Atomic diffusion mechanism

Field-ion microscopy may be used to study surface diffusion. Enumerate the various atom diffusion mechanisms that have been proposed for clean transition metal surfaces [107, 108]. 

Palladium is an interesting metal because it permits the rapid transport of hydrogen through its lattice stmcture via an atomic diffusion mechanism. Thus, a thin Pd membrane can be used as a selective filter for the separation or purification of hydrogen gas. This technology has potentially important implications for a number of industrial chemical conversion applications. 

It is well known that defects play an important role in determining material properties. Point defects play a major role in all macroscopic material properties that are related to atomic diffusion mechanisms and to electronic properties in semiconductors. Line defects, or dislocations, are unquestionably recognized as the basic elements that lead to plasticity and fracture (Fig. 20.1). Although the study of individual solid-state defects has reached an advanced level, investigations into the collective behavior of defects under nonequilibrium conditions remain in their infancy. Nonetheless, significant progress has been made in dislocation dynamics and plastic instabilities over the past several years, and the importance of nonlinear phenomena has also been assessed in this field. Dislocation structures have been observed experimentally. 

Diffusion in the bulk of a crystal can occur by two mechanisms. The first is interstitial diffusion. Atoms in all crystals have spaces, or interstices, between them, and small atoms dissolved in the crystal can diffuse around by squeezing between atoms, jumping - when they have enough energy - from one interstice to another (Fig. 18.6). Carbon, a small atom, diffuses through steel in this way in fact C, O, N, B and H diffuse interstitially in most crystals. These small atoms diffuse very quickly. This is reflected in their exceptionally small values of Q/RTm, seen in the last column of Table 18.1. 

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

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). 

A possible layered precursor to the layered nanoproduct conversion mechanism is thus proposed. The silver clusters formed at the initial heating stage by the partial decomposition of AgSR serve as nuclei at further reaction stages, and their distribution naturally inherits the layered pattern of the precursor. The following growth is mainly controlled by the atom concentration and atom diffusion path, which are both constrained by the crystal structure of the precursor [9]. 

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

The second dimer-opening mode observed resulted when a surface atom diffused to the site of a surface dimer and bumped a nearby atom into the center of the dimer. This mechanism resulted in atoms which occupied lattice sites, and produced a surface dimer which remained open for the course of the simulation. Because the final atomic positions corresponded to lattice sites, and because a high rate of surface diffusion was required to produce the bump , this mechanism was associated with the high-temperature epitaxial growth mode identified by Gossmann and Feldman. 

At present the iron-based alloys diffusion saturation by nitrogen is widely used in industry for the increase of strength, hardness, corrosion resistance of metal production. Inexhaustible and unrealized potentialities of nitriding are opened when applying it in combination with cold working [1-3], It is connected with one of important factors, which affects diffusion processes and phase formation and determines surface layer structure, mechanical and corrosion properties, like crystal defects and stresses [4, 5], The topical question in this direction is clarification of mechanisms of interstitial atoms diffusion and phase formation in cold worked iron and iron-based alloys under nitriding. 

Other than in polymer matrix composites, the chemical reaction between elements of constituents takes place in different ways. Reaction occurs to form a new compound(s) at the interface region in MMCs, particularly those manufactured by a molten metal infiltration process. Reaction involves transfer of atoms from one or both of the constituents to the reaction site near the interface and these transfer processes are diffusion controlled. Depending on the composite constituents, the atoms of the fiber surface diffuse through the reaction site, (for example, in the boron fiber-titanium matrix system, this causes a significant volume contraction due to void formation in the center of the fiber or at the fiber-compound interface (Blackburn et al., 1966)), or the matrix atoms diffuse through the reaction product. Continued reaction to form a new compound at the interface region is generally harmful to the mechanical properties of composites. 

For detailed examples of exchange mechanisms in atomic diffusion on surfaces, see... 

As a test problem for comparing the various methods described above, we have chosen a heptamer island on the (111) surface of an FCC crystal. Partly, this choice is made because it is relatively easy to visualize the saddle point config-mations and partly because there is great interest in the atomic scale mechanism of island diffusion on surfaces (see for example reference 60). The interaction potential is chosen to be a simple function to make it easy for others to verify and extend om results. The atoms interact via a pairwise additive Morse potential... 

In the case of supported metal particles, experimental studies of particle growth mechanisms can determine the type of ripening. Generally, studies on supported noble metallic catalysts at elevated temperatures (>500°C) indicate atomic diffusion from smaller metal particles across the surface of the support to... 

Figure 4.39 Illustration of (a) vacancy, (b) interstitial, and (c) interchange (exchange) mechanisms in atomic diffusion. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

In a molecular dynamic simulation147 of bulk atomic diffusion by a vacancy mechanism, two atoms may occasionally jump together as a pair. The temperature of the simulation is close to the melting point of the crystal. In FTM studies of single atom and atomic cluster diffusion, the temperature is only about one tenth the melting point of the substrate. All cluster diffusion, except that in the (1 x 1) to (1 x 2) surface reconstruction of Pt and Ir (110) surfaces already discussed in Section 4.1.2(b), are consistent with mechanisms based on jumps of individual atoms.148,149 In fact, jumps of individual atoms in the coupled motion of adatoms in the adjacent channel of the W (112) surface can be directly seen in the FTM if the temperature of the tip is raised to near 270 K.150... 

Although the HRTEM movies provide important information about the atomic-scale surface dynamics, they capture only the result of the atomic diffusion events and not directly the individual atomic displacements. To understand the origin of the transport mechanisms, the observations have been complemented with results based on DFT calculations. The calculations show that step edges facilitate methane dissociation and that carbon atoms bind more strongly to step edges than... 

Assess the impact of hydrogen atoms diffusing upstream and being lost at the burner surface. Introduce into the reaction mechanism a pseudoreaction H + H H2 with a rate constant that is very high (close to collision frequency) at room temperature but drops off rapidly with increasing temperature. Compare again species and temperature profiles. 

In many cases, changes in one extensive quantity are coupled to changes in others. This occurs in the important case of substitutional components in a crystal devoid of sources or sinks for atoms, such as dislocations, as explained in Section 11.1. Here the components are constrained to lie on a fixed network of sites (i.e., the crystal structure), where each site is always occupied by one of the components of the system. Whenever one component leaves a site, it must be replaced. This is called a network constraint [1]. For example, in the case of substitutional diffusion by a vacancy-atom exchange mechanism (discussed in Section 8.1.2), the vacancies are one of the components of the system every time a vacancy leaves a site, it is replaced by an atom. As a result of this replacement constraint, the fluxes of components are not independent of one another. 

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 driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

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