Abstract

The search for high-strength alloys and precipitation hardened systems has largely been accomplished through Edisonian trial and error experimentation. Here, we present a novel strategy using high-throughput computational approaches to search for promising precipitate/alloy systems. We perform density functional theory (DFT) calculations of an extremely large space of ∼200,000 potential compounds in search of effective strengthening precipitates for a variety of different alloy matrices, e.g., Fe, Al, Mg, Ni, Co, and Ti. Our search strategy involves screening phases that are likely to produce coherent precipitates (based on small lattice mismatch) and are composed of relatively common alloying elements. When combined with the Open Quantum Materials Database (OQMD), we can computationally screen for precipitates that either have a stable two-phase equilibrium with the host matrix, or are likely to precipitate as metastable phases. Our search produces (for the structure types considered) nearly all currently known high-strength precipitates in a variety of fcc, bcc, and hcp matrices, thus giving us confidence in the strategy. In addition, we predict a number of new, currently-unknown precipitate systems that should be explored experimentally as promising high-strength alloy chemistries.

Abstract

Aging reactions in Mg–RE alloys strengthen magnesium, due to the formation of metastable β^″${\beta }^{″}$ and β^′${\beta }^{\prime }$ precipitates. We use first-principles calculations to critically assess binary Mg–RE (RE = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm and Y) aging reactions, metastable phases and interfacial energy. We find the following. (i) Our calculations correctly predict the formation of different variants of β^′${\beta }^{\prime }$ phases for Mg–RE systems across the RE series. (ii) Surprisingly, the Mg/β^″${\beta }^{″}$ prismatic interfaces are unstable, with a negative interfacial energy. (iii) This interfacial instability implies the existence of a more energetically stable compound than β^″${\beta }^{″}$, which we show to be the β^′${\beta }^{\prime }$ precipitate. By exposing the link between Mg/β^″${\beta }^{″}$ prismatic interfaces and the β^′${\beta }^{\prime }$ structure, we propose that β^′${\beta }^{\prime }$ phase formation is due to an energetic preference for an ordered arrangement of Mg and β^″${\beta }^{″}$. (iv) Our Mg/β^″${\beta }^{″}$ interfacial energy results also indicate that atomically thin β^″${\beta }^{″}$ planar Guinier–Preston zones can form as a precursor to β^′${\beta }^{\prime }$ precipitation.

Abstract

In an effort to understand the exceptional precipitation strength in Mg–RE (RE = rare earth) alloys, we use first-principles density functional theory calculations to study the energetic stability, elastic constants and coherency strain energy of Mg₃RE-D0₁₉${\mathrm{Mg}}_3\mathrm{RE}\text{-}\mathrm{D}{0}_{19}$ precipitate phases in a Mg matrix and make extensive comparisons with experimental and theoretical work, where available. We find the metastable β^′′-D0₁₉${\beta }^{\prime \prime }\text{-}\mathrm{D}{0}_{19}$ phases are energetically competitive with the stable Mg-rich phases for all RE elements. We also investigate the coherency strain energy of Mg–Mg₃RE$\mathrm{Mg}''–''{\mathrm{Mg}}_3\mathrm{RE}$ binary systems using first-principles methods and harmonic elasticity theory. We find the two approaches to computing coherency strain energy in good agreement, indicating the validity of using harmonic elasticity equations, which we extend to hexagonal systems, to study the direction-dependent coherency strain energy of D0₁₉$\mathrm{D}{0}_{19}$ precipitates in Mg–RE binary systems. From our coherency strain calculations, we find the D0₁₉$\mathrm{D}{0}_{19}$ precipitates to strongly prefer prismatic, as opposed to basal, habit planes for all Mg–RE systems. This work thus provides an explanation for the observed prismatic plate-shaped morphology of many Mg–RE precipitates, which is ultimately responsible for their strengthening response.

