## 1 Introduction  
Al-Cu alloys have been under active scientific research and technological development for more than 100 years because of their applications in light weight constructions [1; 2]. Nowadays, they are especially important in aviation and automotive industry. Aluminum alloys show a rich variety of metastable and stable phases from which a few are ordered compounds. Since usually the surface energy is too large to form directly thermodynamically stable phases, alloying elements precipitate in a sequence of clusters, zones and metastable phases. Clusters are non-ordered, locally increased concentrations of solute atoms, zones are locally ordered but do not have a long-range ordering, while stable and metastable phases possess the latter [3]. Zones and some metastable phases are typically fully coherent with the matrix [3]. Precipitation and clustering phenomena of solute atoms in a light metal matrix are the reason for the superior properties of aluminum alloys, i.e., this results in a high strength at a small specific weight. The obtained mechanical properties arise from a suitable thermal treatment of these alloys [2]. Typically, after casting these age hardenable alloys are extruded or rolled to their final form. Thereafter they undergo a solution heat treatment at about \(100\ldots 150\,\mathrm{K}\) below the melting point of aluminum in order to obtain the maximum solubility of the chosen alloying elements [3]. After the heat treatment the materials are quenched to room temperature to freeze-in the finely distributed solute atoms. Storing these alloys then at room temperatures causes the solute atoms to diffuse by the help of quenched-in vacancies [4]. Via this process the solute atoms form agglomerates, which grow subsequently in size. After storing Al-Cu alloys for some hours at room temperature the agglomerates become visible in X-ray diffraction patterns and they are called Guinier-Preston zones according to [PERSON] and [PERSON], who discovered them independently in 1938 [5; 6; 7]. Further storage at elevated temperature causes the growth of meta-stable Al-Cu phases: \(\theta^{\prime\prime}\) Al\({}_{3}\)Cu and \(\theta^{\prime}\) Al\({}_{2}\)Cu [3]. However, in new generation Al-Cu-Li alloys like AA2198, AA2050 or AA2199 besides Al-Cu-Li precipitates these Al-Cu-phases are detected as well [8; 9]. Those Al-Cu-Li alloys are considered for the fuselage of new generation aircrafts due to their high strength and good welding behavior and have been, thus, subject to intense research in recent years (see e.g., [10; 11]), while also Al-Cu alloys are still a matter of active research [12; 13]. However, the understanding of the precipitation process in metallic alloys on the atomic level is still one of the main problems in materials science. It hampers a purposeful improvement of alloys, i.e., an alloy design as a bottom-up approach. Since the atomic structure of small, i.e., sub-nanometer, precipitates is difficult to access experimentally, numerical ab initio simulations are often the only way to obtain data on the geometry of atomic arrangements and their binding properties. Up to now, just a few numerical results on vacancy formation energies and di-vacancy binding energies in aluminum are available [14; 15], which can be compared with accurate experimental data on vacancy formation energies in pure Al (see [16] for an overview). Only recently, research on vacancy binding with different isolated solute atoms has been published for Al [17; 18] and Mg [19]. Results from ab initio calculations can be compared to experiments probing, e.g., vacancies by positron annihilation spectroscopy (PAS) [20; 21; 22; 23] or individual elements by X-ray absorption [24; 25] or small solute atom clusters employing the atom probe methods [26]. Moreover, the recently re-discovered X-ray absorption fine structure (XAFS) spectroscopy is sensitive for the atomic environment of, e.g., Cu-atoms [24; 27]. For the two spectroscopic methods, PAS and XAFS, spectra can be calculated from first principles (For PAS see, e.g., ref.