Modeling of Stacking Fault Energy in Hexagonal-Close-Packed Metals

Table 1

Calculated stable SFE (mJ/m²) and unstable SFE (mJ/m²) for Mg and Mg alloys by DFT with different exchange-correlation functionals.

System	Growth fault ()		Deformation fault ()		Extrinsic fault ()		Twin-like fault ()
	Stable SFE	Unstable SFE	Stable SFE	Unstable SFE	Stable SFE	Unstable SFE	Stable SFE	Unstable SFE
Mg	21^a, 18^b, 16^c, 30^e, 17.98^f, 20^g, 17.1^h, 17.8^i, 18^k	86.2^h	44^a, 36^b, 34^c, 36^d, 60^e, 33.84^f, 33.8^h, 38.3^i, 33^k	97^c, 92^d, 87.6^h	69^a, 58^b, 59^c, 90^e, 52.57^f		51^a, 40^b, 38^c, 39^d, 60^e, 40.55^f	181^c, 111^d
Mg-Li	16.7^j, 28^k		47^d, 48.2^j, 46^k	95^d			56^d, 63.5^j	119^d
Mg-Na	15.7^j		46.8^j		66.7^j
Mg-Al	12.5^j		21^d, 33.6^j	78^d	55.7^j		32^d	96^d
Mg-K	13.5^j		32.5^j		47.5^j
Mg-Ca	13.8^j		33.5^j		49.6^j
Mg-Ti			36^d	112^d			47^d	137^d
Mg-Mn	13.5^j		38^d, 40.3^j	103^d	81.4^j		83^d	149^d
Mg-Fe	3.3^j		52^d, 40.3^j	110^d	79.8^j		80^d	146^d
Mg-Ni			55^d	99^d			81^d	135^d
Mg-Cu	16.6^j		53^d, 40.1^j	97^d	66.4^j		68^d	126^d
Mg-Zn	18.2^h, 8.5^j	91.0^h	37^d, 35.1^h, 30.8^j	86^d, 94.2^h	58.8^j		43^d	195^d
Mg-Sr	15.6^j		33.2^j		46.3^j
Mg-Y	3.7^h, 1.8^j	61.2^h	25^d, 15.7^h, 32.9^j	71^d, 62.1^h	47.1^j		21^d	85^d
Mg-Zr	9.8^j		26^d, 35.3^j	99^d	67.5^j		32^d	119^d
Mg-Ag			49^d	101^d			62^d	127^d
Mg-Nd	10.8^j		32.3^j		51.9^j
Mg-Sn	13.8^j		2^d, 37.2^j	64^d	50.1^j		25^d	79^d
Mg-Pb			4^d	55^d			32^d	80^d

Note:
^aChetty and Weinert calculated with LDA [17].
^bSmith calculated with GGA-PBE [18].
^cWen et al. calculated with GGA-PW91 [28].
^dMuzyk et al. calculated with GGA-PBE; the concentration of alloying atoms was 2% in supercell and 25% in slip layers [29].
^eHu and Yang calculated with LDA [23].
^fFan et al. calculated with GGA-PW91 [22].
^gSandlöbes et al. calculated with GGA-PBE [20].
^hZhang et al. calculated with GGA-PW91; the concentration of alloying atoms was 1% in supercell and 11.1% at the fault plane [32].
ⁱWang et al. calculated with GGA [19].
^jWang et al. calculated with GGA [35].
^kHan et al. calculation with GGA of Mg-1.67% Y alloys [30].