31. Adaptive Crystal Structures of Au-Cu Alloy

31.1. Experimental Results and Previous Computed Results

Figure 31.1.1 H.Okamoto, D.J. Chakrabarti, D.E. Laughlin, and T.B. Massalski, Binary Alloy Phase Diagrams, Second Edition, Ed. T.B. Massalski, ASM International Ohio 1, 358-362 (1990)

Pure gold, pure copper, the gold-copper compounds, and the alloy are found on the same face-centered cubic/tetragonal lattice. There are two well-established phases in the Au-Cu alloy: at stoichiometry AuCu the L1₀ (P4/mmm) phase and at composition AuCu₃ the L1₂ (Pm-3m) phase. The high temperature AuCu Imma phase is a long-range ordered structure consisting of alternating AuCu₃ and Au₃Cu L1₂ units.

Beyond these phases a low temperature phase is suggested at Au₃Cu. It is stable in a comparatively wide concentration range and is classified as L1₂ (Pm-3m). However, its formation temperature (240 \(^{\circ}\)C) is much lower than that of AuCu (385 \(^{\circ}\)C) and AuCu₃ (390 \(^{\circ}\)C). A cluster expansion ground state search by Sanati et al. [1] noticed that the structure around Au₃Cu resembles that of an adaptive crystal structure made up of repeat units of pure-Au and pure-Cu (001) planes. In such an infinitely adaptive crystal structure any composition within a certain concentration range is realized by a fully ordered crystal structure without defects [2].

31.2. Computed Results

A cluster expansion ground state search in a configuration space of 34368 structures does indeed find the two well established phases, the AuCu L1₀ and the AuCu₃ L1₂ phase. Instead of an Au₃Cu L1₂ phase an adaptive crystal structure, composed of repeat units of pure Au- and Cu-planes along (001), is identified in the Au concentration range of 0.65-0.92. In between the concentration range of the adaptive structures and the L1₀ AuCu phase an isolated Au₇Cu₅ P4/mmm phase that has the adaptive structures plane-wise ordering along (001) is also found.

31.3. Significance

The cluster expansion method of MedeA UNCLE is the perfect complementary tool to analyze and understand phase stability. By quickly scanning through a large number of configurations with first principles accuracy stable ground state structures at T=0 K can be identified automatically. These phases can be more complex than originally contemplated and expected.

31.4. Comments

The adaptive crystal structure has been found using DFT calculations at T=0 K. Entropic effects, such as mixing and vibrational entropy, might significantly alter the stable phases around Au₃Cu composition at higher temperatures and may lead to the L1₂ phase being more stable (e.g. at room temperature and above). Such an effect could explain the discrepancy between experimental data and DFT studies.