Metal Alloys

I. Quantum-Mechanical Design of Metal Alloys
II. First-Principles Prediction of Short-Range Order
III. Computer Aided Search for New Materials using Quantum Mechanics
IV. Linear Expansion in Geometrical Objects
V. Quantum-Mechanical Search for Advanced Li-ion battery Materials

I. Quantum-Mechanical Design of Metal Alloys

Metal alloys (e.g., aluminum- and magnesium-based) have great promise to reduce the weight of cars and light trucks without compromising safety. However, much basic science is not yet understood about e.g. Al-alloys, leading alloy designers often to simply "guess" at the parameters to be used in microstructural models. Thus, the role of basic energetic and thermodynamic data in designing metal alloys is crucial towards their application. Researchers working in NREL’s Solid State Theory Group have developed computational techniques for applying highly-accurate "state-of-the-art" first-principles (i.e., completely quantum-mechanical, parameter-free) computational approaches to obtaining thermodynamic properties of alloys. These calculations will play a central role in predicting a new class of modern metal alloys, designed on computers rather than in laboratories.

First-principles quantum-mechanical calculations are computationally expensive; thus, even on today’s fastest computers, the system size which can be simulated by first-principles approaches are limited by computational resources, and thus some "scaling up" of length scales is necessary to treat thermodynamic alloy problems. One method for this scaling up which is currently utilized in NREL’s Solid State Theory Group is in mapping accurate first-principles data onto simpler energy functionals which can then be used on a much larger length scale. The method is known as LEGO, or "Linear Expansion in Geometric Objects". Examples of this type of approach are in precipitation hardening in Al-Cu and Al-Zn alloys: Like most pure metals, aluminum is relatively weak, and therefore need to be strengthened via alloying additions. In precipitation hardening, common in Al-alloys, a small amount of a solute element is added to Al at high temperatures, and then the alloy is quenched down in temperature past the solubility limit of the alloying element. Thus, the solute element begins to precipitate out of the Al matrix, and these precipitates act to pin dislocations, and hence improve mechanical strength. However, without understanding the structure and stability of the precipitated phase, alloy designers cannot fully understand the strengthening mechanism. NREL researchers have predicted the thermodynamic stability and atomic-scale structure of Cu precipitates embedded in an Al matrix. The precipitation is determined by a combination of strain and interfacial energies, and an example of calculated strain energies for Cu embedded in Al is shown in Fig. 1. By using both strain and interfacial in thermodynamic Monte Carlo simulations, one can predict the complete atomic-scale structure of precipitates in Al. An exampleof this kind of hybrid "first-principles/scale up" approach is shown in Fig. 2, which shows the atomic-scale structure of an ordered Cu precipitate in a dilute Al-Cu alloy.

In the case of Al-Zn, our model allows for the first time a prediction of the observed size- and temperature dependence of precipitates in this alloy system. These precipitates consist only of Zn atoms. Examples of precipitates are visible in Fig. 3: In agreement with experimental studies, the precipitates change from a nearly spherical to a more hexagonal/ellipsoidal shape with decreasing temperature and increasing size.

The thermodynamic calculation was performed for a system of more than 200,000 atoms, extending to length scales approaching 200 Å approximately scaling the length scale of the first-principles calculations by a factor of 20-50. With further improvements, length scales of 1000 Å are in sight, thus leading to the possibility of microstructural modeling with completely atomistic approaches.

Selected References:

1. A. Zunger, "First Principles Statistical Mechanics of Semiconductor Alloys and Intermetallic Compounds," in NATO Advanced Study Institute on Statics and Dynamics of Alloy Phase Transformations, edited by P. Turchi and A. Gonis, Plenum Press, New York, 361-419 (1994).

2. Z. W. Lu, B. M. Klein and A. Zunger, "Spin-polarization-induced structural selectivity in Pd₃X and Pt₃X (X=3d) compounds," Phys. Rev. Lett. 75, 1320-1323 (1995).

3. C. Wolverton, V. Ozolins, and A. Zunger, "First-Principles Theory of Short-range Order in Size-mismatched Metal Alloys: Cu-Au, Cu-Ag, and Ni-Au," Phys. Rev. B. 57, 4332 (1998).

4. V. Ozolins, C. Wolverton, and A. Zunger, "Cu-Au, Ag-Au, Cu-Ag, and Ni-Au Intermetallics: First-Principles Study of Phase Diagrams and Structures", Phys. Rev. B 57, 6427 (1998).

