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]

͑1 ϫ 1͒ and ͑2 ϫ 1͒ reconstructions of the (001) SrTiO 3 surface were studied using the first-principles fullpotential linear muffin-tin orbital method. Surface energies were calculated as a function of TiO 2 chemical potential, oxygen partial pressure and temperature. The ͑1 ϫ 1͒ unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the ͑2 ϫ 1͒ Ti 2 O 3 reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the ͑1 ϫ 1͒ surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the ͑2 ϫ 1͒ reconstructions would be easier to image than the ͑1 ϫ 1͒ surfaces. The possibility that the presence of oxygen vacancies would destabilise the ͑1 ϫ 1͒ surfaces was also investigated. If the ͑1 ϫ 1͒ surfaces are unstable then there exists the further possibility that the ͑2 ϫ 1͒ DL-TiO 2 reconstruction [Natasha Erdman et al. Nature (London) 419, 55 (2002)] is stable in a TiO 2-rich environment and for p O 2 Ͼ 10 −18 atm.

First principles calculations of the Σ5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the rôle of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.

Embrittlement by the segregation of impurity elements to grain boundaries is one of a small number of phenomena that can lead to metallurgical failure by fast fracture. Here we settle a question that has been debated for over a hundred years: how can minute traces of bismuth in copper cause this ductile metal to fail in a brittle manner? Three hypotheses for Bi embrittlement of Cu exist: two assign an electronic effect to either a strengthening or weakening of bonds, the third postulates a simple atomic size effect. Here we report first principles quantum mechanical calculations that allow us to reject the electronic hypotheses, while supporting a size effect. We show that upon segregation to the grain boundary, the large Bi atoms weaken the interatomic bonding by pushing apart the Cu atoms at the interface. The resolution of the mechanism underlying grain boundary weakening should be relevant for all cases of embrittlement by oversize impurities.

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