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 103–105 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.
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: D1a, 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.
Fig. 1: Shape-dependence of coherent fcc-Zn precipitates as a function of the unber of Zn atoms and temperature in Al-Zn 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.
We have an online presentation describing the LEGO methodology in HTML
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).
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