Table 1 Results for the calculated entropy-forming-ability (EFA) descriptor, energetic distance from six-dimensional convex hull (ΔH_f) and vibrational free energy at 2000 K (ΔF_vib) for the five-metal carbide systems, arranged in descending order of EFA

System	EFA	ΔH_f	ΔF_vib	Exp.	ε	System	EFA	ΔH_f	ΔF_vib	Exp.	ε	System	EFA	ΔH_f	Exp.	ε
MoNbTaVWC₅	125	156	−14	S	0.063	HfNbTaVWC₅	67	110				TaTiVWZrC₅	50	96
HfNbTaTiZrC₅	100	19	−12	S	0.094	HfMoTaTiVC₅	67	82				NbTiVWZrC₅	50	93
HfNbTaTiVC₅	100	56	−31	S	0.107	HfMoNbTiZrC₅	67	53				HfMoTiVZrC₅	50	96
MoNbTaTiVC₅	100	82				MoNbTaWZrC₅	63	133				HfMoTaVZrC₅	50	92
NbTaTiVZrC₅	83	64				HfMoTaTiZrC₅	63	55				HfMoNbVZrC₅	50	89
HfMoNbTaTiC₅	83	48				NbTaTiWZrC₅	59	61				MoTaVWZrC₅	48	148
NbTaTiVWC₅	77	92	−19	S	0.124	MoTaTiVZrC₅	59	92				MoTaTiWZrC₅	48	94
MoNbTaTiWC₅	77	111				MoNbTiVZrC₅	59	87				MoNbVWZrC₅	48	146
MoNbTiVWC₅	71	122				MoNbTaVZrC₅	59	108				MoNbTiWZrC₅	48	89
MoNbTaTiZrC₅	71	57				HfNbTiVWC₅	59	81				HfMoNbWZrC₅	48	101
HfTaTiVZrC₅	71	73				HfNbTaWZrC₅	59	53				HfTiVWZrC₅	45	99
HfNbTiVZrC₅	71	73				NbTaVWZrC₅	56	119				HfNbVWZrC₅	45	94
HfMoNbTiVC₅	71	77				HfTaTiVWC₅	56	84				HfMoTiVWC₅	45	97
HfMoNbTaZrC₅	71	48				HfMoTaVWC₅	56	139				HfMoTaWZrC₅	45	105	M	0.271
HfMoNbTaWC₅	71	126				HfMoNbVWC₅	56	137				HfTaVWZrC₅	43	97
HfMoNbTaVC₅	71	99				HfNbTiWZrC₅	53	56				MoTiVWZrC₅	40	107
HfNbTaTiWC₅	67	53	~0	S	0.171	HfMoTaTiWC₅	53	84				HfMoTiWZrC₅	38	83	M	0.315
MoTaTiVWC₅	67	128				HfMoNbTiWC₅	53	81				HfMoVWZrC₅	37	141	M	0.325
HfNbTaVZrC₅	67	60				HfTaTiWZrC₅	50	59	~0	S	0.169

Nine compositions are selected for experimental investigation. The lattice distortion, ε, is obtained from the peak broadening in XRD. S: single-phase formed; M: multi-phase formed in experiment. Note that the compositions listed here are nominal, and the actual synthesized compositions can vary due to the presence of carbon vacancies in the anion sublattice. Units: EFA in (eV/atom)⁻¹; ΔH_f and ΔF_vib in (meV/atom); and ε in %

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