Reduced zone

Extended-zone and reduced-zone representations of band diagram for ID lattice with no external potential. 

Fig. 3.16 The efect of introducing a weak potential into the ID lattice is to lift the degeneracy of the energy levels mar to the edge of the Brillouin zone (shown in both extended-zone and reduced-zone representation).

The most widely used pulping process is the kraft process, as shown in Fig. 6-11, which results in recovery and regeneration of the chemicals. This occurs in the recovery furnace, which operates with both oxidizing and reducing zones. Emissions from such recovery furnaces include particulate matter, very odorous reduced sulfur compounds, and oxides of sulfur. If extensive and expensive control is not exercised over the kraft pulp process, the odors and aerosol emissions will affect a wide area. Odor complaints have been reported over 100 km away from these plants. A properly controlled and operated kraft plant will handle huge amounts of material and produce millions of kilograms of finished products per day, with little or no complaint regarding odor or particulate emissions. 

In addition to effects on the concentration of anions, the redox potential can affect the oxidation state and solubility of the metal ion directly. The most important examples of this are the dissolution of iron and manganese under reducing conditions. The oxidized forms of these elements (Fe(III) and Mn(IV)) form very insoluble oxides and hydroxides, while the reduced forms (Fe(II) and Mn(II)) are orders of magnitude more soluble (in the absence of S( — II)). The oxidation or reduction of the metals, which can occur fairly rapidly at oxic-anoxic interfaces, has an important "domino" effect on the distribution of many other metals in the system due to the importance of iron and manganese oxides in adsorption reactions. In an interesting example of this, it has been suggested that arsenate accumulates in the upper, oxidized layers of some sediments by diffusion of As(III), Fe(II), and Mn(II) from the deeper, reduced zones. In the aerobic zone, the cations are oxidized by oxygen, and precipitate. The solids can then oxidize, as As(III) to As(V), which is subsequently immobilized by sorption onto other Fe or Mn oxyhydroxide particles (Takamatsu et al, 1985). 

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. 

Se is concentrated in certain ore deposits, such as roll-front U complexes and Carlin-type gold deposits. Roll-front U deposits occur where U(Vl)-bearing groundwater migrates into reducing zones which precipitate both U(TV) and Se(0) or Se(-II). It may be possible to constrain Se sources and/or ore-forming processes using Se isotope variations. 

Not all of the remobilized phosphate is reprecipitated below the redox boundary. Some escapes by diffusing upward through the pore waters. Once this phosphate enters the oxic zone, it is readsorbed by Fe(ni)OOH along with any Fe that has similarly diffused upward. The Fe that diffuses downward into the sulfete-reducing zone precipitates sulfide to form pyrite (FeS). 

Patrick WH, Ir, Delaune RD. 1972. Characterization of the oxidized and reduced zones in flooded soils. Soil Science Society of America Proceedings 36 573-576. 

The part of a flame beginning directly at the mouth of the burner is called the first reducing zone (300-520 °C). It is followed by the second zone, of complete combustion (1540-1560 °C). The third, oxidizing zone, is in direct contact with the oxygen of the air ( 1540 °C). The heating of glass should be performed at the boundary between the second and third zones. 

Similar to the microbial biofilm preparations described above, free-floating, viable microbial mats are also successful in removal of metals from solution (Bender Phillips, 1994 Vatcharapi jarn, Graves Bender, 1994). Consisting primarily of algae, cyanobacteria and bacteria, microbial mats perform a number of activities which promote metal complexation and subsequent removal. The mat contains oxidizing and reducing zones that aid in the immobilization and precipitation of... 

Preliminary work (10) on the transition from oxidized surface sediment to reduced subsurface sediment in Milltown Reservoir showed that the redox transition occurs in the upper few tens of centimeters. Strong chemical gradients occur across this boundary. Ferrous iron in sediment pore water (groundwater and vadose water) is commonly below detection in the oxidizing surface zone and increases with depth. Arsenic is also low in pore water of the oxidized zone, but increases across the redox boundary, with As(III) as the dominant oxidation state in the reduced zone. Copper and zinc show the opposite trend, with relatively high concentrations in pore water of the oxidized surface sediment decreasing across the redox boundary. 

Equation (4) holds generally at the face center but is valid over the whole face if the crystal point group contains a reflection plane through the zone center that is parallel to the face. It also holds for all k vectors that terminate on a line in the BZ face that is parallel to a binary axis. The E(k) may be described either by a singlevalued function of k (with k > 0), which is called the extended zone scheme, or by a multivalued function of k within the first BZ, the reduced zone scheme (see Figure 17.2). 

Figure 17.2. E(k) for the 1 -D free electron model in (a) the extended zone scheme and (b) the reduced zone scheme.

Find expressions for, and sketch in the reduced zone scheme, FE energy bands along TH in the reciprocal lattice of the bcc lattice. 

Discussion. Nitrate is seen to decrease at a water depth of 8 m (15 m below the surface), whereas iron is low at this depth and rises beneath. This indicates the existence of an oxidizing zone in the upper 8 m of water and a reducing zone below. The nitrate was reduced by ferrous iron to N2, which was expelled into the atmosphere. The tritium data were most informative ... 

PROBLEM 8.6.1. A fictional simple cubic crystal has a lattice constant a = 4.21 A. Compute the four lowest free-electron energy levels along the wavevector k in the reduced zone scheme at the fc-space point (n/2a, 0, 0). 

Upper reducing zone (e) Hottest portion of flame (b) Lower oxidizing zone (c) Lower reducing zone (f)... 

Heat upon a platinum wire in the reducing zone of the Bunsen flame This will reduce any sulphate present to sulphide (as already indicated in test 3). Upon moistening with dilute hydrochloric acid, the sulphide will be converted into the comparatively volatile chloride, and the usual flame test is applied. The presence of barium or of a mixture of strontium and barium will be indicated. 

When a part of the air is supplied as secondary air entering at the middle of the combustor, resulting in the combination of a reducing zone in the bottom and an oxidizing zone at the top, NOx content in the flue gas would decrease. Emission of NOx can thus be controlled by changing the secondary-to-total air ratio. Figure 21 indicates that when this ratio is raised from 0 to 0.6, NOx emission drops from about 300 ppm to 50 ppm for Datong coal. If a secondary-to-total air ratio of 0.5 is used, the expected NOx emission is about 65 ppm. 

The requirement that — 1 < cos ka< 1 used to determine the allowed bands means that the value for k for each band is not unique in the way implied by the extended band scheme shown in Fig. 4.4(b). Instead, the band structure is more properly represented in a reduced zone scheme with —n/a < k < nja, which corresponds to the first Brillouin zone, as shown in Fig. 4.4(c). 

Also plot the bands along a direction pei - endicular to this (towards a zone corner). Plot them only to the corner [/c = AnK / i (/)]. (The points beyond can be seen to lie along a zone edge in the reduced zone.)... 

Tlie displacement of regions of wave number space so tliat each state is represented by a wave number inside the Brillouin Zone equivalent to its wave number outside. The reduced-zone scheme in part (b) gives the second band Fermi surface in the ordinary band dcseription in the Brillouin Zone. 

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