Abstract

Abstract

The mechanical strength of Mg–Al–Zn alloys can be affected by a fine spatial dispersion of β-Mg₁₇Al₁₂ precipitates in the Mg matrix. In an effort to understand the phase stability and the unusual asymmetric off-stoichiometry observed in β-Mg₁₇Al₁₂, we have performed a series of first-principles density functional theory (DFT) calculations of bulk and defect properties of Mg₁₇Al₁₂. Specifically, we consider native point defects (i.e. vacancies and anti-sites) in all four sublattices of Mg₁₇Al₁₂, i.e. 2a, 8c, 24g (Mg) and 24g (Al). The T = 0 K static energies of defect Mg₁₇Al₁₂ supercells indicate that anti-site defects are energetically favored over vacancies, and the lowest anti-site defect formation energies are in 24g sites for both Al_Mg and Mg_Al. These Al-rich and Mg-rich anti-site defect formation energies are similar in magnitude, and thus do not explain the asymmetric off-stoichiometry of Mg₁₇Al₁₂. We also investigate the effect of atomic vibrations via DFT phonon calculations on native point defect free energies of Mg₁₇Al₁₂ and combine these entropic contributions with the point defect formation energies to evaluate the thermodynamics of off-stoichiometry in this phase. We find that the formation of the Al_Mg anti-site is not strongly stabilized by vibrational entropy. Thus, we conclude that the observed asymmetry in the off-stoichiometry of the β-Mg₁₇Al₁₂ phase in the Mg–Al phase diagram is not explained by simple native point defect thermodynamics, and must involve a more complicated defect formation mechanism, such as multi-defect clustering.

Abstract

Solute–vacancy binding is a key quantity in understanding diffusion kinetics, and may also have a considerable impact on the hardening response in Mg alloys. However, the binding energetics between solute impurities and vacancies in Mg are notoriously difficult to measure accurately and are largely unknown. Here, we present a large database of solute–vacancy binding energies in Mg from first-principles calculations based on density functional theory. Our vacancy formation energy and dilute mixing energy, which are byproducts of the solute–vacancy binding calculations, show good agreement with experiments, where available. We have investigated the simple physical effects controlling solute–vacancy binding in Mg and find that there is a modest correlation between binding energy and solute size, with larger solute atoms more favorably binding with neighboring vacancies to relax the strain induced by the solutes. Most early 3d transition metal solutes do not favorably bind with vacancies, indicating that a simple bond-counting argument is not sufficient to explain the trends in binding, in contrast to the case of binding in Al. We also predict positive vacancy binding energies for some commonly used microalloying elements in Mg which are known to improve age hardenability, i.e. Na, In, Zn, Ag and Ca. Even larger vacancy binding energies are found for some other solutes (e.g. Cu, Sn, Pb, Bi and Pt), which await experimental validation.

Abstract

Previous efforts to understand solute–vacancy binding in aluminum alloys have been hampered by a scarcity of reliable, quantitative experimental measurements. Here, we report a large database of solute–vacancy binding energies determined from first-principles density functional calculations. The calculated binding energies agree well with accurate measurements where available, and provide an accurate predictor of solute–vacancy binding in other systems. We find: (i) some common solutes in commercial Al alloys (e.g., Cu and Mg) possess either very weak (Cu), or even repulsive (Mg), binding energies. Hence, we assert that some previously reported large binding energies for these solutes are erroneous. (ii) Large binding energies are found for Sn, Cd and In, confirming the proposed mechanism for the reduced natural aging in Al–Cu alloys containing microalloying additions of these solutes. (iii) In addition, we predict that similar reduction in natural aging should occur with additions of Si, Ge and Au. (iv) Even larger binding energies are found for other solutes (e.g., Pb, Bi, Sr, Ba), but these solutes possess essentially no solubility in Al. (v) We have explored the physical effects controlling solute–vacancy binding in Al. We find that there is a strong correlation between binding energy and solute size, with larger solute atoms possessing a stronger binding with vacancies. (vi) Most transition-metal 3d solutes do not bind strongly with vacancies, and some are even energetically strongly repelled from vacancies, particularly for the early 3d solutes, Ti and V.