Ordering-mediated local nano-clustering results in unusually large Hall-Petch strengthening coefficients in high entropy alloys

Figures & data

Figure 1. Engineering Stress versus Plastic Strain plots for (a) CoFeNi, (b) Al_0.3CoFeNi, (c) CoCrFeNi and (d) Al_0.3CoCrFeNi CCAs. (e) Yield Strength versus 1/√d plots for CoFeNi, Al_0.3CoFeNi, CoCrFeNi and Al_0.3CoCrFeNi CCAs.

Table 1. Lattice friction stress (σ₀) and Hall-Petch strengthening co-efficient (K) values along with the grain size range for each alloy.

Alloy	σ0	K	Grain size (µm)
CoFeNi	157 ± 6	541 ± 34	23–205
Al0.3CoFeNi	151 ± 2	1244 ± 34	38–179
CoCrFeNi	156 ± 3	684 ± 50	23–149
Al0.3CoCrFeNi	149 ± 6	1014 ± 30	29–199

Figure 2. SAED pattern obtained from [101] Zone Axis for CoFeNi CCA. APT results for CoFeNi CCA: Reconstructed ion maps for (b) Fe and (c) Ni. (d) Observed (solid line) and theoretical/binomial (dotted line) frequency distributions for Ni.

Figure 3. (a) SAED pattern obtained from [101] Zone Axis for CoCrFeNi CCA. APT results for CoCrFeNi CCA: Reconstructed ion maps for (b) Ni and (c) Cr. (d) Observed (solid line) and theoretical/binomial (dotted line) frequency distributions for Ni. (e) 3D reconstruction of Ni-Cr rich clusters obtained via cluster analysis and (f) Table listing the composition of the matrix and the Ni-Cr clusters.

Figure 4. (a) SAED pattern obtained from [101] Zone Axis for Al_0.3CoFeNi CCA. APT results for Al_0.3CoFeNi CCA: (b) Reconstructed Ni ion map and (c) Observed (solid line) and theoretical/binomial (dotted line) frequency distributions for Ni. (d) 3D reconstruction of Ni-Al rich clusters obtained via cluster analysis and (e) Table listing the composition of the matrix and the Ni-Al clusters.

Figure 5. (a) SAED pattern obtained from [101] Zone Axis for Al_0.3CoCrFeNi CCA. APT results for Al_0.3CoCrFeNi CCA: (b) Reconstructed Ni ion map and (c) Observed (solid line) and theoretical/binomial (dotted line) frequency distributions for Ni. (d) 3D reconstruction of Ni-Al rich clusters obtained via cluster analysis and (e) Table listing the composition of the matrix and the Ni-Al clusters.

Table 2. Calculated critical shear stress (${\tau }_c$), coherency strengthening, resolved shear stress for overcoming grain boundary barrier (${\tau }_a$), and predicted ${\tau }_a$.

Alloy	${\tau }_c$ (MPa)	Coherency stress (${\sigma }_{\text{coherency}}$, MPa)	Coherency shear stress (${\tau }_{\text{coherency}}$, MPa)	Calculated ${\tau }_a$ (MPa)	Predicted ${\tau }_a$ ($({\tau }_a{)}_{CoFeNi/CoCrFeNi}+{\tau }_{coherency}$, MPa)
CoFeNi	296	–	–	39.5	–
Al0.3CoFeNi	2744	119	41	90.8	80.5
CoCrFeNi	567	–	–	50	–
Al0.3CoCrFeNi	1310	29	10	74	60

Data availability

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