Newton diagrams

Fig. 13. Newton diagram in velocity space for the Y + CH3OH reaction at con = 28.1 kcal/mol. See Ref. 136.

Fig. 15. Newton diagram in velocity space for Y+cyclopropane at Eco = 18.5 kcal/mol. Larger solid circle corresponds to maximum velocities for YCH2 products, while smaller solid circle and smaller dotted circle correspond to maximum velocities for Y-propyne and Y-allene products, respectively. Lab angular distributions for YCH2 (open squares) and YC3H4 (open circles) recorded under identical collision conditions. Solid-line fits to lab angular distributions generated using CM distributions in Fig. 17.

Fig. 33. Newton diagram in velocity space for the reaction Y + cis-2-butene at Ecoll = 26.6 kcal/mol. Circles represent the maximum CM velocity constraints on the indicated metal-containing fragment from the various product channels based on reaction thermodynamics as shown in Fig. 32 and momentum conservation.

Reactions with isobutene led to channels (5), (7), and (8), but no evidence for process (6) was observed. Time-of-flight (TOF) spectra for all four isomers were similar, so only data for the Y + cis-2-butene reaction will be shown. A Newton diagram for this reaction is shown in Fig. 33. 

Fig. 6. Variation of the center-of-mass velocity with beam crossing angle, 7, for the reaction 0(3P) + C2H2 with the 0(3P) and C2H2 beam velocities of 2798ms-1 and 827ms 1, respectively. The Newton diagrams for 7 = 45°, 90°, and 135° are shown (see text).

Fig. 9. HCCO and CH2 product lab angular distributions from the 0(3P) + C2H2 reaction at Ec = 9.5kcalmol 1. Solid lines are best-fit curves obtained from the best-fit product angular and translational energy distributions (adapted from Ref. 33). The Newton diagram of the experiment is also shown there the Newton circles delimit the maximum velocity that the indicated products can attain assuming that all the available energy is channelled into translation.

Fig. 12. Comparison of HCCO product lab angular distributions and TOF spectra at = 22° from the 0(3P) + C2H2 reaction for a beam crossing angle of 7 = 90° (Ec = 9.5 kcal mol 1, setup of Fig. 1) and of 7 = 135° (Ec = 12.6 kcal mol l, setup of Fig. 7). The corresponding Newton diagrams are also shown. Note the higher angular and TOF resolution obtained when 7 = 135°, as witnessed by the wider HCCO lab angular distribution and slower (and wider) TOF spectrum.

Figure 3. Newton diagrams for the two sets of measurements shown in Figs. 4 and 5. On left, He beam source is cooled to liquid-nitrogen temperature and ground-state helium beam is at room temperature, whereas beam temperatures are interchanged on right. This gives same center-of-mass kinetic energy but different laboratory energies for scattered atoms.

Figure 53. Newton diagram for He (2 S) + Ne at 66 meV. Largest partial circle is locus of He velocities from elastic collisions smaller numbered ones represent inelastic production of Ne in various final states. Numbers n correspond to subscripts 3s for states of neon (Paschen notation). Angular rays correspond to positions of maxima or shoulders in angular distribution of Fig. 50.

Figure 54. Sampling of TOF spectra for He + Ne. Time t0 is flight time from beam excitation region to collision center e, expected elastic flight time derived from Newton diagram of Fig. 53, and numbered times those for Ne in various final states (notation as in Fig. 53). Number zero corresponds to beam neon photoexcited by far-UV photons produced as result of energy transfer (see Section III.A.7).

Reactive collisions [2,23,43,44] may be represented by a Newton diagram similar to that already shown for elastic scattering, but now v, the final relative velocity, may differ both in size and magnitude from the initial vector v and, although v is again pivoted at the tip of C, the relative length of its segments is determined by momentum balance between the masses of the products, not those of the reactants. Consequently,... 

Figure 1.5 Example of a Newton diagram for reactive scattering from A + BC — AB + C, assuming that MK = AfB = Mc and VJVBC = (MBC/ fA)1/2. The in-plane pAB vectors must terminate on a circle of radius /tAB and the length of HAB will be directly related to E, the final relative translational energy.

Figure 1.7 The in-plane lab angular distribution of KBr from K + Br2 [2]. The Newton diagram is given for the most probable beam velocities (both beams are unselected and their temperature is given), and the circles indicate the length of u Br vectors corresponding to various values of E (kcal/mole). The simple interpretation of these results is to equate the lab peak at 0 = 17° with a c.m. peak at 0 = 0° (direct forward scattering) and hence estimate 1.2 kcal/mole.

Fig. 19. Newton diagram for direct inelastic scattering of O atoms following impact of O atoms at ( j) = 504 kJ mol and = 60° on a squalane surface.

The Newton diagram can also be applied to the reactive OH products that exit the surface with hyperthermal translational energies (Fig. 20). For the hydrogen-abstraction reaction, Eq. (13) is modified by replacing mo with moH> with (mg - 1), and Wq with ojj, while Eqs. (11) and (12) remain unchanged. The effective surface mass and other dynamical quantities are almost the same as those found for inelastic scattering of... 

The Newton diagram reveals the center-of-mass angular distributions of scattered O and OH flux. In the laboratory reference frame, hyperthermal... 

Fio. 7.—Newton diagrams for the Ba+HX reactions. Most probable velocities are used. The Ba beam is assumed to be effusive, while for the supersonic HX beam it is assumed that =... 

Figure 5. (A) Newton diagram of the reaction, which was studied in a crossed-beam experiment. The other three panels are 3D plots showing the velocity and angular distribution of the product BaO in reaction (8). Panel D is the full signal, which is resolved into two components, a forward-backward symmetric component shown in panel B + a forward component shown in panel C. Adapted from Ref. [102],...

Figure 1. Schematic Newton diagram for the reaction of a halogen atom with molecular hydrogen. The vector designated V is the velocity vector of the HX products in the center-of-mass frame.

Figure 6. Angular distribution in laboratory frame resulting from reaction of NO clusters with O, where 0° is direction of NO beam. Also shown is Newton diagram for (NO)2 + O system.

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