3. Results 39
3.3. MD Simulation of H scattering from Au(111) with Various Conditions
3.3.6. Isotope eect
Hydrogen is a factor of two lighter than deuterium; possessing the same incidence energy, H therefore has a√
2 higher impact velocity than D. To study the isotope eect, I performed MD simulations for deuterium and hydrogen withEinc,D = 3.27eV andEinc,H= 3.33eV, respectively which match the incidence energy values that have been used in experiment.
Tab. 3.27 shows the dierent event probabilities for the calculations that are to be compared to experiment. Only the adiabatic case shows larger discrepancies: the scattering and transmission probability of D is lower than for H while the ad- and absorption probability is higher although the penetrating probability for deuterium (see Tab. 3.21) is lower than for hydrogen. The ratio of the dierent bounce events shows a slight preference for multibounce events in case of hydrogen compared to deuterium. In the nonadiabatic case, the probabilities of scattering, adsorption, penetration and the ratio between the bounce events (see Tab. 3.27 and Tab. 3.21) do not show any remarkable dierence, in accordance with both experiencing the same friction coecient η(r) at a given positionr.
Tab. 3.29 shows that the adiabatic mean energy loss of hydrogen compared to deuterium
110
Table 3.28.: Outcomes (%) for various scattering events resulting from H and D atom collisions with a Au(111) surface for nonadiabatic and adiabatic (in parenthesis) simulations. The Surface-column refers to trajectories wherein H atoms scattered from the rst layer of the surface.
The Roman numerals refer to the lowest subsurface to which penetration occurred. The incidence conditions are θinc = 45◦ along the [10¯1] surface direction, T = 300K with 6×6×6 cell, number of simulated trajectories: 106. For deuterium and hydrogen an incidence energy of 3.27 eV and 3.33 eV, respectively, was used.
bounce events penetrating bounces
Isotope single double multi surface I II III >III H 23 (17) 34 (25) 43 (59) 82 (64) 17 (23) 1 (8) 0 (3) 0 (2) D 22 (18) 33 (27) 45 (55) 83 (70) 16 (23) 1 (5) 0 (1) 0 (1)
is lower while the inclusion of energy loss to electron hole pair excitation shows the reverse behavior, i.e. the nonadiabatic mean energy loss for the hydrogen is larger than that of the D atom. This is also evident from Fig. 3.46(a) and (b). The total energy loss distribution of deuterium (Fig. 3.46(a)) has a slightly dierent shape than that of H due to slightly dierently shaped total energy loss distributions of the individual bounce events. This dierence in shape does not carry into the dierential energy loss distributions at specular angles (see Fig. 3.46(b)).
Here, the dierential energy loss distributions of both isotopes show an almost perfect overlap with one another. The angular distribution along the [10¯1]-direction also does not show any dierent behavior: both that for D and for H are very broad, almost identically formed, showing mostly scattering in forward direction and their peak positions agree well (see Fig. 3.46(c)).
To further explore the isotope eect, I performed calculations for 1000 trajectories for both
Table 3.29.: Energy loss in % of incidence energy for various outcomes resulting from H and D atom collisions with a Au(111) surface for nonadiabatic and adiabatic (in parenthesis) simula-tions. The incidence conditions areθinc= 45◦along the[10¯1]surface direction,T = 300K with6×6×6cell, number of simulated trajectories: 106. For deuterium and hydrogen an incidence energy of 3.27 eV and 3.33 eV, respectively, was used. The mean and maximum energy loss are shown for the total and dierential ELD. The reduced accuracy at specular scattering (θout = 45◦ φout = 60◦ ([10¯1])) is due to the lower signal-to-noise ratio in the dierential ELDs.
