Atom jumping activation energy

For ceramics the value of E varies over quite a wide range from about 50kJ/mol to 800kJ/mol (-0.5 eV per atom to 8eV per atom). The activation energy represents the energy necessary for an atom to jump from one atomic position to another. 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

Carlo-simulations for LI2 superlattice including saddle-point energies for atomic jumps in fact yielded two-process kinetics with the ratio of the two relaxation times being correlated with the difference between the activation barriers of the two sorts of atom. 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

It has been recognized that the behavior of atomic friction, such as stick-slip, creep, and velocity dependence, can be understood in terms of the energy structure of multistable states and noise activated motion. Noises like thermal activities may cause the atom to jump even before AUq becomes zero, but the time when the atom is activated depends on sliding velocity in such a way that for a given energy barrier, AI/q the probability of activation increases with decreasing velocity. It has been demonstrated [14] that the mechanism of noise activation leads to "the velocity... 

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. 

Vq is the frequency of the small oscillation, and AG and AS are, respectively, the difference in Gibbs free energy and entropy of the adatom at the saddle point and the equilibrium adsorption site. Ed is the activation energy of surface diffusion, or the barrier height of the atomic jumps. 

An observation of motion of single atoms and single atomic clusters with STEM was reported by Isaacson et al,192 They observed atomic jumps of single uranium atoms on a very thin carbon film of —15 A thickness or less. Coupled motion of two to three atoms could also be seen. As the temperature of the thin film could not be controlled, no Arrhenius plot could be obtained. Instead, the Debye frequency , kTIh, was used to calculate the activation energy of surface diffusion, as is also sometimes done in field ion microscopy. That the atomic jumps were not induced by electron bombardment was checked by observing the atomic hopping frequencies as a function of the electron beam intensity. 

In Table 16-2, the time scale for elementary activated motion is given in the first place. It is converted into an energy scale by virtue of the E = (2n-h/t) relation, If we assume that the atomic jump length a is 2 A, the time scale may be converted into a diffusion coefficient scale by D = az/(2-t). One notes that (with the exception of /J-NMR) nuclear spectroscopies monitor the atomic jump behavior of relatively fast diffusing species. 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

The wide range of diffusivity magnitudes evident in the diffusivity spectrum in Fig. 9.1 may be expected intuitively as the atomic environment for jumping becomes progressively less free, the jump rates, T, decrease accordingly in the sequence rs > rB rD(undissoc) > rD(dissoc) > VXL. The activation energies for these diffusion processes consistently follow the reverse behavior,... 

To estimate the activation energy of diffusion at lower temperatures let us assume the pre-exponential factor Du to be independent of T and, by the order of magnitude, to be equal to D = A2vk % 10 4cm2s 1 (A % 10 8 cm is the characteristic value of a diffusion jump, vk 1012s 1 is the characteristic frequency of atomic oscillations in a solid). Then from the experimental values of D one can find the activation energy of diffusion Ea = 9 kcalmol 1... 

Diffusion in interstitial solid solutions occurs by interstitially dissolved atoms jumping from one interstitial site to another. For an atom to move from one interstitial site to another, it must pass through a position where its potential energy is a maximum. The difference between the potential energy in this position and that in the normal interstitial site is the activation energy for diffusion and must be provided by thermal fluctuations. The overall diffusion rate is governed by an Arrhenius-type rate equation,... 

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