5. C. Wolverton and A. Zunger, "An Ising-like Description of Structurally-Relaxed Ordered and Disordered Alloys", Phys. Rev. Lett.75, 3162 (1995).

6. S. Müller, C. Wolverton, L.-W. Wang, and Alex Zunger, "Coherent phase stability in Al-Zn and Al-Cu fcc alloys: The role of the instability of fcc-Zn", Phys. Rev. B, accepted

Other References

For a listing of all SST references on the topics "Transition Metal Alloys", "Electronic Structure of Random Networks", and "Light Metal Alloys", click on the "Get References" button below.

II. First-Principles Prediction of Short-Range Order in Alloys

Solid state alloys at high temperatures often undergo a phase transition to a disordered arrangement of the constituent atoms. The arrangement is not random, however, but may exhibit some degree of short-range order, i.e., the excess probability of finding certain pairs of atoms relative to random statistics. For the first time, ``state-of-the-art'' first-principles calculations including the effects of atomic displacements have been extended to high temperatures, and the resulting short-range order predicted. The short-range order has been predicted for a variety of transition metal and semiconductor alloys. The excess pair probabilities associated with short-range order are also a physically measurable effect, and we have compared our parameter-free calculations with experimental measurements, finding excellent agreement. Our calculations have led to an increased understanding of ordering properties in these alloys.

Many transition metal alloy systems are currently being considered as a new class of materials for high-temperature applications. In many cases these applications have been limited to date, however, oftentimes due to a lack of fundamental understanding of the materials properties. Also, in many semiconductor alloys, the degree or extent of ordering is not even known experimentally. The current theoretical calculations demonstrate that ordering processes in alloys may be understood and even predicted (without reference to any experiment) on a fundamental, microscopic level. The theoretical predictions are shown to be highly accurate by comparing with experimental measurements for transition metal alloys, for which an abundance of experimental data exists. These calculational tools are not specific to transition metals, however, thus opening the door to calculations of ordering in the highly technologically important semiconductor alloys, where there exists very little or no experimental data.

Selected References

1. Z. W. Lu, B. M. Klein and A. Zunger, "Atomic short range order and alloy ordering tendencies in the Ag-Au system" Modelling & Simulation in Mat. Sci. 3, 1-18 (1995).

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2. C. Wolverton, V. Ozolins, and Alex Zunger ``First-principles theory of short-range order in size-mismatched metal alloys: Cu-Au, Cu-Ag, and Ni-Au'' Phys. Rev. B. 57, 4332 (1998).

3. C. Wolverton and A. Zunger, ``Ni-Au: A Testing Ground for Theories of Phase Stability'' Comp. Mat. Sci. 8, 107 (1997).

4. C. Wolverton, A. Zunger, and B. Schonfeld, ``Invertible and Non-Invertible Ising Alloy Problems'' Solid State Commun. 101, 519 (1997).

5. Z. -W. Lu, D. B. Laks, S. -H. Wei, and A. Zunger, "First-Principles Simulated Annealing Study of Phase Transitions and Short Range Order in Transition Metal and Semiconductor Alloys", Phys. Rev. B 50, 6642 (1994).

6. S. Müller, C. Wolverton, L.W. Wang and A. Zunger, "Coherent Phase-Stability in Al-Zn and Al-Cu Fcc Alloys: The Role of the Instability of fcc Zn," Phys. Rev. B. (In Press).

7. C. Wolverton, V. Ozolins and A. Zunger, "Short-range Order Types in Metallic Alloys: A Reflection of Coherent Phase Stability," Phys. Rev. B. - in press (1999)

Other References

For a listing of all SST references on the topic "Short Range Order", click on the "Get References" button below.

