Scattering and Trapping of Ar-Pt(lll) System Using
Phantom Particle Model
Toshihiko Ishida, Kenichi Miyagawa and Tomohide Niimi
Department of Electronic-Mechanical Engineering, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Abstract. Energy exchange and trapping probabilities for interaction of gas molecules with a metal surface are calculated
by the Molecular Dynamics method using the Phantom Particles model as a solid surface. The validity of the Phantom
Particle model is confirmed through the power spectra of three directions, the velocity distribution in each layer and the
response to an abrupt change of a preset temperature. Then the Phantom Particle model is applied to gas-surface
interaction for Ar-Pt(lll) system. The flux distributions, the TOP spectrum of gas atoms scattered at the specular angle
and the trapping probabilities are calculated and compared with those of molecular beam experiments, leading to good
quantitative agreement as well.
INTRODUCTION
In these years, space simulation chambers in large scale have been constructed in many facilities in America and
Europe to analyze the impingement of thruster jet with the satellite body and the solar arrays during the firing of an
attitude control thruster. In the interaction between solar panels and a thruster jet, it is pointed out that the heat load
may damage the surfaces and that the contamination on a solar panel reduces a lifetime and a transmission of the
panel. To develop the MEMS (micro electro-mechanical system), where the characteristic dimension is smaller than
the mean free path, it is necessary to understand the flow field structure at the molecular level, including the
accommodation or adsorption of gas molecules to the solid surface. We cannot obtain the high quality thin films for
ULSI devices without knowledge of the interaction between plasma gas and a solid surface, such as chemical
reactions and trapping of gas molecules on a solid surface. Therefore, acquisition of accurate data related to gassurface interaction is an urgent necessity for space science and high technologies including micro fluid flows.
For experimental studies of gas-surface interaction, a molecular beam method mainly has been used. And we
can obtain the information of the energy exchange of gas molecules to the solid surface from the flux intensity
distribution of scattered molecules and the data such as mean velocity, temperature, Mach number from the TOE
spectra. Since these experimental data are obtained in a plane including both the surface normal and incident beam,
we cannot obtain the trapping probabilities and accommodation coefficients which need to detect all scattered
molecules. If a computational method can be developed to realize the flux intensity distribution and velocity of the
scattered molecules consistent with the experimental results, more precise data for gas-surface interaction can be
obtained by combining the calculated data with experimental ones.
In the present study, the Phantom Particle model is applied to predict fundamental properties of gas-surface
interaction, whose validity has been investigated in a preliminary simulation through the power spectra of three
directions compared with the Debye frequency(1), the response to an abrupt change of a preset temperature, and the
velocity distribution in each layer. The basis of this model had been introduced by Adelman and Doll(2), extended
to a three-dimensional model by Tully(3), and developed by Blomer and Beylich(4). However Blomer and
Beylich(4) have neither applied this method to simulation of gas-surface interaction in the same condition as the
molecular beam experiments nor demonstrated the flux distribution or TOE spectra of the scattered molecules. We
independently have decided a parameter of an interaction between a single real atom and a single Phantom Particle.
Also the number of the real atom simulated is extended to 36 in each layer, and the periodic boundary condition is
CP585, Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. A. Gallis
© 2001 American Institute of Physics 0-7354-0025-3/01/$18.00
360
added
of Ar
Ar with
with Pt(lll),
Pt(111), leading
leading to
to
added to
to produce
produce an
an infinite
infinite surface
surface plane.
plane. This
This model
model is
is applied
applied to
to interactions
interactions of
quantitative
agreement
with
experimental
data
performed
by
a
molecular
beam
method.
quantitative agreement with experimental data performed by a molecular beam method.
PHANTOM
PHANTOM PARTICLE MODEL
The
atom and a
The molecular
molecular dynamics
dynamics method
method gives
gives the
the fundamental
fundamental properties on an interaction between a gas atom
solid
solid surface.
surface. AA small
small part
part of
of aa surface
surface area
area is
is simulated
simulated in detail, where each real atom connects with one Phantom
Particle.
heat bath
bath for
for
Particle. The
The Phantom
Phantom Particles
Particles represent
represent the
the other lattice atoms except some real atoms and act as a heat
real
atoms
without
control
of
the
surface
temperature
using
the
velocity
scaling
method.
