.. _AdCrStructAuCualloy: Adaptive Crystal Structures of Au-Cu Alloy ------------------------------------------ .. sectionauthor:: David .. reviewer Walter .. version 3.6 .. status publishable .. expert David .. keywords UNCLE, alloy, cluster expansion .. modules UNCLE, VASP *Keywords: UNCLE, alloy, cluster expansion* The stable phases in the gold-copper alloy were identified using the cluster expansion method as implemented in the *MedeA UNCLE* module. The well-established AuCu L1\ :sub:`0` and AuCu\ \ :sub:`3` L1\ :sub:`2` phases were found by means of an iterative cluster expansion ground-state search. In addition to these two well-established phases an adaptive crystal structure around the Au\ \ :sub:`3`\ Cu stoichiometry range, made up of repeat units of pure-Au and pure-Cu planes along (001), and a Au\ :sub:`7`\ Cu\ :sub:`5` |p4_mmm| phase was identified. Experimental Results and Previous Computed Results ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. _AdCrStructAuCualloy-Figure1: .. figure:: /AppNotes/images/AdCrStruct-AuCu-alloy/AdCrStructAuCualloy-Figure1.png :scale: 70% :align: center 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 L1\ :sub:`0` (|p4_mmm|) phase and at composition AuCu\ \ :sub:`3` the L1\ :sub:`2` (|pm-3m|) phase. The high temperature AuCu |imma| phase is a long-range ordered structure consisting of alternating AuCu\ \ :sub:`3` and Au\ \ :sub:`3`\ Cu L1\ :sub:`2` units. Beyond these phases a low temperature phase is suggested at Au\ \ :sub:`3`\ Cu. It is stable in a comparatively wide concentration range and is classified as L1\ :sub:`2` (|pm-3m|). However, its formation temperature (240 :math:`^{\circ}`\C) is much lower than that of AuCu (385 :math:`^{\circ}`\C) and AuCu\ \ :sub:`3` (390 :math:`^{\circ}`\C). A cluster expansion ground state search by Sanati *et al.* [#Sanati2003]_ noticed that the structure around Au\ \ :sub:`3`\ Cu 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 [#Anderson1973]_. 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 L1\ :sub:`0` and the AuCu\ \ :sub:`3` L1\ :sub:`2` phase. Instead of an Au\ \ :sub:`3`\ Cu L1\ :sub:`2` 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 L1\ :sub:`0` AuCu phase an isolated Au\ :sub:`7`\ Cu\ :sub:`5` |p4_mmm| phase that has the adaptive structures plane-wise ordering along (001) is also found. .. _AdCrStructAuCualloy-Figure2: .. figure:: /AppNotes/images/AdCrStruct-AuCu-alloy/AdCrStructAuCualloy-Figure2.png :scale: 70% :align: center 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. 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 Au\ \ :sub:`3`\ Cu composition at higher temperatures and may lead to the L1\ :sub:`2` phase being more stable (e.g. at room temperature and above). Such an effect could explain the discrepancy between experimental data and DFT studies. .. [#Sanati2003] M. Sanati *et al.*, "Adaptive Crystal Structures: CuAu and NiPt", *Phys. Rev. Lett.* **90**, 045502 (2003) `link `__ .. [#Anderson1973] J. S. Anderson, "On infinitely adaptive structures", *J. Chem. Soc. Dalton Trans.* **10**, 1107 (1973) `link `__ .. admonition:: MedeA modules * *MedeA Environment* * *MedeA VASP* * *MedeA UNCLE* .. only:: html :download: :download:`pdf `