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Structural Materials


An important avenue of improving energy efficiency in transportation is the development of lighter and/or more efficient materials that compose the body of the vehicle. For automobiles, a promising possibility is to replace the aluminum alloys that make up a large portion of the mass of the car with lighter magnesium alloys. Unfortunately, magnesium alloys tend to have poorer mechanical properties than their aluminum counterparts. However, advances in processing and doping magnesium alloys show potential in improving the strength of magnesium alloys, such as the formation of long-period stacking ordered precipitates and the use of rare earth dopants. Another avenue we are exploring for improving efficiency in transportation is next-gen superalloys for jet engine turbine blades based on Co. Calculating the thermodynamic and kinetic properties of Co-based superalloys allows us to understand the physics of the strengthening mechanisms and suggest novel compositions and processing mechanisms with improved strength.

Through the use of density functional theory (DFT), two important questions can be answered. The first is why do these phenomena improve mechanical properties? DFT can predict thermodynamic and kinetic properties that are difficult to determine experimentally, such as enthalpy of formation, free energy, diffusion coefficients, interfacial energy, etc. Having these properties helps to reveal fundamental strengthening mechanisms. This then leads to the second question: are there stronger alloy compositions? This is a very difficult question to answer experimentally as there are MANY elements in the periodic table and systematically investigating them all would be prohibitively expensive in cost, time, and materials. Once the critical properties that govern strengthening mechanisms are known, systematic predictions of those properties with DFT can be readily performed across the entire periodic table through high-throughput computational screening. These predictions guide new experiments which can then guide new calculations. This process is often called Integrated Computational Materials Engineering (ICME).

Aluminum Alloys

Entropically Favored Ordering: The Metallurgy of Al2Cu Revisited

The famous sequence of precipitates which form upon heat treating Al-Cu is part of nearly every metallurgical textbook. Numerous precipitation (and other) experiments have led to a long-standing belief that the energetic ground state of Al2Cu is the θ phase. Modern first-principles calculations at T = 0 K surprisingly predict the energy of the observed Al2Cu-θ phase to be higher than that of its metastable counterpart, θ'. We show that vibrational entropy reverses this energetic preference at T approximately 150~200 degrees C, resolves the apparent discrepancy between theory and experiment, and hence plays a critical (but previously unsuspected) role in the precipitation sequence.

Multiscale Modeling of Precipitate Microstructure Evolution

We demonstrate how three “state-of-the-art” techniques may be combined to build a bridge between atomistics and microstructure: (1) first-principles calculations, (2) a mixed-space cluster expansion approach, and (3) the diffuse-interface phase-field model. The first two methods are used to construct the driving forces for a phase-field microstructural model of
θ'-Al2Cu precipitates in Al: bulk, interfacial, and elastic energies. This multiscale approach allows one to isolate the physical effects responsible for precipitate microstructure evolution.

First-principles study of the nucleation and stability of ordered precipitates in ternary Al–Sc–Li alloys
First-principles density functional calculations are used to study the nucleation and stability of L12-ordered precipitates in Al–Sc–Li alloys. For dilute Al alloys, there are three possible ordered L12 precipitates: Al3Sc, Al3Li, and an Al3Sc/Al3Li core/shell structure. To calculate the nucleation behavior, information about bulk thermodynamics (both static total energies and vibrational free energies), interfacial energetics and coherency strain is required. We found that: the coherency strain energies for forming coherent interfaces between Al/Al3Sc, Al/Al3Li and Al3Sc/Al3Li are relatively small, owing to the small atomic size mismatches; the calculated solubilities of Sc and Li in a-Al alloys are in good agreement with experimental values; the interfacial energies for Al/Al3Sc, Al/Al3Li and Al3Sc/Al3Li for (100), (110) and (111) interfaces are calculated; combining the bulk and interfacial energies yields the nucleation barriers and critical radii for Al3Sc and Al3Li precipitates. The energetic stability of the Al3Sc/Al3Li core/shell structure is compared with individual Al3Sc and Al3Li nuclei, and the range of precipitate sizes for which the core/shell structure is energetically favored is determined quantitatively.

Magnesium Alloys

First-principles study of solute–vacancy binding in magnesium

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. 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.

Thermodynamic stability of Mg-based ternary long-period stacking ordered structures

Mg alloys containing long-period stacking ordered (LPSO) structures exhibit remarkably high tensile yield strength and ductility. They have been found in a variety of ternary Mg systems of the general form Mg–XL–XS, where XL and XS are elements larger and smaller than Mg, respectively. In this work, we examine the thermodynamic stability of these LPSO precipitates with density functional theory, using a newly proposed structure model based on the inclusion of a Mg interstitial atom. We predict the stabilities for 14H and 18R LPSO structures for many Mg–XL–XL ternary systems: 85 systems consisting of XL = rare earths (RE) Sc, Y, La–Lu and XS = Zn, Al, Cu, Co, Ni. We predict thermodynamically stable LPSO phases in all systems where LPSO structures are observed. In addition, we predict several stable LPSO structures in new, as-yet-unobserved Mg–RE–XS systems. Many non-RE XL elements are also explored on the basis of size mismatch between Mg and XL, including Tl, Sb, Pb, Na, Te, Bi, Pa, Ca, Th, K, Sr—an additional 55 ternary systems. XL = Ca, Sr and Th are predicted to be most promising in terms of forming stable LPSO phases, particularly with XS = Zn.

Reference: James E. Saal et al., Acta Mater. 68 (2014) 325-338

Co-based Superalloys

Diffusion coefficients of transition metals in fcc cobalt

Using first-principles density functional theory (DFT), we calculate the diffusivities of 32 different solute elements in fcc cobalt within the formalism of the five-frequency model. For self-diffusion in fcc cobalt, we compare the accuracy of various approximations to the exchange-correlation energy functional of DFT in estimating the activation energy, and find that only the Perdew-Burke-Ernzerhof (PBE) approximation agrees well with experimental reports and all other functionals largely overestimate it. Our calculations also show that an accurate estimation of the self-diffusion coefficient requires explicit calculation of the effective jump frequency and vacancy formation entropy via phonons. Using accurate self-diffusion data and scaling all solute-related attempt frequencies with respect to the attempt frequency for self-diffusion using a simple relation involving the atomic mass and melting temperature of the solute yields solute diffusivities in excellent agreement with experiments, where such data is available. We find that large solutes spontaneously relax toward the nearest neighbor vacancy to relieve the misfit strain, and the extent of this relaxation correlates negatively with the migration energy. Thus, in general, larger solutes have lower migration energies and diffuse faster than smaller solutes in fcc cobalt. Finally, for all the solutes considered, we systematically tabulate the diffusion-related quantities calculated—diffusion prefactors, migration and activation energies—constructing an extensive and accurate first-principles database for solute diffusion in fcc cobalt.

High-throughput Computational Search of Precipitates
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.

Researchers studying this topic


Zugang Mao
Dongwon Shin