Figure
1
shows
a
schematic
real atoms without control of the surface temperature
schematic
illustration
interacts with
with aa Phantom
Phantom
illustration of
of the
the Phantom
Phantom Particle
Particle model
model in
in the present study. While each real atom interacts
Particle
the present
present
Particle and
and only
only 12
12 adjacent
adjacent real
real atoms,
atoms, Phantom
Phantom Particles
Particles have no interactions with each other. In the
model,
model,the
the trajectories
trajectories of
of real
real surface
surface atoms
atoms are
are calculated
calculated according
according to Newton's equation of motion while Phantom
Particles
fluctuating force
force terms.
terms.
Particles follow
follow the
the generalized
generalized Langevin
Langevin equation
equation including the harmonic, damping, and fluctuating
The
periodic
The small
small part
part simulated
simulated in
in detail
detail consists
consists of
of three
three layers
layers each of which 6×6
6x6 real atoms are placed in. The periodic
boundary
boundary condition,
condition, however,
however, extends
extends the
the simulation
simulation area to the infinite surface.
Real Atom=Pt Real Atom =Pt Atom
Atom
Fluctuating
Force
Harmonic
Harmonic
Force
Force
Phantom
Particle
Damping
Force
FIGURE 1.
1. Schematic
Schematic illustration
illustration of Phantom Particle Model
FIGURE
Adelman and
and Doll(2)
Doll(2) had
had led
led to
to the
the generalized
generalized Langevin
Langevin equation
equation including
including aa harmonic
Adelman
harmonic oscillation
oscillation for
for the
the gasgassurface interaction,
interaction, and
and then
then Tully(3)
Tully(3) had
had extended
extended the
the method
method to
to full
full three-dimensional
three-dimensional motion
motion for
surface
for an
an fee
fcc and
and bcc
bcc
lattices. They
They indicated
indicated that
that the
the Phantom
Phantom Particles
Particles act
act as
as the
the heat
heat bath
bath and
and that
that the
the properties
lattices.
properties of
of the
the bulk
bulk lattice
lattice can
can
be reproduced.
reproduced. Tully(3)
Tully(3) also
also illustrated
illustrated characteristics
characteristics of
of the
the surface
surface from
from the
the Fourier
spectra of
be
Fourier spectra
of autocorrelation
autocorrelation of
of
velocities of
of real
real atoms
atoms and
and examined
examined an
an accommodation
accommodation coefficient
coefficient and
and trapping
trapping probabilities
velocities
probabilities of
of xenon
xenon or
or argon
argon
molecules on
on the
the Pt(111)
Pt(lll) surface
surface through
through the
the Phantom
Phantom Particle
Particle model.
model. Blömer
Blomer and
molecules
and Beylich(4)
Beylich(4) combined
combined this
this model
model
with
the
molecular
dynamics
method
to
show
the
response
to
a
change
in
the
preset
temperature
and
the
with the molecular dynamics method to show the response to a change in the preset temperature and the change
change of
of
the rotational
rotational temperature
temperature during
during gas-surface
gas-surface interaction.
interaction. However
However Tully(3),
Tully(3), and
the
and Blomer
Blömer and
and Beylich(4)
Beylich(4) have
have
neither applied
applied this
this method
method to
to the
the simulation
simulation of
of gas-surface
gas-surface interaction
interaction in
in the
the same
same condition
condition as
neither
as the
the molecular
molecular beam
beam
experiments nor
nor demonstrated
demonstrated the
the flux
flux distribution
distribution or
or TOF
TOP spectra
spectra of
of the
the scattered
scattered molecules.
experiments
molecules.
Before any
any calculations
calculations of
of gas-surface
gas-surface interaction,
interaction, the
the validity
validity of
of the
the Phantom
Phantom Particle
Particle model
solid surface
Before
model as
as aa solid
surface
was
confirmed
through
the
power
spectra
of
the
three
directions,
the
response
to
change
of
a
preset
temperature
was confirmed through the power spectra of the three directions, the response to change of a preset temperature and
and
the velocity
velocity distribution
distribution in
in each
each layer,
layer, as
as already
already shown
shown by
by Blömer
Blomer and
and Beylich(4).
Beylich(4). In
In addition,
addition, the
specific heat
the
the specific
heat is
is
examined originally
originally by
by comparing
comparing with
with the
the Debye
Debye model
model in
in the
the present
study. Figure
examined
present study.
Figure 22 shows
shows aa dependence
dependence of
of the
the
specific heat
heat on
on the
the preset
preset temperature,
temperature, where
where the
the circle
circle shows
shows the
the specific
specific heat
specific
heat calculated
calculated by
by the
the Phantom
Phantom Particle
Particle
model
and
the
solid
line
that
expected
by
the
Debye
model.
