Rumpling

The last term is the short-range repulsion. The two first ones give the covalent energy. For resonance integrals varying as 1// , the equihbrium bond length is equal to  

This equation proves that atoms of lower coordination numbers tend to come closer to their first neighbours and that the bond length decreases as Z2 decreases, at constant Z. In MgO(lOO) with m = 2 and n = 5.655, it predicts, for example, an 8.6% bond contraction between an upper edge atom (Zi =4) and a terrace atom (Z2 = 5). The model apphes as well to relaxation effects on planar surfaces. It predicts a 2.8% relaxation of MgO(lOO) terraces (Zi = 5, Z2 = 6), in agreement with most numerical calculations. 

These models of relaxation suggest that a bond-length contraction should also occur around bulk and surface vacancies. However, they have to be modified to account for the charge redistributions which take place around such defects. 

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M, Selim. O, Tetu. M Selim, and P. Rumpl. Bull. Soc. Chim. hranct. 11. 3404... 

FIG. 4 Distorted graphite surface generated according to the rumpled graphite model. (From Ref. 100.)... 

Runkel, /., -riibe, /. beet, beetroot, -rliben-melasse, /. beet(root) molasses, -riiben-zucker, m. beet sugar, beetroot sugar. Runzel, /. wrinkle fold, crease, rumple, bil-dung, /. wrinkling, creasing. 

Zerknallstoss, m. shock of explosion, zerknicken, v.t. crack (esp. by bending), zerknistem, v.i. decrepitate, zerknittem, zerknuUen, v.t. crumple, rumple corrugate. 

He entered, thrusting the door to behind him, and took me in his arms, my smock rumpling under his eager hands, his breath hot on my face. One big hand in the small of my back, one fumbling with his points, and his mouth greedy upon mine. 

ML an ordered c(2 x 2) phase is formed in which the atoms occupy alternate four-fold coordinated hollow sites in the surface (Figure 1.3). This means that in the second substrate layer half of the Ni atoms have an oxygen atom directly above them while the other half have no such near-neighbour. This leads to a rumpling of the second Ni layer, with the Ni atoms below the adsorbates being 0.035 A lower than those that are not covered in this way. This effect is marginal but detectable... 

First, the (0112) face contains an array of equivalent Cr3+ ions in fivefold (square pyramidal) coordination separated by 0.365 nm (corresponding to 6.8 Cr ions/100 A2). The plane defined by the the four oxygen ions surrounding each Cr3+ ion does not coincide with the surface plane, indicating that not only is the surface slightly rumpled but also the direction, where the electric field associated with positive charge is maximized, is not perpendicular to the surface plane. HRTEM images show that these faces are the predominant ones. 

Welton-Cook, M. R., and W. Berndt (1982). A LEED study of the MgO (100) surface identification of a finite rumple. J. Phys. C Solid State Phys. 15, 5691-710. 

For the relaxed surface, the interlayer spacing is hardly changed from the 100 bulk values. However, small surface rumpling does occur on slab optimization in which, for MgO at least, ions move to positions further from the slab center than the Mg ions. This can be quantified by calculahng the dimensionless quanhty ... 

In Pacchioni s calculations it was found that the occupied bonding Ti—O hybridized orbitals tend to form bonds that are stronger between the surface tri-layer and the first sub-surface one than are found between tri-layers in the bulk. For the even slabs this leads to a tendency to form a set of paired tri-layers, which give rise to the observed rumpling, whereas for odd slabs a more regular spacing of the tri-layers in the slab center is achieved. 

The surface relaxation on both SrTiOs (001) terminations has been calculated by various numerical approaches [45,189-193]. The surface rumpling is usually reasonably accounted for, but all calculations predict an inward relaxation for the Ti02 termination, in contradiction to experiments [194-196]. A particular attention has been focused on the energy of surface states, since the first study based on non-self-consistent calculations predicted that they were located deep in the gap [197,198]. All subsequent self-consistent calculations have contradicted this prediction [191,192,199,200], in agreement with photoemission and EELS results [201,202]. When calculated [191,192], the surface energy is rather low, an indication that no surface instability takes place, and there is no evidence of anomalous filling of electronic states. 

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