Table 3 Size and temperature effects on mechanical properties of TiB₂

No. of atoms	T (K)	Dimensions (nm)			Strength (GPa)			Toughness (GPa)			Fracture strain (%)
		a	b	c	[0001]	\([10\overline{1}0]\)	\([\overline{1}2\overline{1}0]\)	[0001]	\([10\overline{1}0]\)	\([\overline{1}2\overline{1}0]\)	[0001]	\([10\overline{1}0]\)	\([\overline{1}2\overline{1}0]\)
720	300	1.51	1.58	2.57	52.72	55.01	63.69	4.33	3.11	4.32	22.0	16.0	18.0
12,960 (S1)	300	4.55	4.73	5.15	53.71	51.36	56.40	4.83	2.77	3.38	26.4	14.3	16.8
141,120 (S2)	300	10.63	11.05	10.30	53.69	51.44	56.41	4.81	2.78	3.37	26.4	14.3	16.8
230,400 (S3)	300	12.14	12.63	12.87	53.71	51.43	56.38	4.82	2.78	3.37	26.3	14.3	16.8
432,000 (S4)	300	15.18	15.79	15.45	53.67	51.47	56.42	4.80	2.78	3.37	26.2	14.2	16.8
720	1200	1.53	1.59	2.60	43.87	45.21	51.34	3.27	2.29	3.07	20.0	16.0	16.0
432,000 (S4)	1200	15.26	15.86	15.52	43.27	41.30	44.67	3.45	1.96	2.32	21.6	12.8	14.1

The directional response to strain is assessed for supercells with sizes ranging from the atomic to the nanoscale. The mechanical properties of TiB₂ are extracted from ML-MD stress/strain data in Fig. 4.

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