Table 2 Validation of the here-developed MLIP (MLIP-[1]) against theoretical and experimental (exp.) room-temperature elastic constants, C_ij

	No. of atoms	T	C₁₁	C₃₃	C₄₄	C₁₂	C₁₃	E	B	G	ν	Source
DFT	192	300	640	446	251	62	91	574	244	260	0.106	Ref. ⁹⁵
AIMD	720	300	588	430	252	79	111	547	244	243	0.126	This work
ML-MD	720	300	588	409	261	85	98	554	236	246	0.113	This work
Exp.	—	300	660	432	260	48	93	565	244	266	0.099	Ref. ⁹⁶
Exp.	—	300	588	503	238	72	84	575	249	255	0.114	Ref. ⁹⁷

The C_ij values for TiB₂ (in GPa, at temperature T (K)) are shown together with the polycrystalline bulk modulus, B (in GPa), shear modulus, G (in GPa), Young’s modulus, E (in GPa), and Poisson’s ratio, ν, compared to reference ab initio and experimental (exp.) data. ref. ⁹⁶ and ref. ⁹⁷ is for TiB₂ single and polycrystal, respectively. AIMD and ML-MD elastic constants were evaluated following ref. ⁸⁶, based on a second-order polynomial fit of the [0001], [10\(\overline{1}0\)], and [\(\overline{1}2\overline{1}0\)] stress/strain data (C₁₁, C₁₂, C₁₃, C₃₃) and of the (0001)\([\overline{1}2\overline{1}0],(10\overline{1}0)[\overline{1}2\overline{1}0]\), and \((10\overline{1}0)[0001]\) shear stress/strain data (C₄₄), assuming strains up to 4%. For details see the Methodology section. Note that values from ref. ⁹⁵ were based on 0 K ab initio calculations coupled to phonon-theory assessments of thermal expansion.

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