In
Fig.
2
it
is
found
the
calculation
results
model and the solid line that expected by the Debye model. In Fig. 2 it is found the calculation results agree
agree with
with
that expected
expected by
by the
the Debye
Debye model
model in
in the
the range
range of
of temperature
temperature higher
higher than
than the
Debye temperature
that
the Debye
temperature 0ÈDD.. This
This means
means
that the
the Phantom
Phantom Particle
Particle model
model gives
gives the
the specific
specific heat
heat of
of 3Nk
3NkB,, showing
showing effectiveness
effectiveness in
that
in the
the range
range of
of temperature
temperature
B
largerthan
thanÈ0D..
larger
D
361
1.5
1.5
C/3Nk B
Calculation
Calculation
Debye Model
Debye
Model
1
• •
cn
0.5
0.5
0
0
ΘD
300
600
300
D
P reset 0
Temperature
T p re [K]
600
FIGURE 2. Specific heat C of the surface
FIGURE
2. Specific heat C of the surface
SIMULATION OF GAS-SURFACE INTERACTION FOR ARGON-PLATINUM(111)
SIMULATION OF GAS-SURFACE INTERACTION FOR ARGON-PLATINUM(lll)
SYSTEM
SYSTEM
The Phantom Particle model is applied to simulations of interaction of an Ar molecular beam with a Pt(111)
Thesurface.
PhantomToParticle
is applied
simulationsofofthe
interaction
an Ar with
molecular
beam with ones,
a Pt(lll)
verify model
its propriety
fromtocomparison
simulationofresults
the experimental
in the
surface.simulation
To verify
comparison
of the simulation
the experimental
ones,
in the
we its
usepropriety
the same from
conditions
as the experiment
by Hurstresults
et al. with
For example,
the incident
angle
of Ar
simulation
we use
the is
same
conditions
as the experiment
by Hurst
et al.
example,beam
the incident
of Arthe
molecular
beam
set at
from the surface
normal
andFor
temperature
at 1.4 K,angle
assuming
èi = 45 degrees
molecular
beam isvelocity
set at 6distribution.
from
the surface
and temperature
beamtoat50,000
1.4 K,time
assuming
t = 45 degrees
Maxwellian
Each
trajectory
of thenormal
argon molecule
is continued
steps orthe
until
Maxwellian
velocity
distribution.
Eachthe
trajectory
ofby
the4rargon
molecule is continued to 50,000 time steps or until
the argon
molecule
escapes from
Pt surface
0, where r0 is the distance to the potential well of the Lennardthe argon
molecule
from
Pt molecule
surface byand
4r0Pt
, where
distance
to the
potential
wellfrom
of the
Jones
potentialescapes
between
the the
argon
atom. rThis
cutoff
distance
4r0 is
determined
theLennardcalculation
0 is the
Jones potential
argon
molecule
Pt atom.
This cutoff
distance
4r0kinetic
is determined
from the calculation
result of between
the total, the
kinetic
and
potentialand
energies
as shown
in Figs.
4. The
energy coincides
with the total
energy
withinkinetic
0.4% at
thepotential
4r0 fromenergies
the surface.
If the total
energy
argon energy
molecule
near the with
surface
result of
the total,
and
as shown
in Figs.
4. of
Thethekinetic
coincides
thebecomes
total
than0.4%
–2kBTats, the
it is4rregarded
as asurface.
trappingIfmolecule
removed
themolecule
calculation.
calculation
of each
energyless
within
the total and
energy
of thefrom
argon
nearAfter
the surface
becomes
0 from the
trajectory,
surface as
is reset
to the molecule
initial condition.
For each
of theAfter
incident
energy and
surface
less than
-2kBTs, the
it isPtregarded
a trapping
and removed
fromcombination
the calculation.
calculation
of each
temperature,
50,000istrajectories
areinitial
simulated.
trajectory,
the Pt surface
reset to the
condition. For each combination of the incident energy and surface
temperature, 50,000 trajectories are simulated.
362
Incident
Incident Ar Molecules
Ar Molecules
Incident
Angle θ i
in-plane
z
Reflection
Angle θ r
y
y
Pt
Surface
Pt (111)
(111) Surface
x
FIGURE 3. Simulation space
FIGURE 3. Simulation space
Gas-Surface Distance
[×r0 ] 5
[xr 0 ] 5
4
4
1 33
2
2
Ei = 6.23 kJ/mol
θ i = 45 degrees
= 45 degrees
Ts = 250 K
1
J=250K
0
H———I————
————I————
Kinetic
KineticEnergy
Energy .
