Energy paths of twin-related lattice reorientation in hexagonal metals via ab initio calculations

doi:10.1016/j.jmst.2017.09.009

Abstract

Abstract:

Employing ab initio calculations, we systematically investigated the energy paths of [101ˉ2]twin-related lattice reorientation in hexagonal metals Be, Mg, Sc, Ti, Co, Y, Zr, Tc, Ru, Gd, Tb, Dy, Ho, Er, Tm, Lu, Hf, Re, and Os. Among the studied systems, lattice reorientation energy increases in the order of Mg, Gd, Tb, Dy, Zr, Tc, Ti, Ho, Y, Co, Er, Sc, Be, Tm, Lu, Hf, Re, Ru and Os. The reorientation process consists of shear and shuffle components. Concerning the significance of shuffle, these hexagonal metals fall into two groups. In the first group, which includes Mg, Co, Ru, Re and Os, regardless of the shear amount, subsequent shuffle is an energy-uphill process, while in the second group, which includes Ti, Tc, Be, Y, Gd, Tb, Dy, Ho, Zr, Er, Sc, Hf, Lu and Tm, shuffle becomes an energy-downhill process if shear component reaches an adequate level (at least 60%). These results qualitatively explain the present observation of lattice reorientation in hexagonal metals, and shed light upon a general understanding on the [101ˉ2] twinning behavior in the aim of improving materials properties.

Key words: Hexagonal metal, Twin, Shear, Shuffle, First-principles

Gang Zhou, Lihua Ye, Hao Wang, Dongsheng Xu, Changgong Meng, Rui Yang. Energy paths of twin-related lattice reorientation in hexagonal metals via ab initio calculations[J]. J. Mater. Sci. Technol., 2018, 34(4): 700-707.

Figures/Tables 10

Table 1 Cutoff energies (Ecut) and k-point meshes used in the calculations, the calculated and experimental lattice constants (a and c) and c/a ratios of 19 hexagonal metals and reorientation energies per atom (E). Experimental lattice constants are taken from Ref. [29].

Symbol	E_cuf (eV)	k-points	a (nm)		c (nm)		c/a		E (meV)
			Cal.	Exp.	Cal.	Exp.	Cal.	Exp.
Be	450	23 × 23 × 23	0.2286	0.2266	0.3584	0.3567	1.568	1.574	51.51
Mg	350	19 × 19 × 19	0.3209	0.3194	0.5211	0.5183	1.624	1.623	16.55
Sc	550	11 × 11 × 11	0.3309	0.3320	0.5268	0.5162	1.592	1.555	48.47
Ti	450	13 × 13 × 13	0.2950	0.2936	0.4684	0.4650	1.587	1.584	38.42
Co	450	19 × 19 × 19	0.2507	0.2492	0.4069	0.4024	1.623	1.615	44.92
Y	400	15 × 15 × 15	0.3648	0.3657	0.5732	0.5675	1.571	1.552	43.71
Zr	450	11 × 11 × 11	0.3232	0.3235	0.5148	0.5168	1.593	1.597	36.09
Tc	550	15 × 15 × 15	0.2738	0.2750	0.4394	0.4399	1.605	1.599	37.77
Ru	400	13 × 13 × 13	0.2705	0.2716	0.4281	0.4279	1.583	1.576	163.96
Gd	450	15 × 15 × 15	0.3634	0.3642	0.5781	0.5737	1.591	1.575	23.01
Tb	450	15 × 15 × 15	0.3606	0.3631	0.5697	0.5680	1.580	1.564	28.54
Dy	450	15 × 15 × 15	0.3592	0.3619	0.5650	0.5633	1.573	1.556	34.93
Ho	450	15 × 15 × 15	0.3578	0.3605	0.5618	0.5593	1.570	1.552	41.54
Er	450	15 × 15 × 15	0.3559	0.3586	0.5585	0.5559	1.569	1.550	47.54
Tm	400	15 × 15 × 15	0.3538	0.3562	0.5554	0.5525	1.570	1.551	52.73
Lu	450	13 × 13 × 13	0.3505	0.3524	0.5549	0.5480	1.583	1.555	57.35
Hf	550	13 × 13 × 13	0.3195	0.3203	0.5051	0.5063	1.581	1.581	63.07
Re	600	17 × 17 × 17	0.2761	0.2775	0.4458	0.4482	1.615	1.615	79.20
Os	600	13 × 13 × 13	0.2735	0.2759	0.4391	0.4354	1.606	1.578	248.98

Fig. 1. Initial (a), saddle point (b), final (c) atomic configurations during the twin-related lattice reorientation. Lattices orientations are indicated. The reorientation process consists of expansion and contraction (double headed arrows), which is equivalent to pure shear, as well as individual atomic shuffles (blue and red arrows).

Fig. 2. Reorientation energy maps against relative shear and shuffle in Mg (a) and Ti (b).

Fig. 3. Reorientation energy maps against relative shear and shuffle in Co (a), Ru (b), Re (c) and Os (d).

Fig. 4. Reorientation energy maps against relative shear and shuffle in Tc (a), Be (b), Y (c), Gd (d), Tb (e), Dy (f), Ho (g), Zr (h), Er (i), Sc (j), Hf (k), Lu (l) and Tm (m).

