Concurrent substitutional and displacive phase transformations in Al-Mg-Si nanoclusters

M. A. van Huis, M. H. F. Sluiter, J. H. Chen, and H. W. Zandbergen

Phys. Rev. B 76, 174113 – Published 26 November 2007

Abstract

Al-Mg-Si nanoclusters embedded in aluminum transform through a delicate interplay of two characteristically distinct phase transformations: a diffusion-controlled substitutional transformation associated with solute enrichment and a swift displacive transformation involving collective shifts of columns of atoms once a critical enrichment has been reached. Through first-principles calculations, we show that these transformations are inseparable. Moreover, we show in atomistic detail how precipitates that are not superstructures of the matrix form from a supersaturated solid solution.

Received 24 September 2007

DOI:https://doi.org/10.1103/PhysRevB.76.174113

Authors & Affiliations

M. A. van Huis^1,2,*, M. H. F. Sluiter^2,3, J. H. Chen^1,2, and H. W. Zandbergen¹

¹National Centre for HREM, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, NL-2628 CJ Delft, The Netherlands
²Netherlands Institute for Metals Research, Delft University of Technology, Mekelweg 2, NL-2628 CD Delft, The Netherlands
³Laboratory of Materials Science, Delft University of Technology, Mekelweg 2, NL-2628 CD Delft, The Netherlands

^*Corresponding author. FAX: +31 152782351. m.a.vanhuis@tudelft.nl

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Vol. 76, Iss. 17 — 1 November 2007

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Images

Figure 1
(Color online) Illustration of a needle-shaped ${Mg}_{4} {Si}_{6} Al$ nanocluster as embedded in aluminum (blue). Only two Al planes are shown for clarity. The needle consists of Mg atoms (green), Si atoms (yellow), and Al atoms. The columns of shifting Al atoms (red) within the nanocluster are indicated with arrows. At the bottom, two monoclinic unit cells are indicated. The crystal structure is shown in detail in Fig. 3.Reuse & Permissions
Figure 2
Potential energy change during the transition from phase $A$ to phase $B$ , with the activation energy $E_{act}$ and the energy difference $Δ U_{A \to B} = U_{B} - U_{A}$ . (a) Unfavorable transition $(Δ U > 0)$ with activation energy $E_{act}$ . (b) Favorable transition $(Δ U < 0)$ with activation energy $E_{act}$ . (c) Favorable $(Δ U < 0)$ , barrierless transition $(E_{act} = 0)$ . The energy profile of subfigure (b) is characteristic of a nucleation and growth process, while subfigure (c) is characteristic of a displacive transformation.Reuse & Permissions
Figure 3
(Color online) Phase transformation from pre- $β^{″}$ to $β^{″}$ at composition ${Mg}_{4} {Si}_{6} Al$ . The shift of the Al atoms from $y = 0.0$ to $y = 0.5$ actually corresponds to shifts of atomic columns because the structure is periodic along the monoclinic $b$ axis (the viewing direction). The lattice dimensions are fully commensurate with the Al lattice; see Fig. 4a. (a) Pre- $β^{″}$ configuration, fcc type. (b) Partial $β^{″}$ configuration after the shift of the central atomic column. (c) Full $β^{″}$ configuration when all columns have shifted. A few ${Si}_{2}$ columns, characteristic of the needle-type structures, are indicated.Reuse & Permissions
Figure 4
(Color online) Left-hand side: energy change per supercell as a function of the displacement $y$ of the shift atom (i.e., energy change per atom in the shift column). See Fig. 2 for definitions of the energies $E_{act}$ and $Δ U$ . The shift constitutes the phase transition form pre- $β^{″}$ to partial $β^{″}$ and is schematically displayed in Figs. 3a, 3b Right-hand side: supercell structures of the pre- $β^{″}$ phases with composition varying from pure Al to ${Mg}_{4} {Si}_{7}$ and ${Mg}_{5} {Si}_{6}$ . Note that for the latter two, the central shift atoms are Si and Mg atoms, respectively.Reuse & Permissions
Figure 5
(Color online) Illustration of the $0.5 b$ shift (upwards in the figure) of the column of Al atoms in the ${Mg}_{4} {Si}_{6} Al$ precipitate embedded in fcc Al. The solid circles are atoms in the top ${(100)}_{Al}$ plane $(x = 0.5)$ ; the open circles are atoms in the bottom ${(100)}_{Al}$ plane $(x = 0.0)$ . See Figs. 1, 3 for the orientation relationships of the nanoclusters with the Al matrix. (a) Pre- $β^{″}$ arrangement, before the $0.5 b$ shift and with an Al vacancy on top of the shift column. (b) $β^{″}$ arrangement after the $0.5 b$ shift. Two “half” vacancies remain at the two ends of the shifted column.Reuse & Permissions

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