Cell index truncation

Returning to the problem of the cell index truncation, we can see from equations (1.51) and (1.67) that there are six physical quantities to be properly truncated in this procedure ... 

Fig. 8. Common types of bulk chemical ordering in cubic metals and the corresponding low-index truncated bulk surfaces. The LIq and LIj ordered stractures consist of (001) and (111) oriented planes of equal atoms, respectively, and, hence, do not preserve the cubic symmetry, leading to tetragonal (LIq) or rhomboedric (Llj) distortion. The cell shown for the Llj stmc-ture is not a unit cell the unit cell is twice as long in all three directions.

It can be seen from equation (1.51) that the major difficulties in applying the HF CO method arise when calculating the two-electron integrals whose number is proportional to m for each upper (cell) index triplet (q, qi, q2). The method can be applied reasonably only if the three infinite sums in equations (1.48) and (1.51) can be truncated with a... 

The functions associated with these tableaux according to (10.3.4) provide a 20-dimensional irrep of U(4), the group of transformations that mix the orbitals 0,..., 4. To pass to the subgroup U(3) of transformations that mix only the first three orbitals 2. 3> we simply scratch out the cells containing orbital index 4. The 20 x 20 irrep of U(4) then reduces to a block form in which the blocks provide irreps of U(3), whose basis vectors are labelled by indicating the truncated tableaux that remain. There is an 8x8 block, with index symmetry... 

Figure 2.8 Top and side views of the structures of the low-index bulk-truncated (i.e., unreconstructed) surfaces of the diamond lattice. In each subfigure, the size of the atoms decreases as one moves deeper into the selvedge. The dangling bonds on the surface atoms (in a single unit cell) are also indicated. For the (001) surface, the dehy-bridized p states are also shown on the...

Figure 3.4.2 The amplitude along a crystal truncation rod, assuming the amplitude of a single unit cell to be equal to 1. Bulk Bragg peaks occur for integer values of the diffraction index /. The amplitude at these...

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