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Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.

 

To obtain thorough understandings of precipitation process in heat-treatable Mg-Ca-Zn alloy, we revisited the precipitation process of a Mg-0.3Ca-0.6 Zn (at.%) dilute alloy during isothermal aging at 200 °C using an aberration-corrected scanning transmission electron microscope, atom probe tomography, and first-principles calculations. The monolayer G.P. zones form on the (0002)α plane in the peak-aged condition and transform into tri-atomic layer η'' and η' plates with a thickness of a single unit-cell height. The η' plates, then, form in pairs and stacks with energetically favorable 4–5 atomic layers of pure magnesium between the plates. While such a transformation path is similar to that seen in Mg-RE-Zn alloys (RE: rare-earth elements), the unique structure of coarse η1 plates that precipitate after the η' plates leads to a different precipitate microstructure evolution from the Mg-RE-Zn system. The η1 phase (Mg7Ca2Zn3) is unevenly distributed in the matrix after 100 h of aging and finally evolves to the equilibrium η phase (Mg10Ca3Zn6) phase with a hexagonal structure. First-principles calculations of energetics were performed to further identify the crystal structure and stability of the precipitates, supporting the following new precipitation sequence: S.S.S.S. → G.P. zones → η'' → η' → η' pairs and stacks / η1 → η 

Dilute Mg-Al-Ca-Mn alloys exhibit excellent strength-ductility combinations in the peak-aged condition due to ordered, single atomic layer Guinier-Preston (GP) zones. The present work explains why rolled sheet material is softer and less responsive to aging, as compared to extruded. Using crystal-plasticity modeling, it is shown that the initial texture of the rolled material permits the soft modes, basal slip and twinning, to accommodate more of the strain during in-plane tension, and they are less responsive to hardening by the finely dispersed GP zones. Even with the same number density of GP zones, the extruded material is stronger in tension along the extrusion axis due to an initial texture which forces higher relative activity of prismatic slip, a mode previously shown to be strongly affected by the GP zones. The present work reemphasizes the significant role of the initial texture in determining the strength and anisotropy of non-cubic metals and alloys. 

Mg-Sn and Mg-Zn alloys exhibit a strong age-hardening effect and have become promising bases for high-strength and low-cost Mg alloys. However, the atomic structures and phase stabilities of various precipitates and intermetallic compounds during the heat treatment in these systems remain unclear. Here we use a combined approach of first-principles calculations and cluster expansion (CE) to investigate the atomic structures and thermodynamic stabilities of the experimentally reported precipitates as well as orderings on the FCC and HCP lattices in Mg-Sn and Mg-Zn alloys. From the low energy structures searched by CE, potential Guinier–Preston (GP) zones are identified from preferred HCP orderings. The slow convergence for CE of HCP Mg-Zn, compared with that of Mg-Sn system, is attributed to the long-ranged interactions resulting from the larger lattice mismatch. This study could help design better age-hardened Mg alloys.