Periodic-zone scheme

Since states on opposite faces of the zone are entirely equivalent, one may repeat the bands and the Fermi surface by constructing identical zones around every lattice wave number, as shown in Fig. 16-7. In this representation, called the periodic-zone scheme, the second-band Fermi surface is seen to consist (again, for the simple cubic structure) of three closed lens-shaped segments. The advantage of this representation is that all discontinuous jumps in wavenumber have been eliminated the wave numbers connected by diffractions have been plotted... 

The rounding off of the Fermi surface in the periodic-zone scheme also corresponds to a distortion of the free-electron sphere in the extended-zone scheme. That distortion, calculated for aluminum, is shown in F ig. 16-9. It has the effect of reducing the total area of free surface and, as we shall sec, in the case of covalent solids the same effect eliminates the entire surface. 

The secDnd-band Fermi surface from Fig. 16-6 displayed in the periodic zone scheme. A Brillouin Zone can be constructed at any point in order to specify the Fermi surface two possibilities are shown as dashed-line and solid-line squares. 

Here uf = u exp(277ig r) is, like w, periodic with the period of the lattice, and k = k - 27rg is a reduced wave vector. Repeating this as necessary, one may reduce k to a vector in the first Brillouin zone. In this reduced zone scheme, each wave function is written as a periodic function multiplied by elkr with k a vector in the first zone the periodic function has to be indexed, say ujk(r), to distinguish different families of wave functions as well as the k value. The index j could correspond to the atomic orbital if a tight-binding scheme is used to describe the crystal wave functions. 

Comparison of profundal diffusion rates with observed increases in the hypolimnion (Table III) indicated that pore-water diffusion calculated from these profiles was probably not an important transport mechanism for Hg in this seepage lake. For the June-July period, pore-water diffusion accounted for only 13% of the hypolimnetic increase. For the July-August interval, pore-water diffusion could account for only 7% of the observed increase. Therefore, we can assume that the buildup in the hypolimnion is more likely a result of redissolution of recently fallen particulate matter at the sediment surface than of direct pore-water diffusion. Our present sampling scheme (2-cm intervals) precludes evaluation of dissolution in the uppermost sediments and would require much more detail (<1 cm) in the sediment-water interfacial zone. 

FIG. 11.26 Schematic presentation of the polarized structure of the polymer thin Rim. The curve hovi the amplitude of the induced polarization In the film. A stands for the period of the induced grating. The refractive index of the zones polarized Mer upward or downward is the same. Scheme is not to the scale. ... 

In Scheme 3, the alkalinity concentration is plotted against pH from Lake Horkkajarvi, in southern Finland (61°13 N, 25°10 E). Lake Horkkajarvi is a truly meromictic lake where water column mixing periods, due to homothermal conditions, are absent [26]. hi northern temperate zones, lakes usually circulate twice a year, i.e. in spring and fall, but in a meromictic lake permanent stratification separates the lake into two layers. The stabilising forces in Lake Horkkajarvi are high electrolyte concentration and the sheltered position of the landscape. The lake is 1.1 ha in area with a maximum and mean depth of 13 and 7 m, respectively. It is a humic lake greatly affected by the allochthonous carbon load the water colour in units of mg Pt 11 is >200. 

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