Sublattice

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

It is possible to systematically alter the net magnetic moment of ferrites by chemical substitutions. A very important industrial appHcation is the increase of the magnetic moment in mixed MnZn-ferrites and NiZn-ferrites. When Zn ions are introduced in Mn-ferrite or Ni-ferrite, these ions prefer to occupy A-sites. Because is nonmagnetic, the A-sublattice magnetization is reduced and consequendy the total net magnetic moment is increased. 

The saturation magnetization, J), is the (maximum) magnetic moment per unit of volume. It is easily derived from the spia configuration of the sublattices eight ionic moments and, hence, 40 ]1 per unit cell, which corresponds to = 668 mT at 0 K. This was the first experimental evidence for the Gorter model (66). The temperature dependence of J) (Fig. 7) is remarkable the — T curve is much less rounded than the usual BdUouia function (4). This results ia a relatively low J) value at RT (Table 2) and a relatively high (—0.2%/° C) temperature coefficient of J). By means of Mitssbauer spectroscopy, the temperature dependence of the separate sublattice contributions has been determined (68). It appears that the 12k sublattice is responsible for the unusual temperature dependence of the overall J). 

The magnetic moments of the heavy RE elements (Gd, Tb, Dy, etc) are coupled antiparallel to the magnetic moments of the TM elements (Fe, Co, etc). The REj TM alloys are therefore ferrimagnetic below their Curie temperature (T )- The heavy TM moments form one magnetic sublattice and the RE moments the other one. In contrast, the light RE moments (eg, Nd, Pr) couple parallel to the moments of TM. The RE spia is always antiparallel to the TM spia, but for the light RE elements, the orbital momentum is coupled antiparallel to the spia and larger than the spia. 

Fig. 6. Schematic of band gap energy. Eg, for the three types of electronic and ionic conductors. For electronic conductors the comparison is made of the relative occupancy of valence and conduction bands. For ionic conductors, the bands correspond to the relative occupancy of ionic sublattices. For (a),...

The role of cerium in these lighting phosphors is not as the emitting atom but rather as the sensitizer. The initial step in the lighting process is the efficient absorption of the 254 nm emission Ce ", with broad absorption bands in the uv, is very suitable. This absorbed energy is then transferred to the sublattice within the crystalline phosphor eventually the activator ion is fed and emission results. Cerium, as a sensitizer ion, is compatible in crystal lattices with other lanthanide ions, such as Eu and Tb, the usual activator atoms. 

The vacant sites will be distributed among the N lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a conesponding number of vacancies on die N lattice sites. In the case of ionic species, it is necessaty to differentiate between cationic sites and anionic sites, because in any particular substance tire defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, tire random distribution of the n vacancies on the N lattice sites cair be achieved in... 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

Of course, the above discussion apphes only to systems exhibiting domain wall structure, i.e., to weakly inhomogeneous phases formed on surfaces with low corrugation of the gas-solid potential and characterized by the presence of more then one type of equivalent sublattices. When this is not the case, i.e., when the dense incommensurate phase can be considered to be... 

The isomorphous diiodides of Ce, Pr and Gd stand apart from all the other, salt-like, dihalides. These three, like LaH, are notable for their metallic lustre and very high conductivities and are best formulated as (Ln ,2I",e", the electron being in a delocalized conduction band. Besides the dihalides, other reduced species have been obtained such as LnsCln (Ln = Sm, Gd, Ho). They have fluorite-related structures (p. 118) in which the anionic sublattice is partially rearranged to accommodate additional anions. 

It should be emphasized here that usual tracer diffusion experiments in LI2 ordered alloys due to diffusion of majority atoms mainly over their own sublattice do not give any of the strongly desired information about ordering kinetics. The study of order-order relaxations in contrast, yields a selective information Just about those atomic Jump processes which are related to ordering phenomena. 

In the case of Ni-Al the martensitic transformation occurs in a composition range between 62 and 67 at.% Ni where the excess Ni is accommodated randomly on the A1 sublattice. The resulting c/a ratio of the LIq structure is around 0.85, depending on composition. Below 63 at.% Ni the martensite structure has a (52) sequence of close packed planes (Zhdanov notation) which is currently denoted as 14M (formerly as 7R). At higher Ni contents this typical sequence is lost and the martensite plates are simply internally twinned without a specific periodicity. 

We consider an AB alloy which consists of an equal number of A and B sites. For the subsequent analysis, every site is uniquely associated with either an A or a B sublattive. The following is trivially generalised to A iBn alloys. The alloy is not quite stoichiometric, and has the composition A Bj.x, where for the validity of the independent defect approximation we must suppose x to be within a few percent of 0.5. Each site of each sublattice can be occupied by its own atom, an atom of the other kind (an antisite defect) or a vacancy. There are therefore six species for which we define the concentrations on each sublattice ... 

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