Rippled reconstruction

The (100) surface of a TMC is a neutral surface composed of equal numbers of metal and carbon atoms (Fig. 1). All the TMC(IOO) clean surfaces prepared in ultrahigh vacuum conditions show (1 X 1) low-energy electron diffraction (LEED) patterns, and no lateral reconstruction has been found. However, LEED I-V analysis studies of the TaC(lOO) (3,4) and HfC(lOO) (3) surfaces have revealed that rippled reconstructions are brought about on these surfaces. The rippled reconstruction includes displacements of surface atoms vertical to the surface the metal atoms and carbon atoms are uniformly displaced inward and outward, respec-... 

As already pointed out by Jauch [30], the series appearing in the exponential factor that modulates m (x) in (6) has a finite number of terms, and can therefore give rise to series termination artefacts. In particular, although the exponentiation will ensure positivity of the resulting density, series termination ripples will be present in the reconstructed map whenever the spectrum of the modulation required by the observations extends significantly past the resolution of the series appearing in the exponential. This in turn will depend both on the true density whose Fourier coefficients are being fitted, and on the choice for the prior prejudice. 

Due to termination of the series, however, p(r) is severely affected by ripples. In addition, especially in the case of non-centrosymmetric crystals, the phase of vector F(S) is not known with precision and this affects a correct reconstruction of the density. Therefore, Fourier summation cannot be used for precise and accurate mapping of electron density. On the other hand, a model is necessary to overcome these limitations and to produce a function that is sufficiently close to the real, quantum mechanical />(r) in all regions of the crystal. 

Non-perfect reconstruction The passband ripple which is typical for QMF filter designs can lead to time domain artifacts which can be audible even if they are at very low amplitudes. 

It seems that the described scenario is complete in the sense that the surface has no other possibiUties to react on the truncation of bonds. Yet, this is only true for elemental surfaces. In compounds, there are additional degrees of freedom for the structural change off bulk termination. So, when for appropriate surface orientations the unit cell of surface-parallel layers contains more than one chemical species, there can be intraunit cell relaxations without changing the lateral translational symmetry of the surface (in some literature, in particular on semiconductor surfaces, such cases are included in the group of surface reconstructions). As an example. Figure 4.3a displays the termination with such a chemically mixed layer for an ordered ahoy, whereby the sublayer of one chemical species relaxes vertically and differently than that of the other species causing surface rippling. When surface-parallel layers are - for a different... 

D. A. Chester and S.J. Riederer, Ripple Suppression During Reconstruction in Transverse Tomography, Phys. Med. Biol., 20, (1975) 632-636. 

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