The structures of the polar surfaces of ZnO are studied using ab initio calculations and surface x-ray diffraction. The experimental and theoretical relaxations are in good agreement. The polar surfaces are shown to be very stable; the cleavage energy for the (0001)-Zn and ͑0001 ͒-O surfaces is 4.0 J͞m 2 comparable to 2.32 J͞m 2 for the most stable nonpolar (1010) surface. The surfaces are stabilized by an electronic mechanism involving the transfer of 0.17 electrons between them. This leads to 2D metallic surface states, which has implications for the use of the material in gas sensing and catalytic applications. DOI: 10.1103/PhysRevLett.86.3811 PACS numbers: 68.03.Cd, 68.35.Bs, 73.20.At The ionic model has provided the basis for our understanding of the very wide range of physical phenomena displayed by "ionic" crystals [1][2][3][4]. The model underpins our understanding of, for instance; cohesive properties, complex dielectric and optical response, and novel magnetic and electronic behavior including giant magnetoresistance and superconductivity [2]. One of the interesting consequences of the ionic model is that certain "polar" surfaces of ionic crystals will have a surface energy that diverges with sample size due to the generation of a macroscopic electrostatic field across the crystal. A definitive description of this behavior and the classification scheme which is now widely used were given by Tasker in 1979 [5]. Remarkably, a large number of naturally occurring materials have morphologies which display polar surfaces. In recent years a variety of stabilizing mechanisms have been demonstrated to operate at particular surfaces which typically involve the quenching of the macroscopic field either through the reconstruction of the surface, or the presence of adsorbates on the surface [3]. However, in some cases it appears that clean, unreconstructed surfaces are stable, at variance with Tasker's conclusions. A notable example is zincite (ZnO). A possible mechanism for the stability of these systems is a rearrangement of the electronic structure resulting in an effective charge transfer between the polar surfaces removing the macroscopic field which would otherwise be present. To date, no first principles investigation of such a phenomenon has been performed, although semiempirical calculations on SrTiO 3 indicate that such a mechanism might be operating [6,7]. Recently, similar effects have also been observed for thin film ionic materials grown on metallic substrates such as NaCl(111) on aluminum [8].ZnO crystallizes in the Wurtzite structure which does not have a center of inversion. Consequently, when the crystal is cleaved normal to the c axis in a manner which breaks the fewest interatomic bonds, two different polar surfaces are formed on opposite sides of the crystal, each having only one type of ion in its outermost plane. Thus, such a system may be considered to be a "slab" of material with the Zn cation outermost for the (0001)-Zn surface and the O anion outermost on the ͑0001͒-O surface. In orde...

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The structure of the Al70Pd21Mn9 surface has been investigated using high resolution scanning tunnelling microscopy (STM). From two large five-fold terraces on the surface in a short decorated Fibonacci sequence, atomically resolved surface images have been obtained. One of these terraces carries a rare local configuration in a form of a ring. The location of the corresponding sequence of terminations in the bulk model M of icosahedral i -AlPdMn based on the three-dimensional tiling T * (2F ) of an F-phase has been estimated using this ring configuration and the requirement from the LEED work of Gierer et al. that the average atomic density of the terminations is 0.136 atoms per A 2 . A termination contains two atomic plane layers separated by a vertical distance of 0.48Å. The position of the bulk terminations is fixed within the layers of Bergman polytopes in the model M: they are 4.08Å in the direction of the bulk from a surface of the most dense Bergman layers. From the coding windows of the top planes in terminations in M we conclude that a Penrose (P1) tiling is possible on almost all five-fold terraces. The shortest edge of the tiling P1, is either 4.8Å or 7.8Å. The experimentally derived tiling of the surface with the ring configuration has an edge-length of 8.0 ± 0.3Å and hence matches the minimal edge-length expected from the model.

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