Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first principles considerations.We employ Monte Carlo simulations, taking as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition, and using a few features of the experimental Patterson function. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of τ , the golden mean.

Engineering lattice thermal conductivity requires to control the heat carried by atomic vibration waves, the phonons. The key parameter for quantifying it is the phonon lifetime, limiting the travelling distance, whose determination is however at the limits of instrumental capabilities. Here, we show the achievement of a direct quantitative measurement of phonon lifetimes in a single crystal of the clathrate Ba7.81Ge40.67Au5.33, renowned for its puzzling ‘glass-like’ thermal conductivity. Surprisingly, thermal transport is dominated by acoustic phonons with long lifetimes, travelling over distances of 10 to 100 nm as their wave-vector goes from 0.3 to 0.1 Å−1. Considering only low-energy acoustic phonons, and their observed lifetime, leads to a calculated thermal conductivity very close to the experimental one. Our results challenge the current picture of thermal transport in clathrates, underlining the inability of state-of-the-art simulations to reproduce the experimental data, thus representing a crucial experimental input for theoretical developments.

The electronic structures of the stable face-centered-icosahedral alloy Alzppd2pMnqp and of a hierarchy of rational approximants to the icosahedral phase have been calculated using ab initio pseudopotential, linear-muKn-tin-orbital (LMTO), and tight-binding (TB)-LMTO techniques. The description of the atomic structure is based on a projection from six-dimensional space, with acceptance volumes chosen such as to reproduce the observed di8'raction data. For the lowest-order approximants (1/1 and 2/1 with 128 and 544 atoms in the periodically repeated cell), the electronic eigenvalues and eigenfunctions have been calculated self-consistently using LMTO and ab initio pseudopotential techniques. For the 1/1 approximant, we have also performed a relaxation of the idealized structure using the Hellmann-Feynman forces. For the higher-order approximants (we go up to the 8/5 approximants with 41 068 atoms), the electronic densities of states and the spectral functions have been calculated from the TB-LMTO Hamiltonian via a real-space recursion technique. The electronic density of states (DOS) of the higher-order approximants is characterized by a structure-induced minimum at the Fermi level, indicating the possibility of a Hume-Rothery-type electronic mechanism for the stabilization of the icosahedral phase. However, in the lowest-order approximants the DOS minimum is either Qattened or shifted away from the Fermi energy. This is in contrast to the simple icosahedral alloys such as Al-Cu-Li, where the DOS minimum exists in the quasiperiodic phase and in the crystalline approximants.Hence it appears that for the facecentered icosahedral alloys, the structure-induced DOS minimum may be not only a generic, but also a specific property of the quasicrystalline phase. In addition to the spectral properties, we have also studied the character of the electronic states via a calculation of the participation ratio. We 6nd that the states in the vicinity of the Fermi level tend to be more localized than in the rest of the valence band and that the localization is related to certain aspects of the quasicrystalline structure. This is important for understanding the anomalous transport properties of these alloys.

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the beta-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calculations found its energy to be greater than the energy of the alpha-rhombohedral (red) form, implying beta cannot be stable at low temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in conflict with the thermodynamic requirement that entropy vanish at low temperature. Using electronic density functional theory methods and an extensive search of the configuration space we find a unique, energy minimizing pattern of occupied and vacant sites that can be stable at low temperatures but that breaks the beta-rhombohedral symmetry. Even lower energies occur within larger unit cells. Alternative configurations lie nearby in energy, allowing the entropy of partial occupancy to stabilize the beta-rhombohedral structure through a phase transition at moderate temperature.Comment: 12 pages, 5 figure

The present study reinvestigates the Al-Ce and Al-Nd phase diagrams and reoptimizes their thermodynamics using the CALPHAD method. First-principles energy calculations play an important role in terms of sublattice formalism and phase-stability prediction, demonstrating that they should be effectively integrated into experimental investigations and thermodynamic assessments. Specifically, current experimental results and theoretical calculations show that Al 2 Nd (or Al 2 Ce) should be treated as a stoichiometric compound phase rather than as the solution phase that was proposed in previous studies. Further, a new compound, AlCe 2 , is found stable at high temperatures (648 °C to 775 °C) in the Al-Ce system. It forms through a peritectic reaction of liquid and AlCe phases at 775 °C, and decomposes into AlCe and ␤AlCe 3 at 648 °C and below. Since the AlCe 2 phase is not retained at room temperature by quenching experiments, it is suggested that AlCe 2 may be isostructural with the previously known compound AlNd 2 (oP12). Based on current differential thermal analysis (DTA) measurements and theoretical calculations, it is also proposed that there is an ␣/␤Al 3 Ce polymorphous transition occurring at 973 °C in the Al-Ce system and an ␣/␤Al 3 Nd polymorphous transition occurring at 888 °C in the Al-Nd system. The ␤Al 3 RE phase may be isostructural with ␤Al 3 Y (hP12). Finally, the previously described ␤Al 11 RE 3 phase (rare earth elements (RE) ϭ La, Ce, Nd, or Pr) is proposed to have a stoichiometry of Al 4 RE (tI10), based on direct evidence from differential scanning calorimetry (DSC) measurements.

It is proposed that quasicrystal structure determination should include the calculation of cohesive energies using realistic potentials. A class of atomic decoration models for i-AlMn is then presented, adopting the ''canonical-cell'' tiling geometry, with ''Mackay icosahedron'' clusters placed on all its nodes. The remaining atomic positions are based, as far as possible, on the known structure of ␣-AlMnSi. These models guarantee good local packing of the atoms, whose displacements away from ''ideal'' positions are specified by only a moderate number of parameters. Certain atomic sites are uncertain as regards their occupancy and/or chemistry; variations of the decoration rules on these sites must be compared, in order to discover the correct one. Our models are well adapted to be relaxed under an effective Hamiltonian to optimize the cohesive energy; we show how the energies found in such relaxations can be used to extract an effective tile-tile Hamiltonian, as would be needed for future studies of phason elasticity and the development of long-range order. In addition, we clarify concepts needed for decoration models in general ͑in particular, the ways in which elaborate, more realistic decorations may be evolved from simpler ones͒. We also show that these decoration models are closely related, but not identical, to quasiperiodic structures defined using six-dimensional formalism.

No abstract

We calculate the cohesive energies of Fe-based glass-forming alloys in the B-Fe-Y-Zr quaternary system. Our ab-initio calculations fully relax atomic positions and lattice parameters yielding enthalpies of mixing at T=0K. We examine both the known equilibrium and metastable phases as well as a selection of plausible structures drawn from related alloy systems. This method, generally reproduces experimentally determined phase diagrams while providing additional information about energetics of metastable and unstable structures. In particular we can identify crystalline structures whose formation competes with the metallic glass. In some cases we identify previously unknown structures or observe possible errors in the experimental phase diagrams.