Diffusion in Amorphous Metals

Extensive measurements show that self-diffusivities in the relaxed glassy state are time independent and closely exhibit Arrhenius behavior (i.e., In Z), vs. 1/T plots appear as essentially straight lines) [8-11]. The diffusion therefore is thermally activated (in contrast to self-diffusion in the liquid above Tg as described in Section 10.1). 

The mechanism by which the self-diffusion in the relaxed state occurs is not firmly established at present. However, there are reasons to believe that for certain atoms in glassy systems, self-diffusion occurs by a direct collective mechanism and is not aided by point defects in thermal equilibrium as in the vacancy mechanism for self-diffusion in crystals (Section 8.2.1).2 These reasons include  

2The ring mechanism in Section 8.1.1 is an example of a direct mechanism. 

Further discussion of self-diffusion in relaxed metallic glasses and other disordered systems may be found in key articles [7, 10, 14, 18, 19]. 

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W. Frank, U. Hamlescher, H. Kronmuller, P. Scharwaechter, and T. Schuler. Diffusion in amorphous metallic alloys—Experiments, molecular-dynamics simulations, interpretation. Phys. Scripta, T66 201-206, 1996. 

This model has been applied by Richter and Springer [32] for H diffusion in Nb doped with nitrogen impurities, by Hempelmann [33] for H diffusion in some intermetallic compounds and by Richter et al. [34] for H diffusion in amorphous metals. 

H. Mehrer and G. Rummel. Amorphous metallic alloys—diffusional aspects. In H. Jain and D. Gupta, editors, Diffusion in Amorphous Materials, pages 163-176, Warrendale, PA, 1994. The Minerals, Metals and Materials Society. 

SSAR is observed when the binary diffusion couples listed in Table 2.4 are heated to an appropriate reaction temperature, TR. Examples of typical values of JR are given in Table 2.4. It is well known that amorphous metallic alloys tend to crystallize in laboratory timescales upon heating to temperatures close to their glass-transition temperature, T% [2.16]. For a typical practical timescale (e.g., minutes), one can define crystallization temperature as the temperature at which a significant fraction of an amorphous sample undergoes crystallization in the specified time. The time required for an amorphous phase to crystallize can be identified with t 2 of Fig. 2.6 (see discussion in Sect 2.1.3). In the low temperature regime (well below Tg), atomic diffusion in amorphous alloys is... 

Self-diffusion in amorphous Fe35Co5oBi5 and FeegCo Bis alloys was investigated using radioactive Fe and Co tracer atoms by [1994Pav]. It was found that the diffusivity of Fe equals to that of Co and it is independent of mutual concentration of the transition metal in alloys. The mean activation enthalpy was calculated. 

Diffusion coefficients in amorphous solids such as oxide glasses and glasslike amorphous metals can be measured using any of the methods applicable to crystals. In this way it is possible to obtain the diffusion coefficients of, say, alkah and alkaline earth metals in silicate glasses or the diffusion of metal impurities in amorphous alloys. Unlike diffusion in crystals, diffusion coefficients in amorphous solids tend to alter over time, due to relaxation of the amorphous state at the temperature of the diffusion experiment. 

Catalysis by sol gel doped silica-based materials has become in the last 20 years a prominent tool to synthesize a vast number of useful molecules both in the laboratory and in industrial plants.12 The underlying basic concept of all sol-gel applications is unique one or more host molecules are entrapped by a sol-gel process within the cages of an amorphous metal oxide where they are accessible to diffusible reactants through the inner pore network, which leads to chemical interactions and reactions (Figure 5.3). 

R. Kirchheim, Solubility, diffusivity and trapping of hydrogen in dilute alloys, deformed and amorphous metals-II, Acta Metallurgica, 30(6) (1982) 1069-1078. 

Furthermore, recent radiotracer experiments have shown that metals such as Cu, Ag, and Au can diffuse into various polymers including polyimides and polycarbonates at elevated temperatures. Arrhenius type temperature dependences are not always found. This is not unexpected considering the distribution of saddle-point energies in amorphous polymers [F. Faupel, R. Willecke (1994)]. 

Figure 10.6 Tracer diffusivities in glassy NisoZrso of various solute atoms as a function of their size (as measured by their metallic radii) [25]. Reprinted, by permission, from H. Hahn and R.S. Averback, "Dependence of tracer diffusion on atomic size in amorphous Ni-Zr," Phys. Rev. B, Vol. 37, p. 6534. Copyright 1988 by the American Physical Society.

R. Kirchheim. Hydrogen solubility and diffusivity in defective and amorphous metals. Prog. Mater. Sci., 32(4) 261-325, 1988. 

Results with Ni have shown [589, 590] that the amorphous metal can be more active than the crystalline material, but the small decrease in Tafel slope for the amorphous electrode is outweighed by the higher overpotential at low current densities (Fig. 33). An increase in temperature raises the Tafel slope substantially, presumably on account of the incipient crystallization of Ni. Higher adsorption strength on amorphous Ni is pointed out, while surface diffusion of Had is suggested as the possible r.d.s. 

In this chapter, diffusion in solid materials, that is, metals, oxides, and nanoporous crystalline, ordered, and amorphous materials is discussed. We first study diffusion in a phenomenological, general form afterward the diffusion of atoms in crystals by means of knowledge obtained from studies of diffusion in metals is discussed. Thereafter, those phenomena that are exclusive to oxides are separately discussed. Finally, diffusion in nanoporous materials is described. 

MOCVD process as well as the oxidation problem of the diffusion barrier, the low temperature MOCVD process is required which usually results in amorphous or weekly crystallized as-deposited thin films. Therefore, high temperature post-annealing is an absolute necessity. The upper limit temperature of the post-annealing is about 800°C considering the interdiffusion between the BST and electrodes at higher temperature and process integration issues such as degradation of the metal contact resistance. 

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