Interstitial species

Leute and Stratmann [1237] have shown that the double conversion between CdTe and HgSe is strongly influenced by intrinsic doping. The pathway for reaction is identified as the movement of interstitial species,... 

To make contact with atomic theories of the binding of interstitial hydrogen in silicon, and to extrapolate the solubility to lower temperatures, some thermodynamic analysis of these data is needed a convenient procedure is that of Johnson, etal. (1986). As we have seen in Section II. l,Eqs. (2) et seq., the equilibrium concentration of any interstitial species is determined by the concentration of possible sites for this species, the vibrational partition function for each occupied site, and the difference between the chemical potential p, of the hydrogen and the ground state energy E0 on this type of site. In equilibrium with external H2 gas, /x is accurately known from thermochemical tables for the latter. A convenient source is the... 

The difference between interstitial species and interpolated species is one of scale. Interstitial sites are thought of as normally unoccupied positions in relatively closely packed crystal structures. One tends to speak of interpolation when foreign atoms enter larger normally unoccupied volumes, cages, or tunnels in a structure, which otherwise remains topotactically unchanged. 

Alefeld and co-workers (24, 25) have discussed the hydrogen-hydrogen attractive interaction by using the elasticity theory developed for defects in solids by Eshelby and others (46). The strength of the elastic dipole moment is related to the volume expansion resulting from the interstitial hydrogen (25) (Equation 10), where P is the strength of the elastic dipole caused by the interstitial species... 

Assume that the interstitial species is initially uniformly distributed and that an edge dislocation is suddenly introduced into the crystal. 

The preceding analysis provides a powerful method for determining the diffusivities of species that produce an anelastic relaxation, such as the split-dumbbell interstitial point defects. A torsional pendulum can be used to find the frequency, u>p, corresponding to the Debye peak. The relaxation time is then calculated using the relation r = 1/ojp, and the diffusivity is obtained from the known relationships among the relaxation time, the jump frequency, and the diffusivity. For the split-dumbbell interstitials, the relaxation time is related to the jump frequency by Eq. 8.63, and the expression for the diffusivity (i.e., D = ra2/12), is derived in Exercise 8.6. Therefore, D = a2/18r. This method has been used to determine the diffusivities of a wide variety of interstitial species, particularly at low temperatures, where the jump frequency is low but still measurable through use of a torsion pendulum. A particularly important example is the determination of the diffusivity of C in b.c.c. Fe, which is taken up in Exercise 8.22. 

An important question concerning these compounds is, What factors govern the ratio of carbon to interstitial species in these compounds . No simple answer to this is at present available. 

As illustrated in the previous section, the metal-rich rare earth metal halides and their interstitial derivatives provide a vast collection of compounds that transcends the structural chemistry of both molecules and extended solids. On the one hand, these substances can be considered as connected or condensed clusters of the MgXi2-or MgXg-type, which may contain interstitial species. On the other hand, many of them can be derived from the structures of simple salts, e.g. NaCl or La20jS. 

For the rare earth metal halides and their interstitial derivatives, a simple ionic model related to the aforementioned electron counting rules has been successful to rationalize a number of structural and physical observations. This model, which has been repeatedly used in the preceding section, assigns to each halide an oxidation state of — 1, and to the highly electropositive rare earth metal, usually its maximum oxidation state, which in most cases is trivalent. If interstitial species occurs, these accept any excess electrons to the extent of becoming closed shell ions. Any additional electrons will then enter the metal-centered band. The following examples will address the validity and the limitations of such a treatment. 

The most frequently encountered interstitial species are the second period main group elements C and N. From the main group atoms in the periodic table, B and Si have also been reported to occupy interstitial sites in the reduced rare earth halides. Their valence atomic orbitals, s, p,, p and p, transform as a g + ti in an octahedral field (Bursten et al. 1980). In addition to the ajg orbital, the metal-metal bonding levels of the clusters also contain a t u orbital which is well suited to overlap strongly with the orbitals on the interstitial. Figure 41 illustrates the molecular orbital diagram... 

At this point, we note that except for H in Nb InH (Simon et al. 1967) and CsNbgli j H (Imoto and Corbett 1980), no other kind of interstitial species has been observed at the center of the metal octahedron in MgXg clusters. Possible explanations include the restrictive size of the interstitial site as well as X Z repulsions through the faces of the octahedron. In any case, since no examples exist in the rare earth halide family and no detailed theoretical treatment has been undertaken, we shall not discuss this specific example further. 

Earlier, we questioned how to partition the charge between the octahedral cluster and the interstitial species, especially for those like B, Si or Fe. With the C2 units, a chemical and structural check exists to monitor the extent of charge transfer, as well as the number of electrons that remain in cluster valence levels, i.e. electrons that contribute to metal-metal bonding. In fact, a simple ionic treatment in conjunction with the qualitative molecular orbital scheme for the C2 dimer can reasonably predict the expected C-C distance. For the rare earth elements, these donate as many of their valence electrons as the nonmetallic species can accommodate. For... 

Students often interpret molecules as the parb des describe by any chemical formula. Molecules consist of discrete (well-defined) units and consequently exist only for covalent species, not for ionic or interstitial species. 

The mechanisms of nitriding and carburizing involve the transfer of the diffusing species to the surface, the establishment of a diffusing species activity gradient which drives the diffusion process, and the diffusion for itself, may be accompanied by the formation of nitrides or carbides (on the surface or in the core). The diffusion of interstitial species into a metal can only proceed if it exists a chemical potential (or activity) gradient of those species between the surface and the core of the material. 

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