Applying precipitate–host lattice coherency for compositional determination of precipitates in Al–Mg–Si–Cu alloys

Abstract

The present paper reports experimental and theoretical studies on the structure of the metastable C precipitate forming during precipitation hardening in Al–Mg–Si–Cu (6xxx) alloys. We describe the procedure of deriving an initial unit cell model based on experimental data and how this is further refined by quantitative use of nanobeam electron diffraction patterns. A reliable 3D refinement was prevented by the small precipitate thickness and its disorder/intergrowth with other phases, necessitating the development of a more theoretically based methodology for precipitate composition determination. We find that for experimental results to be acceptably reproduced in density functional theory-based calculations on bulk candidate structures, these would have to not only minimise precipitate formation enthalpy, but also reproduce the experimentally reported negligible lattice mismatch with the Al matrix along the precipitate main growth direction. We argue, through comparison of the isostructural Q′ and Q precipitate phases of Al–Mg–Si–Cu alloys, why the experimentally reported (semi-)coherency of metastable precipitates must be included as an optimisation criterion in a general theoretical analysis. The C phase structure determined has a monoclinic unit cell with space group P2₁/m, cell dimensions a _C = 10.32 Å, b _C = 4.05 Å, c _C = 8.10 Å, β _C = 100.9°, coherency relations with the matrix:  ∥ ⟨150⟩_Al,  ∥ ⟨001⟩_Al,  ∥ ⟨100⟩_Al and composition Mg₄AlSi_{3+ x} Cu_{1− x} , with x ∼ 0.3. The non-integer number of atoms in the unit cell emphasises that the concept of a unit cell for this phase is weakly defined.

Keywords:

• age hardening
• metastable phases
• density functional theory
• nanodiffraction
• coherency

Acknowledgements

This work was financially supported by the Research Council of Norway via two projects: FRINAT project (‘Fundamental investigations of solute clustering and precipitation’) and the BIA programme ‘Kimdanningskontroll (nucleation control)’, which is supported by Norwegian industry: Hydro Al, Steertec Raufoss AS. The authors would also like to thank the NOTUR project for use of their computing facilities, and Dr. René Vissers (previously at NTNU) for support during MSLS refinements. C.D. Marioara wishes to thank Dr. C.B. Boothroyd from Technical University of Denmark for providing the HAADF-STEM image in Figure 2 and Professor H.W. Zandbergen at TU Delft for allowing use of their TEM for NBD experiments.