Total θout= 45◦ φout= 60◦
Isotope Mean Peak Mean Peak
H 39.2 (13.1) 14.0 (1.65) 37 (11) 14 (0.75) D 36.1 (16.7) 12.7 (2.91) 33 (14) 12 (2.6)
isotopes with the same incidence energy of 3.31 eV for normal incidence at T = 0K for the electronically adiabatic and nonadiabatic case. To separate the contribution due to the adiabatic and nonadiabatic energy loss, I also performed an MD simulation at the above conditions where I keep the Au atoms xed at their equilibrium positions of the relaxed slab (MDEF-SS). For all these calculations, I compare the positions of the peaks of the total energy loss distribution due to the single-bounce events for hydrogen with those of deuterium.
In the electronically adiabatic case, when the energy loss to ehp is switched o, the total energy loss distribution due to single-bounce events of hydrogen peaks at 55meV and that of the deuterium at ∼ 2 times higher energy losses of 105meV (Fig. 3.47, blue), resulting in an energy dierence of 50 meV. The comparison of the positions of the peaks for H and D for the MDEF-SS calculations with the solid surface peak at 255meV for the deuterium atom and at
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0
0.2 0.4 0.6 0.8 1.0
Eloss(eV)
A.U.
(a)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Eloss(eV)
ProbabilityDensity(1/eV)
(b)
-1.0 -0.5 0.0 0.5 1.0 r sin(θ)
75°
60°
45°
30°
0° 15°
-15°
-30°
-45°
-60°
-75°
(c)
Figure 3.46.: Energy loss distribution for nonadiabatic scattering of H (black, solid) and D (red, solid) and the electronically adiabatic scattering results (light, dashed), (a) total, (b) specular scattering (θout = 45◦, φout = 60◦). (c) Angular distribution of scattering in [10¯1] -direction for H (black) and D (red). θis the polar angle and negative values correspond to scattering in backward direction.
112
-0.10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 50
100 150
Eloss (eV)
Countsper10meVbin
50 meV
100 meV 40 meV
Figure 3.47.: Total energy loss distribution due to single-bounce events for dierent isotopes (H solid, D dashed) atEinc= 3.31eV electronically adiabtic at 0 K (blue), electronically nonadiabatic with frozen surface (red) and nonadiabatic at 0 K (black).
∼√
2 higher energy losses of 355meV for the H atom, resulting in an dierence in energy loss to ehp of 100 meV (Fig. 3.47, red). It should be noted that the energy loss to electron hole pairs clearly is much larger than that to phonons for both hydrogen and deuterium.
If the electronically nonadiabatic case with a surface temperature of 0 K is considered (that is, if both adiabatic and nonadiabatic eects are considered together), the dierence in energy loss amounts to40meV (Fig. 3.47, black).
The adiabatic energy loss can be estimated by means of the Baule limit which can be repre-sented in terms of the projectile-surface mass ratio µ=m/M:
∆Ead= 4µ
(1 +µ)2Einc (3.1)
It follows that for the same incidence energy
∆Ead(D)
∆Ead(H) = 4µD
(1 +µD)2Einc: 4µH
(1 +µH)2Einc≈ mD
mH
= 2. (3.2)
The nonadiabatic energy loss due to friction is given by the integral
∆Ena = Z
η(r)v·ds (3.3)
along the entire trajectory. Here, v is the particle's velocity and s the distance along the trajectory. Assuming the friction coecient to be independent on the particle's position, the ratio of the nonadiabatic energy loss ∆Ena for deuterium and hydrogen can be estimated to be proportional to their velocitiesv:
∆Ena(D)
∆Ena(H) ≈ ηvD
ηvH
≈ vD
vH
≈
p2Einc/mD
p2Einc/mH
= rmH
mD
= 1
√2 (3.4)
One would therefore expect that deuterium should experience a factor of √
2 lower energy loss than hydrogen at the same incidence energy. This eect is opposite to that for the adiabatic collisions which becomes clear if Eq. (3.2) is compared to Eq. (3.4).
In conclusion, the isotope eect on the energy loss to phonons and to electron hole pair operates into opposite directions in the simulations, leading to almost a compensation for H and D whose energy loss behavior is therefore very similar.