Orientation-dependent time-integrated

By exploiting the orientation dependence of the nuclear resonant scattering signal, the diffusion mechanism can be elucidated at the atomic level. The orientation-dependent time-integrated intensity (ODIN) is given by... 

Let us discuss first the case in which only the first term is present. In the Solomon and Bloembeigen equations for / , (i = 1, 2) there is the cos parameter at the denominator of a Lorentzian function. Up to now cos has been taken equal to that of the free electron. However, in the presence of orbital contributions, the Zeeman splitting of the Ms levels changes its value and cos equals xs / o or (g/h)pBBo- When g is anisotropic (see Fig. 1.16), the value of cos is different from that of the free electron and is orientation dependent. The principal consequence is that another parameter (at least) is needed, i.e. the 0 angle between the metal-nucleus vector and the z direction of the g tensor (see Section 1.4). A second consequence is that the cos fluctuations in solution must be taken into account when integrating over all the orientations. Appropriate equations for nuclear relaxation have been derived for both the cases in which rotation is faster [40,41] or slower [42,43] than the electronic relaxation time. In practical cases, the deviations from the Solomon profile are within 10-20% (see for example Fig. 3.14). 

In general, Co in Eq. 27 is dependent upon the free surface orientation and the value of / in the cell as well as the size of time increment At. However, due to the explicit nature of the time integration illustrated here, dependency of Co on Af becomes out of question. As a result, Co is a function of the free surface orientation (or normal vector n) and Cq so that... 

Orientation dependence of time-integrated NFS from an FeAl single crystal at a temperature of 1030 °C. Solid circles represent the measured data, while the solid lines are model calculations assuming the following different types of jumps (a) jumps of the Fe atoms to nearest-neighbor sites, (b) jumps to second nearest-neighbor sites, (c) jumps to third nearest-neighbor sites, and (d) a combination of [110] and [001] jumps at a ratio of 1.9 1. (Reproduced from Ref. 90 with permission of Kluwer Academic Publishers.)... 

A very general approach was considered by Wardlaw and Marcus, who proposed the evaluation of the number of states in Eq. (4.5) via Monte Carlo integration, but with the inclusion of the full orientation dependent Vlr. With the advances in computational abilities at the time, this allowed... 

In the first case, that is with dipoles integral with the main chain, in the absence of an electric field the dipoles will be randomly disposed but will be fixed by the disposition of the main chain atoms. On application of an electric field complete dipole orientation is not possible because of spatial requirements imposed by the chain structure. Furthermore in the polymeric system the different molecules are coiled in different ways and the time for orientation will be dependent on the particular disposition. Thus whereas simple polar molecules have a sharply defined power loss maxima the power loss-frequency curve of polar polymers is broad, due to the dispersion of orientation times. 

Without essential limitation of generality it may be assumed that the orientation of the molecule and its angular momentum are changed by collision independently, therefore F(JU Ji+, gt) = f (Jt, Ji+i)ip(gi). At the same time the functions /(/ , Ji+ ) and xp(gi) have common variables. There are two reasons for this. First, it may be due to the fact that the angle between / and u must be conserved for linear rotators for any transformation. Second, a transformation T includes rotation of the reference system by an angle sufficient to combine axis z with vector /. After substitution of (A7.16) and (A7.14) into (A7.13), one has to integrate over those variables from the set g , which are not common with the arguments of the function / (/ , /j+i). As a result, in the MF operator T becomes the same for all i and depends on the moments of tp as parameters. 

Region III, IV the late stage of SD, i.e., the process where the oriented domains grow with self-similarity. The reason for the time dependences of the integrated intensity is unclear. 

---