arXiv:cond-mat/0302027v1 [cond-mat.mtrl-sci] 3 Feb 2003 Bonding in MgSi and AlMgSi Compounds Relevant to AlMgSi Alloys Anders G. Frøseth ∗ and Ragnvald Høier Norwegian University of Science and Tecnology (NTNU), N-7034 Trondheim, Norway Peter M. Derlet Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Sigmund J. Andersen and Calin D Marioara SINTEF Materials Technology, Applied Physics, N-7050 Trondheim, Norway (Dated: February 6, 2008) The bonding and stability of MgSi and AlMgSi compounds relevant to AlMgSi alloys is investi- gated with the use of (L)APW+(lo) DFT calculations. We show that the β and β ′′ phases found in the precipitation sequence are characterised by the presence of covalent bonds between Si-Si nearest neighbour pairs and covalent/ionic bonds between Mg-Si nearest neighbour pairs. We then investigate the stability of two recently discovered precipitate phases, U1 and U2, both containing Al in addition to Mg and Si. We show that both phases are characterised by tightly bound Al-Si networks, made possible by a transfer of charge from the Mg atoms. I. INTRODUCTION Precipitation or age hardened alloys are today one of the most important alloy types in industry. In the AlMgSi alloy system, Mg-Si and Al-Mg-Si precipitates formed during specific heat treatments give rise to a very significant increase in strength. The precipitation se- quence is generally accepted to be: SSSS → Mg/Si Clusters → GPZ → β ′′ → β ′ → β, (1) where GPZ refers to a Guinier Preston Zone and SSSS refers to a Super Saturated Solid Solution. Very little is known about the early stages of the precipitation pro- cess. However, it is believed that when the SSSS is heat treated Mg and Si atoms quickly diffuse substitu- tionally to form small clusers due to the large amount of quenched-in vacancies 1 (a large part of the vacancies move to interfaces like surfaces and grain boundaries in the later stages of the heat treatment). Although the details are hard to investigate experimentally, several studies of such clustering have been carried out using atom probe microscopy 2,3 . The first phase which can be resolved using high resolution electron microscopy (HREM) is the GPZ. From this, a model of its crystal structure has recently been proposed 4 . The structure of the proceeding phase, β ′′ , was also solved using electron microscopy techniques 5 , a result which has later been supported by ab initio calculations 6 . Earlier it was believed that the GPZ, β ′′ and β phases all had the stoichiometry of the β phase, Mg 2 Si, and that alloys should be optimized accordingly. Thus, the termi- nal β phase was of primary importance. Later however, it had been confirmed that the β ′′ gives a greater contri- bution to the hardness due to its semi-coherent interface with the aluminium matrix and needle-like shape, which is more effective for dislocation pinning 7 . The β ′′ stoi- chiometry has been shown to be Mg 5 Si 6 5 . Recently, several additional phases have been identi- fied experimentally 8,9,10 , giving the extended precipita- tion sequence: SSSS → Mg/Si Clusters → GPZ → β ′′ (2) → (β ′ + U 2+ U 1+ B ′ ) → β. In ref. 8 the phases U 1, U 2 and B ′ are referred to as type A, B and C respectively. These three phases, in addition to β ′ , are often grouped together since little is known about their interdependence. However it is believed that the peak of concentration with respect to time for each of these structures follows the ordering given by the above precipitation sequence 8 . They all form relatively late in the precipitation sequence usually at temperatures in the range 200-300 ◦ C, and in Si-rich alloy compositions. It has been considered a general rule of thumb that successful aluminium precipitation hardening alloys con- tain secondary and ternary alloying elements which are larger and smaller than aluminium 11 . Now, the concept of atom size in this context must be based on the type of bonding involved. One can have either ionic, metallic or covalent radii for the constituent elements giving dramat- ically different values for atomic size 12 . It is clear that when studying the electronic density of compound struc- tures this type of concept may lead to an oversimplifica- tion. It it therefore interesting to carry out a theoretical study of the electronic structure and bonding character- istics of the relevant phases with respect to their relative stability. This is the purpose of the present work, where we employ full potential ab initio methods based on Den- sity Functional Theory (DFT) to investigate the bonding within the above mentioned structures. In section II we describe the Linear Augmented Plane Wave + local or- bitals approach, (L)APW+(lo), used for all calculations. Section III describes the results obtained for the three models of precipitate phases containing only Mg and Si (β ′′ , β ′ , and β), and section IV deals with the phases containing Al, Mg and Si (U 1 and U 2).