Flemming J H Ehlers

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

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 Mg4AlSi3+ x Cu1− 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.

Phase stabilization principle and precipitate-host lattice influences for Al–Mg–Si–Cu alloy precipitates

In this work, we seek to elucidate a common stabilization principle for the metastable and equilibrium phases of the Al–Mg–Si–Cu alloy system, through combined experimental and theoretical studies. We examine the structurally known well-ordered Al–Mg–Si–Cu alloy metastable precipitates along with experimentally observed disordered phases, using high angle annular dark field scanning transmission electron microscopy. A small set of local geometries is found to fully explain all structures. Density functional theory based calculations have been carried out on a larger set of structures, all fully constructed by the same local geometries. The results reveal that experimentally reported and hypothetical Cu-free phases from the set are practically indistinguishable with regard to formation enthalpy and composition. This strongly supports a connection of the geometries with a bulk phase stabilization principle. We relate our findings to the Si network substructure commonly observed in all Mg–Al–Si(–Cu) metastable precipitates, showing how this structure can be regarded as a direct consequence of the local geometries. Further, our proposed phase stabilization principle clearly rests on the importance of metal-Si interactions. Close links to the Al–Mg–Si precipitation sequence are proposed.

The Dual Nature of Precipitates in Al-Mg-Si Alloys

Precipitates in Al-Mg-Si-(Cu) alloys all contain a similar hexagonal arrangement of Si-atoms. Precipitates come and go but their inner Si ordering appears to vary little throughout the precipitation process. In order to improve understanding of precipitation and the related material properties, it is becoming increasingly clear that this includes a good understanding of the hexagonal Si-network, its relation to the precipitates and the Al matrix. Previous studies have revealed that adding Cu atoms to the ternary system, causes the Si network to twist slightly in the matrix about its hexagonal axis, favoring different precipitates. Here we investigate these two rotations. It is shown they can be viewed as a mirror of the network itself about a {310} Al plane. Since precipitates are coherent, the Si-network with its triangular arrangements of Si must also match a fourfold arrangement of Al on the {100} planes. Sets of Al lattice positions exist which can approximate the tree-fold Si symmetry, according to the experimentally observed orientations, and one or more large super-cells can be found having near fit in both lattices. The mirror plane is a main plane in one such super-cell. We show that the mirror leaves every seventh node of the network unchanged, thus defining a smaller hexagonal super-cell in the network, similar to the B’ or Q’/Q phase, where corners are invariant, but where the Si contents is flipped.

The Role of the Si Network to the Stabilization of Hardening Precipitates in the Al‐Mg‐Si(‐Cu) Alloy System

Al-Mg-Si(-Cu) alloys are an important group of age hardening materials and possess some of the more complex precipitation sequences: In Al-Mg-Si, none of the metastable hardening precipitates can be described as weakly distorted versions of equilibrium phases, while in Al-Mg-Si-Cu, one of the main hardening precipitates is not associated with a unit cell. For both sequences, however, more than a decade of experimental work has revealed that a Si substructure with projected hexagonal symmetry when viewed in precipitate main growth axis projection is shared among all metastable phases. The present work seeks to clarify theoretically the significance of the Si network to phase stabilization while also quantifying the level of similarities among the various phases possessing this structure. Based on these results, very clear suggestions for a common precipitate nucleation mechanism emerge.

3D Hybrid Atomistic Modeling of β″ in Al-Mg-Si: Putting the Full Coherency of a Needle Shaped Precipitate to the Test

A key input of a truly predictive integrated computational materials engineering (ICME) scheme for an age hardenable Al alloy is the formation enthalpies — including interfacial and strain contributions — for the main hardening precipitate(s). The basic desire to compute these numbers with ab initio methods for essentially all relevant precipitate sizes continues to face limitations in the context of the associated requirements for the model system extensions. These obstacles manifest themselves in particular when considering a density functional theory framework based description of the full precipitate-host lattice interface — needed in order to incorporate accurately electronic interactions as well as the strain evolution along high misfit directions. Recent work within our group has made it possible to carry out this interface modeling for a fully coherent precipitate at a comparatively weak level of approximation. We describe here our first attempts to employ this scheme for 3D hybrid modeling of fully coherent needle-shaped β″, the main hardening phase in the Al-Mg-Si alloy system. Examining a physically sized precipitate, we found this structure to fully adapt to the host lattice along its main growth (needle) direction, with the cell dimensions in the precipitate cross-section falling non-negligibly below the experimental values for both compositions (Mg5Si6, Mg5Al2Si4) tested. Further, the theoretical value of 107.8° for the β″-Mg5Si6 monoclinic angle βP is markedly off the experimental value of 105.3°±0.5°, potentially supporting the presence of non-negligible amounts of Al in the β″ phase.

Matrix Coherency Strain and Hardening of Al-Mg-Si

Standard and high resolution transmission electron microscopy (TEM) and advanced post processing of the TEM images have been applied for quantitative characterization of the hardening particle structure of an Al-Mg-Si alloy optimized for formation of the metastable phase β’. The relation between the structural characterization and the mechanical properties has been developed. A first attempt is presented on visualization and quantification of the coherency strain field of β’, based on a combination of Vienna Ab-initio Simulation Package (VASP) calculations and continuum mechanical modelling.