Potential
Potential Energy
Energy
Total
Total Energy
Energy
Energy [×10
-20
J]
3
2
1
00
\i
-1-1
0
1000
1000
2000
3000
2000
3000
Time Step
Step
Time
4000
4000
FIGURE
4. 4.Histories
of of
thethe
distance
of Ar
from
the the
surface
and and
threethree
kindskinds
of energy
Histories
distance
of Ar
from
surface
of energy
FIGURE
363
SIMULATIONRESULTS
RESULTSAND
ANDDISCUSSION
DISCUSSION
SIMULATION
FluxDistribution
Distribution
Flux
Figures 55 are
are the
the flux
flux distributions
distributions ofof argon
argon molecules
molecules scattered
scattered from
from the
the Pt(lll)
Pt(111) surface
surface atat the
the surface
surface
Figures
temperatureTTs s==250
250and
and705
705 K,
K,respectively.
respectively. In
In Figs.
Figs. 55 the
the abscissas
abscissas are
are the
the reflection
reflection angle
angle measured
measured from
from the
the
temperature
surfacenormal,
normal,the
thecircles
circlesshow
showthe
thecalculated
calculateddistribution
distributionand
andthe
thesquares
squaresthe
theexperimental
experimentaldata
databy
byHurst
Hurstetetal.(5)
al.(5)
surface
Wecan
can see
see from
from Figs.
Figs. 55 that
that the
the peak
peak ofof the
the distribution
distribution shifts
shifts toward
toward the
the surface
surface normal
normal (toward
(toward the
the smaller
smaller
We
reflection
angle)
and
the
width
of
the
distribution
becomes
wider
with
an
increase
in
the
surface
temperature.
Alsoitit
reflection angle) and the width of the distribution becomes wider with an increase in the surface temperature. Also
is
evident
that
the
calculated
flux
distributions
agree
well
quantitatively
with
the
experimental
data.
is evident that the calculated flux distributions agree well quantitatively with the experimental data.
Caluculation
Calculation
Hurstetetal.
al.
Hurst
t]
D
6.23kJ/molkJ/mol
EEt i==6.23
45degrees
degrees
0.θ i==45
250 K
K
T s =250
T=
0.5
1
Intensity
Intensity
1
Caluculation
Caluculation
Hurstetetal.
al.
Hurst
6.29 kJ/mol
Ei =6.29kJ/mol£.=
45degrees
degrees
Q.θ i==45
705KK
T.Ts==705
0.5
a
at
00
30
30
60
90
60
90
Reflectionangle
angle [degrees]
[degrees]
Reflection
00
30
30
60
90
60
90
Reflection angle
angle [degrees]
[degrees]
Reflection
(a)
(b)
(b)
(a)
w
w
=(a)
250
K
and
(b)705
705K.
K.
Flux
distribution
of
Ar
scattered
from
Pt(111)
at
T
FIGURE
5.
FIGURE 5L Flux distribution of Ar scattered from Pt(l 11) at Ts s=(a) 250 K and (b)
TOF Spectra
TOF Spectra
Figures 6 show the TOF spectra of argon molecules scattered at the specular angle from Pt(111) surface whose
temperatures
are set
Ts =spectra
250 and
705 K,
respectively.
Theat abscissa
of each
means the
arrival
time
Figures 6 show
the at
TOF
of argon
molecules
scattered
the specular
anglefigure
from Pt(lll)
surface
whose
normalized
by
the
flight
path
divided
by
the
mean
velocity
of
the
incident
molecular
beam.
The
solid
curve
shows
temperatures are set at Ts = 250 and 705 K, respectively. The abscissa of each figure means the arrival time
the calculated
spectrum
and the
broken
the experimental
one
determined
by Hurst
et al.(5)
In Figs.
we can
normalized
by the
flight path
divided
by curve
the mean
velocity of the
incident
molecular
beam.
The solid
curve6 shows
see
the
peak
of
the
spectra
shifts
toward
shorter
flight
time
with
an
increase
in
the
surface
temperature.
The
the calculated spectrum and the broken curve the experimental one determined by Hurst et al.(5) In Figs. 6 we can
calculated
spectrum
agrees
with
the
experimental
one
except
slight
difference
between
the
peak
positions.
