Interstitial-Substitutional Mechanism

Many impurities have both an interstitial solubility, M, and a substitutional solubility, N. These interstitial impurity atoms and substitutional impurity atoms can diffuse independently or interdependently. Usually, is larger than M, but substitutional diffusion is much slower than interstitial diffusion. In Si, these two components of diffusion appear to move interdependently. They are related by a 

The movement of impurities becomes primarily controlled by the rate of this dissociation. 

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The kinds of substitution mechanisms that may be relevant to super-low concentration elements such as Pa involve intrinsic defects, such as lattice vacancies or interstitials. Vacancy defects can potentially provide a low energy mechanism for heterovalent cation substitution, in that they remove or minimise the need for additional charge balancing substitutions. Formation of a vacancy per se is energetically unfavourable (e.g., Purton et al. 1997), and the trace element must rely instead on the thermal defect concentration in the mineral of interest, at the conditions of interest. Extended defects, such as dislocations or grain boundaries, may also play a key role, but as these are essentially non-equilibrium features, they will not be considered further here. 

Another system obeying Fick s law is one involving the diffusion of small interstitial solute atoms (component 1) among the interstices of a host crystal in the presence of an interstitial-atom concentration gradient. The large solvent atoms (component 2) essentially remain in their substitutional sites and diffuse much more slowly than do the highly mobile solute atoms, which diffuse by the interstitial diffusion mechanism (described in Section 8.1.4). The solvent atoms may therefore be considered to be immobile. The system is isothermal, the diffusion is not network constrained, and a local C-frame coordinate system can be employed as in Section 3.1.3. Equation 2.21 then reduces to... 

The structure of the solid solutions is very complex. Investigations have shown that partial (and only partial) occupancies of up to five interstitial atomic positions occur. These atomic positions are situated between the icosahedra of the stmcture. In a few cases a substitutional mechanism for the solid solubility has been demonstrated, similar to the silicon... 

A variety of other y-type phases with high Li+ conductivity are derived from the Li3X04 phases with X = P, As, or V. The substitution mechanisms are of the type X (Si, Ge, Ti) - - Li, and lead to the creation of interstitial Li+ ions which are responsible for the high ionic conductivity. The highest conductivity at room temperature, 4 x 10 S cm , is found in the series Li3+j (Gej Vi j )04. Neutron diffraction has been nsed to locate the interstitial lithium ions, to determine their site occnpancy, and correlate the high ionic conductivity with the connectivity of the interstitial sites ... 

The diffusion of dopants in semiconductors has been briefly discussed in Sect. 2.1.3. At an atomic scale, the diffusion of a FA in a crystal lattice can take place by different mechanisms, the most common being the vacancy and interstitial mechanisms in silicon and germanium (see for instance [25]). The interstitial/substitutional or kick-out mechanism, which is an interstitial mechanism combined with the ejection of a lattice atom (self-interstitial) and its replacement by the dopant atom is also encountered for some atoms like Pt in silicon. 

Silver ion vacancies move by a simple replacement mechanism in which a lattice silver ion at a nearest neighbor or 110 position (here the braces are used to represent a set of equivalent lattice positions) moves first into an interstitial position and then into the vacancy. Replacement by direct motion along a [110] direction is thought to be a higher energy process [18]. Monovalent impurities like Au+ and Cu+ diffuse like silver ions [18]. Na + and K + diffuse by a vacancy substitution mechanism in which the ion moves into a nearest neighbor vacancy position. Divalent cation impurities diffuse by exchange with an associated vacancy. Trivalent cations require a second vacancy for electrical neutrality. Their diffusion involves the concerted motion of this neutral complex [18]. Finally anions and anion impurities... 

Atomic diffusion in solids is of increased interest since the phenomenal growth in VLSI (very large-scale integration) of transistors on the silicon chip. An interstitial or substitutional mechanism of diffusion is said to occur when atoms occupy specific sites in a lattice. In an interstitial mechanism of diffusion, impurity jumps from one interstitial site to the next. In the substitutional mechanism of diffusion, impurity jumps from one lattice site to the neighboring vacant lattice site. Since the... 

The diffusion of implanted Zn was studied, at 625 to 850C, by means of secondary ion mass spectrometry. A substitutional-interstitial diffusion mechanism was suggested to explain how deviations of the local Ga interstitial concentration from its equilibrium value regulated Zn diffusion. The Ga interstitial diffusion coefficient was described by ... 

The Au was found to diffuse via a complex mechanism involving a vacancy-controlled interstitial-substitutional equilibrium. This led to very complex diffusion concentration profiles. The experimental data on the self-diffusion coefficient of Si was described by ... 

They interpreted the marked effect of the simultaneous addition of carbon and La on the creep life due to the I-S (interstitial-substitutional) interaction, which forms clusters by chemical affinity around dislocations (Monma and Suto 1966). That is, carbon and La (which has a large atomic radius) form clusters with a large apparent size of the solute atmosphere around dislocations, which markedly decrease the moving velocity of dislocations by anchoring them to the atmosphere. Dislocations can move, however, by a process in which the solute atoms migrate with dislocations, and this will be controlled by the diffusion rate of the solute. The diffusion rate of La atoms is considered to be small, especially when they form clusters by the I-S interaction. Further detailed research is required on this diffusion controlled mechanism. 

Chemical erosion can be suppressed by doping with substitutional elements such as boron. This is demonstrated in Fig. 14 [47] which shows data for undoped pyrolitic graphite and several grades of boron doped graphite. The mechanism responsible for this suppression may include the reduced chemical activity of the boronized material, as demonstrated by the increased oxidation resistance of B doped carbons [48] or the suppressed diffusion caused by the interstitial trapping at boron sites. 

In some materials, semiconductors in particular, interstitial atoms play a crucial role in diffusion. Thus, Frank and Turnbull (1956) proposed that copper atoms dissolved in germanium are present both substitutionally (together with vacancies) and interstitially, and that the vacancies and interstitial copper atoms diffuse independently. Such diffusion can be very rapid, and this was exploited in preparing the famous micrograph of Figure 3.14 in the preceding chapter. Similarly, it is now recognised that transition metal atoms dissolved in silicon diffuse by a very fast, predominantly interstitial, mechanism (Weber 1988). 

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

Other single-crystal x-ray diffraction studies of transition element dopants in jS-rh boron are based on the results of a refinement of the /3-rh boron structure that establishes the occurrence of four new low-occupancy (3.7, 6.6, 6.8 and 8.5%) B positions in addition to the earlier known ones. The dopant elements studied, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, Nb, Hf and Ta, do not enter B positions in the framework, but they enter the Al, A2, D and E positions. In some cases the doping elements have been studied at several concentrations for each element and for different cooling rates. The percentage occupancies of certain positions are eorrelated with the atomie sizes of the dopants. The bond distances between the polyhedra are shorter than those within the polyhedra. The mechanism of doping for some cases is denoted displacive, rather than interstitial or substitutional, because of competing interactions between the six different partially occupied B positions and dopant atoms. 

Substitutional impurities replace one metal atom with another, while interstitial impurities occupy the spaces between metal atoms. Interstitial impurities create imperfections that play important roles in the properties of metals. For example, small amounts of impurities are deliberately added to iron to improve its mechanical... 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

Figure 5.11 Diffusion mechanisms (a) exchange (e) and ring (r) diffusion (b) kick-out diffusion, leading to (c) a substitutional defect and a self-interstitial.

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