Atomic defects in the ordered compound<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mn>2</mml:mn><mml:mn/></mml:math>-NiAl: A combination of<b><i>ab initio</i></b>electron theory and statistical mechanics

Abstract

For an ideal model of a homogeneous thermodynamically stable ordered compound $B2\ensuremath{-}{\mathrm{Ni}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ the effective formation energies and volumes of vacancies and antistructure atoms as well as the Ni and Al activities are calculated by a combination of the ab initio electron theory with a generalized grand canonical statistical approach. For nonstoichiometric compounds the structural defects are Ni vacancies (for $x&lt;0.5)$ or Ni antistructure atoms on the Al sublattice (for $x&gt;0.5).$ At stoichiometry $(x=0.5)$ the calculated effective Ni vacancy formation energy agrees quite well with experimental data. For $x&lt;0.5$ the theory predicts a shrinkage of the sample with increasing temperature (superimposed to the usual anharmonic lattice expansion) due to thermal annihilations of structural Ni vacancies, in contrast to the experimental observation. The reason for this discrepancy is probably deviations of the structure of real $B2\ensuremath{-}{\mathrm{Ni}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ from the ideal model.