What are CMAs?
Giant unit cells and inherent structural disorder are the most pronounced features of complex metallic alloy phases (CMAs). Prominent examples of CMAs are approximant phases of icosahedral quasicrystals as shown below. In the Al-Mg-Zn system the τ1-phase crystallizes with 160 atoms and the τ2-phase with 676 atoms per unit cell. In addition a primitive quasicrystalline phase of unknown structure has been observed. The crystal structure with more than 1000 atoms per unit cell forms in the related Ga-Mg-Zn system whereas the crystal structure with about 2900 atoms is still hypothetical.
The crystal structure of most CMAs can be described conveniently by large geometrical units, i.e., with a cluster substructure. Clusters of icosahedral symmetry, e.g., the Mackay icosahedron or the Bergman cluster, have been studied in our group to understand the formation of the clusters and their influence on phase stability and physical properties. The crystal structures below are conveniently described as packings of large structural units of icosahedral symmetry—Bergman clusters—despite the large number of atoms per unit cell.
Network of Excellence Complex Metallic Alloys
The 
Network of Excellence Complex Metallic Alloys (NoE CMA) is funded by the European Commission within the 6th Framework Programme Nanosciences-Materials-Processes. Established in July 2005, it consists of 22 partners in 12 European countries including the Max Planck Society. The main objective of the NoE CMA is to form an integrated body dedicated to the intelligent search for new metallic materials and their development towards technological applicability. The collaboration between the NoE CMA partners lead to the creation of a European Centre for Metallic Alloys and Compounds (C-MAC) in September 2008.
At the MPI for Chemical Physics of Solids in Dresden CMAs are studied with focus on structure, formation, thermodynamic stability, physical properties, and chemical bonding. The main objective of our work is to understand disorder phenomena in CMAs and their influence on phase stability.
Phase Stability
Recent phase diagram studies using state of the art techniques have shown that CMAs occur frequently not only in multinary but also in binary systems. Our knowledge on phase formation and structure of CMAs is now growing fast but due to the vast number of possible systems is still from being complete. Because phase diagram studies are tedious, expensive and time consuming, special attention has been paid during the last two decades primarily to Al and Mg based systems promising the design of advanced light metal intermetallics.
Phase stabilities are determined experimentally by exploring the temperature-composition parameter space at finite temperatures. This is state-of-the art all over the world. However, phase diagrams containing a number of CMAs within a small temperature-composition range are challenging. An example is shown on the right side. Three different CMAs with 160, 1532 and 1944 atoms per unit cell form in the Mg-Pd system at the compositions 81 at.%, 80 at.% and 79 at.% Mg, respectively.
Modelling and Structure Prediction
At low temperature phase diagrams and the structure of phases are difficult to investigate because no thermodynamic equilibrium state can be reached within an acceptable time. Here, modelling using first principles and pair potential studies has proven to be very helpful to find the ground state structure. At the same time they provide clues to the understanding of how a particular structure is stabilized. Valuable information can be obtained on the influence of the structural vacancies and the substitution defects on the phase stability. Quite often this information allows to predict the stability of ternary extensions and therefore to speed up laboratory work. The figure on the left side shows as an example the computed convex hull of the binary system Ag-Mg. The CMAs ε-Ag15Mg51 and γ'-Ag9Mg37 have nearly the same ground state energy as expected empirically.
In addition, atomic pair potentials can be probed. This approach can provide information on the main factors stabilizing a given crystal structure and allows to understand the chemical reasons for stability of the distinct structural motifs, e.g., clusters and the influence of the entropy. The next step is to check the predictive power of the theoretical (conceptual) description. This can be done for example by varying temperature, pressure, composition, electric or magnetic fields to find out the influence on the free enthalpy. An example is shown on the right side. The effective pair potentials for Mg-rich Ag compounds together with the reduced pair distribution function G(r) of the predicted crystal structure of γ'-Ag9Mg37 is plotted. The structure of the low temperature phase has been found by a simulated annealing approach and is in agreement with the experimental determined structure.
Short and Long Range Order
A large number of CMAs exhibit perceptible homogeneity ranges up to several atomic percent. Even those CMAs with narrow homogeneity ranges have turned out to be in many cases non-stoichiometric phases with intrinsic disorder, which implies that an ordered crystal structure is unstable in the experimental accessible phase field with respect to decomposition. Put differently, entropic contributions play an important role for phase formation and stabilization at higher temperatures. Structure determination of disordered CMAs is in many cases a formidable task and comprises the investigation of long and short range order as a function of composition and temperature as well as structural defects as function of the history of the materials. The structures of crystalline CMAs are obtained from X-ray and neutron diffraction investigations. Powder diffraction gives information for a larger sample, whereas smaller specimens ranging from micro- to nanometers are investigated using single crystal structure analysis, selected area electron and convergent beam electron diffraction. For perfect crystals short range order (coordination polyhedra) is determined by the long range order. In case of pronounced disorder the crystalline (quasicrystalline) state gives only the average structure. Structural vacancies and substitutional disorder are most important for CMAs and often accompanied by local displacements. Site occupation factors give information on concentration and distribution of the structural vacancies and the substitutional defects. However, the short range order, i.e., the local structure, has to be studied using a number of local probes, e.g. total scattering methods, transmission electron microscopy, extended X-ray absorption fine structure, Mössbauer spectroscopy, nuclear magnetic resonance to name some. Defects like dislocations or planar faults are quite important for the mechanical properties. They are investigated primarily by imaging techniques. The figure on the right side shows as an example the nano-twinned structure of Mg64Pd17.
This work is done with the collaboration of