We present a sampling method for Brillouin-zone integration in metals which converges exponentially with the number of sampling points, without the loss of precision of normal broadening techniques. The scheme is based on smooth approximants to the 5 and step functions which are constructed to give the exact result when integrating polynomials of a prescribed degree. In applications to the simple-cubic tight-binding band as well as to band structures of simple and transition metals, we demonstrate significant improvement over existing methods. The method promises general applicability in the fields of total-energy calculations and many-body physics.

The microscopic mechanism leading to stabilization of cubic and tetragonal forms of zirconia (ZrO 2 ) is analyzed by means of a self-consistent tight-binding model. Using this model, energies and structures of zirconia containing different vacancy concentrations are calculated, equivalent in concentration to the charge compensating vacancies associated with dissolved yttria (Y 2 O 3 ) in the tetragonal and cubic phase fields (3.2 and 14.4% mol respectively). The model is shown to predict the large relaxations around an oxygen vacancy, and the clustering of vacancies along the 111 directions, in good agreement with experiments and first principles calculations. The vacancies alone are shown to explain the stabilization of cubic zirconia, and the mechanism is analyzed.

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The origin of the relative stability of the cubic, tetragonal, and monoclinic phases of zirconia ͑ZrO 2 ͒ is investigated. To obtain accurate energies we adopt a new all-electron bandstructure approach within the local density approximation, based on muffin tin orbitals. We also develop a self-consistent tightbinding model with which to study the energies for different structures. The tight-binding model enables us to analyze ab initio and experimental phase stabilities in terms of ionic versus covalent effects, including polarization of the anions, and promises to be useful for rapid simulation of more complex systems. [S0031-9007(98)07811-9]