Cascade mixing

In addition to recoil mixing, other ballistic phenomena are possible during ion irradiation and implantation. For example, enhanced atomic mixing can occur when multiple displacements of target atoms result from a single incident ion. In the multiple displacement process, an initially displaced target atom (primary recoil) continues the knock-on-atom processes, producing secondary recoil atom displacements which in turn displace additional atoms. The multiple displacement sequence of collision events is commonly referred to as a collision cascade. 

Calculations of the mean energy of atoms in a cascade show that most recoils are produced near the minimum energy necessary to displace atoms, Ed. Due to the low-energy stochastic nature of these displacement events, the initial momentum of the incident particle is soon lost, and the overall movement of the atoms in a collision cascade becomes isotropic. This isotropic motion gives rise to an atomic redistribution that can be modeled as a random-walk of step size defined by the mean range of an atom with energy near Ed. The effective diffusivity, Dcas, for a collision cascade-induced random-walk process is expressed in the diffusion equation as (Andersen 1979) 

The primary features of (13.5) and (13.6) are that the effective diffusion coefficient should scale with the dose, / , and the damage energy, Fu, in good 

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Figure 3. Superstructure for cascaded mixed refrigerant systems...

The second case study is to cool gas stream from 35 °C to -160 °C, and the detailed energy flow is given in Figure 5. In this example, cascade mixed refrigerant systems is optimized with 3 °C of ATmin. 

Even in the ab en(pe of preferential sputtering, i.e, SA=Sg, it is not necessarily the case that the concentration ratio of A and B is uniform with depth under steady state ion bombardment. The subsurface layer can have a different concentration ratio from the bulk or the top surface even if the latter two are identical. This can occur because of the subsurface effects of ion bombardment discussed below, which can produce an altered subsurface composition. As a result, there are two altered layers possible the top surface layer where composition at steady state is completely controlled by RgA and the subsurface layer where composition is controlled by segregation, radiation induced diffusion, radiation induced segregation, recoil implantation and cascade mixing. 

Cascade mixing has been treated as a diffusion problem where it can be shown that the number of ion induced defects is usually very much larger than the thermally generated defects for temperatures below several hundred degrees centigrade (37). The crossover point depends on the sample and ion beam parameters. Cascade mixing can produce effective diffusion coefficients of the order... 

Typically, the steady state mode of a mixing reactor is characterised by isothermal conditions. Therefore, the temperature field in the reaction zone can be changed during the process (generally for the cascade mixing reactors). 

Fig. 10. Filter effect of delay tank in recycle path (solid) and cascaded mixing tank of same size (dashed) for reactor-separator system.

Fig. 4.10 Depth profile of one monolayer of Ag buried between 100 nm of evaporated Si and 300 nm of evaporated Si on a Si substrate to illustrate taking advantage of cascade mixing from the primary ion beam for quantitative interfacial analysis (Cameca IMS 3f with an 8 keV O2 beam)...

Ronghening, segregation, diffnsion, cascade mixing, and recoil implantation of the spnttered snrface will distort the shape of a profile collected, as well as the depth resolution. These issnes are covered further in Section 5.3.2.4.I. 

Retrospective approaches are more limited as they can only be appUed in ideal cases on atomically smooth spatially homogeneous surfaces if a sufficient amount of information on the system exists. This is realized because such approaches require knowledge of either the instrument s response function (a function that describes the loss of depth resolution apparent under a predefined set of conditions) or the processes describing cascade mixing along with any ion-induced diffusion and/or segregation processes active. Smooth samples are required to ease the computational burden. 

As derivation of response functions is easier than describing, in an analytical manner, the intricacies of the processes responsible for the loss of depth resolution (cascade mixing and so on) this is the general approach of choice. Even so, response functions exhibit a complex dependence on the incoming ion, the substrate, the signal recorded and the instrumental conditions used. 

Ion-induced mixing due to recoil implantation, or cascade mixing leading to an additional broadening of the profile. 

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