We
see the peak of the spectra shifts toward shorter flight time with an increase in the surface temperature. The
calculate the
experimental
of the scattered
molecules
Maxwellian
distribution
usingWe
the
calculated
spectrum
agrees TOF
with spectrum
the experimental
one except
slightassuming
differencethebetween
the peak
positions.
data of the
and temperature
given molecules
by Hurst etassuming
al. Thisthe
means
that the distribution
experimental
velocity
calculate
the macroscopic
experimental velocity
TOF spectrum
of the scattered
Maxwellian
using
the
distribution
shows only velocity
the directand
scattering
process
of the
molecules.
general,
is pointed
out that thevelocity
velocity
data
of the macroscopic
temperature
given
by Hurst
et al. InThis
meansit that
the experimental
distribution
of
the
scattered
molecules
consists
of
the
direct
scattering
process
with
the
macroscopic
velocity
and the
distribution shows only the direct scattering process of the molecules. In general, it is pointed out that the velocity
adsorption
and
desorption
process
without
that.
Therefore,
the
slight
difference
of
the
peak
positions
might
be the
due
distribution of the scattered molecules consists of the direct scattering process with the macroscopic velocity and
to
no
consideration
of
the
adsorption
and
desorption
process
for
data
by
Hurst
et
al.
We
believe
that
the
Phantom
adsorption and desorption process without that. Therefore, the slight difference of the peak positions might be due
model is very
effective
to predict
the TOF spectra
of for
the data
molecules
scattered
the surface,
especially
the
toParticle
no consideration
of the
adsorption
and desorption
process
by Hurst
et al. from
We believe
that the
Phantom
width
of
the
spectra
and
change
of
the
peak
position
depending
on
surface
temperature.
Particle model is very effective to predict the TOF spectra of the molecules scattered from the surface, especially the
width of the spectra and change of the peak position depending on surface temperature.
364
1
1
6.29kJ/mol
kJ/mol
E i ==6.29
E i == 6.23
6.23 kJ/mol
kJ/mol
θi =
= 45
45 degrees
degrees
Intensity
Calculation
Hurst et al.
0.5
0.5
00
Intensity
TTss =
K
= 250
250 K
>>
+->
•1-H
CO
,. =4545degrees
degrees
θi =
1
22
Time
Time
3
= 705 K
TT
s s= 705 K
———Calculation
Calculation
———Hurst
Hurstetetal.al.
0.5
0.5
4
00
1
22
Time
Time
(a)
(a)
3
4
(b)
(b)
FIGURE6.6. TOF
250 K and (b) 705 K.
TOF Spectra
Spectra of
of Ar
Ar scattered
scattered from
FIGURE
from Pt(111)
Pt(l 11)atatthe
thespecular
specularangle
angleatatTsT=(a)
s =(a) 250 K and (b) 705 K.
Average Energy Distribution
Average Energy Distribution
Using the TOF spectra, one can calculate the average energies <£r> of the scattered molecules normalized by the
Using the TOF spectra, one can calculate the average energies <Er> of the scattered molecules normalized by the
energy
E of the incident beam, as shown in Figs. 7. The abscissas in Figs. 7 are the reflection angle measured from
energy Et i of the incident beam, as shown in Figs. 7. The abscissas in Figs. 7 are the reflection angle measured from
the surface normal. In Figs. 7 the average energies show the tendency of the inelastic scattering explained by the
the surface normal. In Figs. 7 the average energies show the tendency of the inelastic scattering explained by the
hard-cube model at angles larger than 30 degrees where the calculated distribution is close to the experimental one
hard-cube model at angles larger than 30 degrees where the calculated distribution is close to the experimental one
by Hurst et al.(5) At the small angles, however, the former deviates from the latter. This might be attributed to the
by Hurst et al.(5) At the small angles, however, the former deviates from the latter. This might be attributed to the
statistical
the scattered
scattered argon
argon molecules
moleculesasasshown
shownininFigs.
Figs.5.5.
statisticalerror,
error,that
thatis,
is,the
theinsufficient
insufficient number
number of
of the
-i
3
|
i
i
3
Calculation
Calculation
n Hurst
et al.
al.
Hurst et
EEti == 6,23
6.23 kJ/mol
kJ/mol •
9θti =
= 45
45 degrees
degrees
7^
T s == 250
250 K
K
2
V
< E r> /E i
< Er > /E i
A^
• Calc
Calculation
ulation
n
Hurst
Hurst etet
a l.al.
