and twin boundaries in the undeformed state hinders the ductile behavior and causes the embrittlement of HEA-Fb. Twinning is different in 4-Y, where twins form during tensile deformation [see Figs. 10(c) and 10(d)].

In preliminary work, striking differences in their ductility at RT are found for the hexagonal-close-packed rare-earth-based high-entropy alloy (HEA-Fb) and medium-entropy alloy (4-Y).⁸ As a conclusion to the earlier paper, the configurational entropy is not decisive for the observed differences in their tensile behavior. Now a detailed electron microscopy analysis (SEM, TEM, STEM, and EDS in STEM) of HEA-Fb and 4-Y, both in an undeformed state and after tensile tests, reveals different microstructure changes due to tensile deformation at RT.

Significant differences in the twinning behavior between HEA-Fb and 4-Y are identified in detail. In HEA-Fb, twins already exist in the undeformed state, while in 4-Y, twins form during tensile deformation. In HEA-Fb, the observed twins are straight, while in 4-Y, they have lenticular shapes. The twin boundaries in undeformed HEA-Fb are already oxidized. After tensile deformation, 4-Y has a higher density of twins than HEA-Fb. The twin orientations in both alloys are indexed as $[ 2 ¯ 201 ]$⁠, while the parental grains are indexed with the perpendicular $[ 11 2 ¯ 0 ]$ orientation. Consequently, similar twinning modes in HEA-Fb and 4-Y are activated. At least two different orientations of twins are found in each alloy. In HEA-Fb, the two different orientations of the twins on the $[ 2 ¯ 201 ]$ zone axis are rotated by 70° to each other. Different from that, in 4-Y, the two orientations of twins on the $[ 2 ¯ 201 ]$ zone axis are rotated by 180° to each other.

A pileup of dislocations is found at the twin boundaries in 4-Y, along with dislocations inside the twins. Twins and their interactions with dislocations create a twinning-induced plasticity (TWIP) effect in 4-Y. TWIP effects are characteristic of alloys with low stacking fault energy, contributing to the alloy’s beneficial ductility. Contrary to that, pre-existing twins in HEA-Fb weaken the alloy. Here, the oxidation of the twin boundaries in the undeformed state provides preferential starting points for crack propagation, which leads to dramatic embrittlement.

This study provides valuable insights into the microstructural mechanisms influencing hexagonal rare-earth-based HEA tensile behavior. The results confirm that conventional concepts for mechanical behavior apply to HEA-Fb and 4-Y, rather than unique high-entropy effects. Furthermore, a TWIP effect in 4-Y is identified and provides an exciting starting point for future alloy development with multicomponent hexagonal metals.

The authors acknowledge the German Research Foundation (DFG) for the financial support by GL181/56–2 and FE 571/4-2 as part of the Priority Program SPP 2006 “Compositionally Complex Alloys—High Entropy Alloys (CCA-HEA).” Electron microscopy was partly performed at the Center for Electron Microscopy and Analysis (CEMAS) at The Ohio State University. The authors acknowledge the advice on initial S/TEM and EDS investigations from Dr. Anna Manzoni, Bundesanstalt für Materialien Berlin, and the support by the preparation of first TEM lamella via ion milling from Christiane Förster, Helmholtzzentrum Berlin.

The authors have no conflicts to disclose.

Laura Rosenkranz: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Qianqian Lan: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Milan Heczko: Formal analysis (supporting); Investigation (supporting); Writing – review & editing (supporting). Ashton J. Egan: Data curation (supporting); Investigation (supporting); Writing – review & editing (supporting). Michael J. Mills: Resources (supporting); Supervision (supporting). Michael Feuerbacher: Funding acquisition (equal); Resources (supporting); Supervision (supporting); Writing – review & editing (supporting). Uwe Glatzel: Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of the study are available from the corresponding author upon reasonable request.