Jump vector

Figure 9 The probabilities of the jump lengths of the tracer atom for T = 320 K and l = 401 lattice spacings. Filled circles correspond to experimental values (measured at this temperature and terrace size), open circles are from the model described in the text, and the solid curve is the continuum solution described in Section 3.3. The distribution depends only on the magnitude of the jump lengths with no directional dependence. (Each dataset is normalized separately such that the probabilities corresponding to a subset of the jump vectors, 1 < r < 6, add up to unity. These are the probabilities that are determined with good accuracy in the experiment.)...

The jump vector. A, wUl obviously depend on the mechanism and the structure. For example, an atom diffusing through the octahedral interstitial sublattice in an FCC metal, with lattice spacing a (Fig. 6.6), must jump the distance between interstitial sites, A = fl/V2. This is, of course, the same distance an atom diffusing by the vacancy mechanism must jump. It will be recalled that for every atom in a close-packed stmcture, there are two tetrahedral interstitial sites and one octahedral interstitial site. The reader might ask if the distances between the tetrahedral sites ate the same. 

All jumps (to nearest neighbor sites only) have the same jump length f and are characterized by jump vectors S , i = 1,... 

Here P(r,t) and U(i,t) denote the probabilities of finding a hydrogen in the occupied and unoccupied layers, respectively r and are the jump rates within the occupied and unoccupied layers, respectively (both along the jump vectors Sj to S4), and Tq and are the change-over rates from the occupied to the empty layer and vice versa, respectively (both along the jump vectors S to S ). This jump model yields a 2x2 jump matrix and subsequently an incoherent scattering function consisting of two Lorentzians. 

As the grain boundary fails, the value of S gradually decreases from an initial value close to unity to zero, point at which complete failure is acheived. The coupling between normal and tangential failure in mixed-mode situations is captured by defining S in terms of the L2-norm of the normalized displacement jump vector A, as indicated by Equation 2 and illustrated in Figure 2. 

Here R is a jump distance and fid) a correlation factor to take into account of the degree of the incoherency due to an angle, 0, between the jump vector, R and the wave vector of the 14.4 keV y-ray, k. fifi) depends both on crystal structures and on the diffusion mechanism, as discussed in [30]. 

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