Cr_1-xAl_xN is established for many applications like in automotive, machining, and semiconductor industries, and hence its structure, elastic properties, and phase stability as a function of the chemical composition are of vital importance. Here we present ab initio calculations of cubic (c), hexagonal (h), and orthorhombic Cr_1-xAl_xN in combination with continuum mechanical investigations of the decomposition process into the stable phases c-CrN and h-AlN with the intermediate step of metastable c-AlN. We show that calculations of Cr_1-xAl_xN in their ferromagnetic (FM) and antiferromagnetic (AFM) state have an excellent correlation to experiments. For AFM c-Cr_1-xAl_xN the lattice parameter decreases from 4.139 to 4.069 Å with increasing x from 0 to 1 in agreement with experiments (4.139 to 4.060 Å). The energy of formation suggests that the cubic phase can be stabilized for x in the range of 0.48-0.75, depending on the metal-sublattice population. This can be understood by considering the Al distribution induced changes in the electronic structure and configurational entropy. Synthesized by plasma-assisted vapor deposition, Cr_1-xAl_xN is reported to crystallize in the cubic modification for x of 0.6-0.71. With increasing Al content from x = 0 to 1 the bulk modulus of c-Cr_1-xAl_xN increases from 245 to 252 GPa, respectively.

The calculated enthalpy change for the separation of supersaturated c-Cr_1-xAl_xN into c-CrN and c-AlN has a maximum of ~0.038 eV/at (7.27 kJ/mol) at x ~0.5. Using continuum mechanical investigations the contribution of strain energy for a fully constrained condition of this decomposition process is ~55 J/cm³ (0.58 kJ/mol) at x ~0.5. Estimating the entropy term by an ideal binary mixture the chemical driving force for decomposition of c-Cr_1-xAl_xN into c-CrN and c-AlN is already at temperatures between 800 and 900°C smaller than the strain energy. This can explain the experimental observations that c-Cr_1-xAl_xN decomposes by forming stable h-AlN without the intermediate step of metastable c-AlN.

In metallic ultrathin films, these states influence the Density of States at the Fermi level and, thus, many properties (superconducting transition temperature, resistivity) of thin fims depend on them. We have shown recently that for Pb/Cu(111) the contribution of these states to the total energy of the system determines its structural stability, which oscillates with the thickness, giving rise to islands with preferred or "magic" height.

Here, variable temperature STM is used to visualize the thermal evolution of Pb films deposited on Cu(111) at 60 K, a temperature low enough to allow the kinetically hindered initial growth of flat films of even forbidden thicknesses. Tunnelling Spectroscopy is used to determine the local thickness of Pb. This allows the quantitative determination of the temperature dependence of the population of the different atomic layer and the roughening temperature of each atomic height, which oscillates with bilayer periodicity and a longer beating period, as dictated by the Fermi surface of Pb. Conditions are found to stabilize, by this quantum effect, particular thicknesses up to room temperature, resulting in Pb films which are atomically flat over lateral distances of microns, limited only by the perfection of the substrate.

The magic height effect is employed to grow an atomically flat Pb film on a 50 micron-thick, ultra-perfect Si (111) wafer, which acts as an ideal mirror for He atoms. This "quantum mirror" will be used to focus a beam of He atom down to 100 nm and it is an essential part of the atom microscope with sub-micron spatial resolution currently under construction.