III. Computer-Aided Search for New Materials Using Quantum-Mechanics

Perhaps the most intriguing aspect of the spectacular success that semiconductor-based high technology has had in the past 50 years is the tiny number of species (core materials) on which these technologies are based. Even considering a broad range of semiconductor devices—transistor, computer chips, solid state lasers, detectors, solar cells, light-emitting diodes, etc.—there are only about ten basic semiconductors (all belonging to the same crystal type!), that enables these strategic technologies. This is a strikingly narrow material base, considering the number of core materials that enable other technologies: e.g., the 10^3–10⁵ species used in metallurgy, polymer technologies, biotech, and the pharmaceutical drug industry. Thus, it is entirely possible that we are currently missing the crucial breakthrough material for present-day and future electronic devices. But how is one to search for new stable materials? Even if one considers only two types of atoms, there are as many as 2**N crystal structures possible on a lattice with N sites. Even for N=35, this equals the number of stars in our galaxy! Theoretical physicists at the National Renewable Energy Laboratory (NREL) in Golden, Colorado have developed a new strategy that enables one, using fast computers and concepts from Quantum Mechanics to search this astronomic space of possibilities for the "winning combination" of atoms producing novel, stable crystal structures. This approach—Linear Expansion in Geometric Objects (LEGO)—is based on the recognition that even complex crystal structures can be viewed as a collection of simple Geometric Objects such as pairs of atoms (dumbbells), triangles of atoms, etc. By assigning to each Geometric Object an (quantum-mechanical) energy value, one can rapidly scan hundreds of thousands of candidate structures (obtained by different assemblies of the Geometric Objects), looking for the one with the lowest overall energy. This LEGO approach has already predicted a number of previously unsuspected intermetallic compounds, that were missed by the conventional approach of trial-and-error. This could revolutionize the way in which novel materials are sought.

IV. "Linear Expansion in Geometric Objects": Recent Application and Advances

• The LEGO method was applied to predict, from first principles, the electrochemical potential of a Li battery (C. Wolverton and A. Zunger, Phys. Rev. Lett. 81, 606 (1998)).

• Previously-unsuspected ordered phase of Cu₇Pt was predicted and subsequently observed experimentally (see "online LEGO presentation").

• Three previously ordered structures of Pd-Pt were predicted: Pd₃Pt(L1₂), PdPt(L1₁), and PdPt₃(L1₂). Experimental testing is awaited (see "online LEGO presentation").

• Novel, previously unknown phases of Rh-Pt are predicted: D1_a, D0₂₂, X2, and "40" (see "online LEGO presentation").

• Size- and temperature dependence of precipitate shpaes are predicted for Al-Zn: Based on a detailed study abou the coherent phase stability of Al-Zn (S. Müller, L.-W. Wang, Alex Zunger, and C. Wolverton, Phys. Rev. B 60, 16448 (1999)), the relation between sizes and shapes as a function of temperature was predicted in remarkable agreement with experiment, and explained in terms of energetics. We found that although the precipitates are created by an inherently kinetic heat treatment process, the entire series of their size vs. shape realtion can be explained in terms of thermodynamic arguments and understood in terms of strain and chemical energies (S. Müller, C. Wolverton, Lin-Wang Wang, and Alex Zunger, Acta. Mater., in press).

• Time-dependence of the distribution of precipitate shapes and sizes are predicted: Beside the relation between size and shape of an individual precipitate, the size- and shape distribution as a function of aging time t and temperature T is essential to understand at which T and t the distribution of sizes and shpaes is most efficient in order to pin dislocations. For this, the "Linear Expansion in Geometric Objects" Hamiltonian was successfully used in a Kinetic Monte Carlo program. It turns out that the growth of precipitates follows the rules of classical Ostwald-ripening.

• Low-temperature ground states are determined for Cu-Zn: a-brass is the most important phase of Cu-Zn. We find that at low temperature the system will order into a novel structure, so-called DO₂₃ (S. Müller and Alex Zunger, submitted to Phys. Rev. B).

• Three low-temperature ground-states are detected in Ag-Pd: We were able to predict three low temperature ground-states at concentrations of 25%, 50%, and 75% Palladium and the corresponding coherent phase boundaries. This discovery will lead to an important addition in the existing phase-diagram of Ag-Pd.

V. Quantum-mechanical simulations able to predict precipitate shapes in metal alloys

Fig. 2: Size-shape relatoin of Zn precipitates for two of the temperatures in Fig. 1. While the lines denote the results from our calculations, the points are n="center" class="center">

Fig. 2: Size-shape relatoin of Zn precipitates for two of the temperatures in Fig. 1. While the lines denote the results from our calculations, the points are taken from different experiments studies done at T = 300 K and T = 200 K.

Online Presentation of LEGO methodology

We have an online presentation describing the LEGO methodology in HTML

Selected Reference

1. A. Zunger, "First Principles Statistical Mechanics of Semiconductor Alloys and Intermetallic Compounds," in NATO Advanced Study Institute on Statics and Dynamics of Alloy Phase Transformations, edited by P. Turchi and A. Gonis, Plenum Press, New York, 361-419 (1994).

Other References

For a listing of all SST references on the topic "Statistical Mechanics of Alloys", click on the "Get References" button below.