Ion trajectory calculation

For accurate ion trajectory calculation in the solid, it is necessary to evaluate the exact positions of the intersections of the asymptotes (A A2) of the incoming trajectory and that of the outgoing trajectories of both the scattered and recoiled particles in a collision. The evaluation of these values requires time integrals and the following transfonnation equations ... 

Theoretically, each electrode should have a hyperbolic cross section for optimized geometry of the resulting quadrupole field, and thus for optimized performance. [103,104] However, cyclindrical rods are often employed instead, for ease of manufacture. By adjusting the radius of the rods carefully (r = 1.1468ro), a hyperbolic field may be approximated. [113] However, even slight distortions of the ideal quadrupole field either from interference with external fields or due to low mechanical precision or inadequate shape of the device cause severe losses of transmission and resolution. [114] The expected advantages of hyperbolic rods [115] have been demonstrated by ion trajectory calculations [110,116] circular rods cause a reduction in macromotion frequency because of an increased residence time of the ions in close vicinity to the rods this in turn means reduced resolution. 

In practice, the ion optical properties of an ion source are optimized by means of ion trajectory calculations. [31] The standard tool for this task is the SIMION software suite, [32-35] while there are others, too. [36] Thus, the optimum number, positions, voltages, and eventually shapes of the plates are determined (Fig. 5.11). In order to compensate for slight mechanical deviations from theory and for effects exerted by contamination of the plates during elongated use, the voltages can be adjusted to yield optimum conditions. 

In order to evaluate the changes to the performance of the ion trap, caused by the perturbation to the trapping field due to the addition of holes in the ring electrode to enable our fluorescence measurements, we have carried out ion trajectory calculations in several models of the modified Esquire 3000-1- QIT. Franzen [87,91,92] demonstrated previously the utility of ion trajectory calculations in investigation of the modified hyperbolic angle trap, but considered only ion motion in the axial direction. Here, we discuss results from several SIMION models, which have been constructed with different numbers and sizes of holes in the ring electrode. Fourier analysis of ion trajectories is used to determine secular frequencies, frequency shifts. 

Fig. 3.1. Selected ion trajectories calculated for an octopole illustrating the influence of the rf field. The ions start in the center, but with different stability parameters rim, initial energies Em, and two directions (between and towards the rods). Details are explained in the text.

Figure 4 SIMION ion trajectory calculations of an on-axis SID device with (A) precursor ion deflection in single deflection mode, (B) precursor ion deflection in double deflection mode, and (C) precursor and product ion trajectories in double deflection mode. Numerical labels represent the voltages applied to the electrodes. Reproduced with permission from Durkin DA, Schey KL, (1998) Characterization of a new in-line SID mode and comparison with high energy CID. International Journal of Mass Spectrometry and Ion Processes 174 63-71.

Classical ion trajectory computer simulations based on the BCA are a series of evaluations of two-body collisions. The parameters involved in each collision are tire type of atoms of the projectile and the target atom, the kinetic energy of the projectile and the impact parameter. The general procedure for implementation of such computer simulations is as follows. All of the parameters involved in tlie calculation are defined the surface structure in tenns of the types of the constituent atoms, their positions in the surface and their themial vibration amplitude the projectile in tenns of the type of ion to be used, the incident beam direction and the initial kinetic energy the detector in tenns of the position, size and detection efficiency the type of potential fiinctions for possible collision pairs. 

Before we do this, though, we point out that for a simple diatomic molecule, assuming ideal conditions, one can in principle calculate the rate of the uni-molecular process. This is so because the lower excited states of the ion are (relatively) few and well separated. If the potential curves are then given, the value of the rate can be provided. For a polyatomic molecule, two great complications immediately arise (1) the number of lower excited states increases tremendously and (2) multidimensional potential energy surfaces make trajectory calculations intractable. 

The essence of Monte-Carlo models is to calculate the path of an ion as it penetrates a crystal. Early versions of these models used the binary collision approximation, i.e., they only treated collisions with one atom at a time. Careful estimates have shown that this is an accurate procedure for collisions with a single row of atoms (Andersen and Feldman, 1970). However, when the rows are assembled into a crystal the combined potentials of many neighboring atomic rows affect ion trajectories near the center of a channel. For this reason, the more sophisticated models used currently (Barrett, 1971, 1990 Smulders and Boerma, 1987) handle collisions with far-away atoms using the continuum string approximation,... 

Figure 4.18 Trajectory calculations for the scattering of a parallel beam of 1 keV He+ ions by Si02 the inset shows a Si04 tetrahedron (from Brongersma and van Leer-dam [41]).

From a more general point of view, the trajectory calculations on the Hj/Hj system suggest that SIKIE predictions for ion- nolecule reactions based solely on differing synunetry correlations for even and odd I may not be readily realized under... 

In field ion microscopy, one would also like to know how the field distributes itself above an emitter surface. This information is important in the quantitative interpretation of many field ion emission phenomena and experiments. It is also important in calculating the ion trajectory to enable a proper aiming in an atom-probe analysis. Unfortunately, not only does each tip have its own particular shape, but the presence of lattice steps also complicates the situation immensely. There are so far no reliable calculations for the field distribution above an emitter surface, nor for predictng the ion trajectory, nor yet for where the probe-hole... 

Dynamics effect discussed so far deals with reaction systems, in which an unstable intermediate exists in a shallow well on the PES connecting the reactant and product states. These putative intermediates have been biradicals, radical ions, carbenes, or post-TS complexes. Trajectory calculations showed examples where reacting molecules stride over a shallow well to give product directly or cases where the lifetime of the species trapped in a well is short enough to avoid thermal equilibration and quickly escape to the product. In these cases, reactions occurred effectively in a concerted manner, although the PES dictates a stepwise mechanism. 

A quadrupole mass-filter stability diagram can be created. The shaded area in Fig. 7 shows regions in a-q space where the calculated ion trajectories are stable. 

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