Abstract
The metastable β′ phase is often the most effective hardening precipitate in Mg-Gd based alloys. In this paper, the structural, elastic and electronic properties of the recently identified β′-Mg7Gd precipitate in Mg-Gd binary alloys were investigated using first-principles calculations based on density functional theory. The lattice mismatches between the coherent β′-Mg7Gd precipitate and α-Mg matrix are discussed and used to rationalize the experimentally observed morphology of the precipitate. The mechanical properties were investigated through analysis of the single-crystal elastic constants and the polycrystalline elastic moduli. It is found that β′-Mg7Gd is brittle in nature. Strong covalent bonding in β′-Mg7Gd, as inferred from its electronic structure, further explains its mechanical properties. Our theoretical results show good agreement with experimental measurements.
Similar content being viewed by others
References
Nie J F, Oh-ishi K, Gao X, et al. Solute segregation and precipitation in a creep-resistant Mg-Gd-Zn alloy. Acta Mater, 2008, 56: 6061–6076
Gao L, Chen R S, Han E H. Microstructure and strengthening mechanisms of a cast Mg-1.48Gd-1.13Y-0.16Zr (at.%) alloy. J Mater Sci, 2009, 44: 4443–4454
Gao X, He S M, Zeng X Q, et al. Microstructure evolution in a Mg-15Gd-0.5Zr (wt.%) alloy during isothermal aging at 250°C. Mater Sci Eng A, 2006, 431: 322–327
Honma T, Ohkubo T, Hono K, et al. Chemistry of nanoscale precipitates in Mg-2.1Gd-0.6Y-0.2Zr (at.%) alloy investigated by the atom probe technique. Mater Sci Eng A, 2005, 395: 301–306
He S M, Zeng X Q, Peng L M, et al. Precipitation in a Mg-10Gd-3Y-0.4Zr (wt.%) alloy during isothermal ageing at 250°C. J Alloys Compd, 2006, 421: 309–313
Honma T, Ohkubo T, Kamado S, et al. Effect of Zn additions on the age-hardening of Mg-2.0Gd-1.2Y-0.2Zr alloys. Acta Mater, 2007, 55: 4137–4150
Yamada K, Hoshikawa H, Maki S, et al. Enhanced age-hardening and formation of plate precipitates in Mg-Gd-Ag alloys. Scrip Mater, 2009, 61: 636–639
Nie J F, Muddle B C. Characterisation of strengthening precipitate phases in a Mg-Y-Nd alloy. Acta Mater, 2000, 48: 1691–1703
Nishijima M, Hiraga K, Yamasaki M, et al. Characterization of beta’ phase precipitates in an Mg-5 at% Gd alloy aged in a peak hardness condition, studied by high-angle annular detector dark-field scanning transmission electron microscopy. Mater Trans, 2006, 47: 2109–2112
Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B, 1996, 54: 11169–11186
Blochl P E. Projector augmented-wave method. Phys Rev B, 1994, 50: 17953–17979
Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B, 1999, 59: 1758–1775
Perdew J P, Chevary J A, Vosko S H, et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys Rev B, 1992, 46: 6671–6687
Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations. Phys Rev B, 1976, 13: 5188–5192
Methfessel M, Paxton A T. High-precision sampling for Brillouin-zone integration in metals. Phys Rev B, 1989, 40: 3616–3621
Blochl P E, Jepsen O, Andersen O K. Improved tetrahedron method for Brillouin-zone integrations. Phys Rev B, 1994, 49: 16223–16233
Nishijima M, Hiraga K. Structural changes of precipitates in an Mg-5 at% Gd alloy studied by transmission electron microscopy. Mater Trans, 2007, 48: 10–15
Gao L, Zhou J, Sun Z M, et al. Electronic origin of the anomalous solid solution hardening of Y and Gd in Mg: A first-principles study. Chinese Sci Bull, 2011, doi: 10.1007/s11434-010-4052-0
Kittel C. Introduction to Solid State Physics. New York: Wiley, 2005
Zhang H, Shang S, Saal J E, et al. Enthalpies of formation of magnesium compounds from first-principles calculations. Intermetallics, 2009, 17: 878–885
Ganeshan S, Shang S L, Wang Y, et al. Effect of alloying elements on the elastic properties of Mg from first-principles calculations. Acta Mater, 2009, 57: 3876–3884
Wang Y, Liu Z K, Chen L Q, et al. First-principles calculations of β″-Mg5Si6/α-Al interfaces. Acta Mater, 2007, 55: 5934–5947
Polmear I J. Magnesium alloys and applications. Mater Sci Technol, 1994, 10: 1–16
Birch F. Finite elastic strain of cubic crystals. Phys Rev, 1947, 71: 809–824
Beckstein O, Klepeis J E, Hart G L W, et al. First-principles elastic constants and electronic structure of α-Pt2Si and PtSi. Phys Rev B, 2001, 63: 134112
Voigt W. Lehrbuch der Kristallphysik. Leipzig: Taubner, 1928
Tang B Y, Wang N, Yu W Y, et al. Theoretical investigation of typical fcc precipitates in Mg-based alloys. Acta Mater, 2008, 56: 3353–3357
Wang N, Yu W Y, Tang B Y, et al. Structural and mechanical properties of Mg17Al12 and Mg24Y5 from first-principles calculations. J Phys D-Appl Phys, 2008, 41: 195408
Hort N, Huang Y D, Kainer K U. Intermetallics in magnesium alloys. Adv Eng Mater, 2006, 8: 235–240
Pugh S F. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos Mag, 1954, 45: 823–843
Ganeshan S, Shang S L, Zhang H, et al. Elastic constants of binary Mg compounds from first-principles calculations. Intermetallics, 2009, 17: 313–318
Pettifor D G. Theoretical predictions of structure and related properties of intermetallics. Mater Sci Technol, 1992, 8: 345–349
Born M, Huang K. Dynamical Theory of Crystal Lattices. Oxford: Oxford University Press, 1954
Author information
Authors and Affiliations
Corresponding authors
Additional information
This article is published with open access at Springerlink.com
About this article
Cite this article
Gao, L., Zhou, J., Sun, Z. et al. First-principles calculations of the β′-Mg7Gd precipitate in Mg-Gd binary alloys. Chin. Sci. Bull. 56, 1142–1146 (2011). https://doi.org/10.1007/s11434-010-4061-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-010-4061-z