document: The first-principles calculations are performed using the Cambridge Serial Total Energy Package (CASTEP) [21] which implements the plane-wave pseudopotential DFT method. The exchange correlation functional is approximated using the generalized gradient approximation (PBE-GGA) [22], and the electron–ion interactions are described by Vanderbilt-type ultrasoft pseudopotentials [23]. The plane wave basis set is truncated at a cutoff of 400eV, and the Brillouin-zone sampling was performed using the Monkhorst-Pack scheme with a k-point spacing in reciprocal space of 0.04Å−1. Tests show that these computational parameters give results that are sufficiently accurate for present purposes. The ferromagnetism of nickel is accounted for by performing all calculations using spin polarization, starting at a ferromagnetic initial configuration and relaxing towards its ground state. However, for all compositions considered, the ground state electronic structure of each alloy is found to exhibit only very weak ferromagnetism, and the effect is not thought to influence their phase stability. Table 1 shows the calculated equilibrium lattice constants of the η phase at various Ti concentrations, using partially ordered ηP structures. The change in lattice constant upon Ti alloying is relatively small, but can be related to the ∼10% larger covalent radius of Ti. The calculated lattice constants are in good agreement with the experimental values, which relate to an alloy with a Al/Ti ratio of ∼2.75.
doc_bio_tags: O O O O O O O B I I I I B O O O O O O O O O B I I O O O O B I I O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O
extractive_keyphrases: alloy cambridge serial total energy package castep electron–ion interactions exchange correlation functional ferromagnetism generalized gradient approximation nickel plane wave spin polarization ti ηp structures
abstractive_keyphrases: al brillouin-zone sampling electron first-principles calculations ion k-point spacing monkhorst-pack scheme pbe-gga plane-wave pseudopotential dft method ti alloying vanderbilt-type ultrasoft pseudopotentials