Fig. 5. Contour maps of shuffle energies at different relative shears in Mg (a) and Ti (b). The thick violet curves denote level zero.

Fig. 6. Contour maps of shuffle energies at different relative shears in Co (a), Ru (b), Re (c) and Os (d). The solid violet curves denote level zero in each subfigure.

Fig. 7. Contour maps of shuffle energies at different relative shears in Tc (a), Be (b), Y (c), Gd (d), Tb (e), Dy (f), Ho (g), Zr (h), Er (i), Sc (j), Hf (k), Lu (l) and Tm (m). The solid violet curves denote level zero in each subfigure.

Fig. 8. Reorientation energy against Young’s modulus for hexagonal metals. The linear plotting and the Pearson correlation coeffcient (r) are indicated (the bigger the absolute value of r, the stronger the correlation).

Fig. 9. 3D charge density difference maps of initial and saddle point with isosurface values of 12 e nm-3 in pure Mg (a, b) and 45 e nm-3 in pure Ti (c, d). Yellow and cyan colors represent gaining and losing electrons, respectively.

References

[1]	C. Lou, X.Y. Zhang, G.L. Duan, J. Tu, Q. Liu, J. Mater. Sci. Technol. 30(2014)41-46.
[2]	Y. Zhang, C. Lou, J. Tu, Q. Liu, J. Mater. Sci. Technol. 29(2013) 1123-1128.
[3]	D. Sarker, J. Friedman, D.L. Chen, J. Mater. Sci. Technol. 31(2015) 264-268.
[4]	D. Sarker, J. Friedman, D.L. Chen, J. Mater. Sci. Technol. 30(2014) 884-887.
[5]	K.M. Zhang, J.X. Zou, J. Li, Z.S. Yu, J. Mater. Sci. Technol. 30(2014) 263-267.
[6]	J.R. Dong, D.F. Zhang, J. Sun, Q.W. Dai, F.S. Pan, J. Mater. Sci. Technol. 31(2015)935-940.
[7]	N. Tahreen, D.F. Zhang, F.S. Pan, X.Q. Jiang, D.Y. Li, D.L. Chen, J. Mater. Sci. Technol. 31(2015) 1161-1170.
[8]	H.C. Pan, F.H. Wang, L. Jin, M.L. Feng, J. Dong, J. Mater. Sci. Technol. 32(2016)1282-1288.
[9]	J. Xu, B. Guan, H.H. Yu, X.Z. Cao, Y.C. Xin, Q. Liu, J. Mater. Sci. Technol. 32(2016) 1239-1244.
[10]	M.H. Yoo, Metall. Trans. A 12 (1981) 409-418.
[11]	E. Roberts, P.G. Partridge, Acta Metall. 14(1966) 513-527.
[12]	A. Akhtar, Metall. Trans. A 6 (1975) 1105-1113.
[13]	B.Y. Liu, J. Wang, B. Li, L. Lu, X.Y. Zhang, Z.W. Shan, J. Li, C.L. Jia, J. Sun, E. Ma,Nat. Commun. 5(2014) 4297.
[14]	A. Ostapovets, P. Molnar, R. Groeger, 6th International Conference onNanomaterials by Severe Plastic Deformation (2014) 012134.
[15]	A. Kumar, J. Wang, C.N. Tome, Acta Mater. 85(2015) 144-154.
[16]	W. Wu, Y.F. Gao, N. Li, C.M. Parish, W.J. Liu, P.K. Liaw, K. An, Acta Mater. 121(2016) 15-23.
[17]	A. Ishii, J. Li, S. Ogata, Int. J. Plast. 82(2016) 32-43.
[18]	H. Zong, X.D. Ding, T. Lookman, J. Li, J. Sun, E.K. Cerreta, A.P. Escobedo, F.L.Addessio, C.A. Bronkhorst, Phys. Rev. B 89 (2014) 220101.
[19]	Y. Zhang, B. Li, J. Tu, Q. Sun, Q. Liu, Mater. Res. Lett. 3(2015) 142-148.
[20]	B. Li, X.Y. Zhang, Scr. Mater. 125(2016) 73-79.
[21]	Z. Liao, J. Wang, J.F. Nie, Y.Y. Jiang, P.D. Wu, MRS Bull. 41(2016) 314-319.
[22]	G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251-14269.
[23]	G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169-11186.
[24]	P.E. Blochl, Phys. Rev. B 50 (1994) 17953-17979.
[25]	G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758-1775.
[26]	J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77(1996)3865-3868.
[27]	D. Sheppard, P. Xiao, W. Chemelewski, D.D. Johnson, G. Henkelman, J. Chem.Phys. 136(2012) 074103.
[28]	J. Tu, X.Y. Zhang, J. Wang, Q. Sun, Q. Liu, C.N. Tome, Appl. Phys. Lett. 103(2013) 051903.
[29]	W. Martienssen, H. Warlimont, Springer Handbook of Condensed Matter andMaterials Data, Springer,Berlin, 2005.
[30]	J. Capek, G. Farkas, J. Pilch, K. Mathis, Mater. Sci. Eng.A 627 (2015) 333-335.
[31]	A. Chapuis, J.H. Driver, Acta Mater. 59(2011) 1986-1994.