6 . 2 9kJ/mol
kJ/molE£i ;==6.29
=
45
degrees
t
θ9
=
45
degrees
i
= 705 K
TT
s s= 705 K
•
•
•
•
2
V
1
1
D
00
30
30
60
90
90
R eflection angle
angle [degrees]
Reflection
00
30
30
60
60
RReflection
eflection angle
angle[degrees]
[degrees]
(a)
(b)
(a)
(b)
Average energy
energy distribution of scattered
FIGURE7.7. Average
FIGURE
scattered Ar
Armolecules
moleculesatatTTs s=(a)
=(a)250
250KKand
and(b)
(b)705
705K.K.
365
9090
Energy Exchange Rate
Energy Exchange Rate
The energy exchange rates are examined separately for the normal and a tangential energy. The energy exchange
2
2
rate of
theenergy
normal
energy isrates
calculated
from (<E
= (<Eand
>-<Elcos2^energy.
of the
rn>-<Ein>)/<E
rcos a^rtangential
l>)/<Elcos
l> and that
The
exchange
are examined
separately
for2 thein>normal
The^energy
exchange
2
2
tangential
energy
(<E
£>-<E
£>)l<E
£>
=
(<E
sin
^
>-<E
sin
^
>)/<E
sin
^
>,
where
E
and
2
2 Er are the 2kinetic energies of
r
i
i
r
r
l
l
/
l
t
rate of the normal energy is calculated from (<Ern>-<Ein>)/<Ein> = (<Ercos èr>-<Eicos èi>)/<Eicos èi> and that of the
the
incidentenergy
and scattered
molecule,
respectively,
and < >2means the 2average. Figures 8 show the energy exchange
2
tangential
(<Ert>-<E
it>)/<Eit> = (<Ersin èr>-<Eisin èi>)/<Eisin èi>, where Ei and Er are the kinetic energies of
rate
of
the
normal
and
tangential
energy,
calculated
energies.
In8Figs.
abscissa
is the
the incident and scattered molecule, respectively, andfor
< >several
means incident
the average.
Figures
show8,thethe
energy
exchange
incident
energy
and
the
solid
circles
are
the
simulation
results
at
6
=
45
degrees
and
T
=
250
K.
The
solid
t
s
rate of the normal and tangential energy, calculated for several incident energies. In Figs. 8, the abscissa iscurve
the
means
theenergy
energyand
exchange
rate
for full
of the atArè molecules
to the Pt surface and the broken line
incident
the solid
circles
areaccommodation
the simulation results
i = 45 degrees and Ts = 250 K. The solid curve
means
equalsrate
to the
average
energy of the
scattered
molecules
fullyPt accommodated
the solid
BTs which
meansE=2k
the energy
exchange
for full
accommodation
of the
Ar molecules
to the
surface and the to
broken
line
surface
at
T
.
In
the
case
ofE=2k
T
,
of
course,
the
energy
exchange
rate
equals
zero
theoretically.
s
B sthe average energy of the scattered molecules fully accommodated to the solid
means Ei=2k
T
which
equals
to
B s
It is clear
the Tenergy
exchange rates for the normal and tangential energy are very different.
surface
at Ts. from
In theFigs.
case8ofthat
Ei=2k
B s, of course, the energy exchange rate equals zero theoretically.
The It
normal
energy
indicates
the
similar
tendency
to rates
full accommodation,
whereas
the tangential
remains
is clear from Figs. 8 that the energy exchange
for the normal and
tangential
energy areenergy
very different.
constant
over
the
wide
range
of
the
incident
energy.
This
means
that
the
energy
exchange
of
the
gas
molecules
with
The normal energy indicates the similar tendency to full accommodation, whereas the tangential energy remains
the
solid surface
dominated
exchange
of theThis
normal
the same of
tendency
the previous
constant
over theiswide
range ofbythethe
incident
energy.
meansenergy,
that theshowing
energy exchange
the gas as
molecules
with
studies
for surface
relatively
incidentbyenergy,
i.e., theofthermal
scattering
regime.
the solid
is low
dominated
the exchange
the normal
energy,
showing the same tendency as the previous
studies for relatively low incident energy, i.e., the thermal scattering regime.
3
(< E rt >-< E it >)/< E it >
(< E rn>-< E in >)/< E in >
3
• Calculation
Calculation
Full
FullAccommodation
Accommodation
2
θi = 45 degrees
Ts = 250 K
1
0
-1
0
2kBTs
10
20
I
'
Calculation
Calculation
Full
Accommodation
Full Accommodation
2
=45
45degrees
degrees
θ0.i =
.
Ts = 250 K
1
0
-1
0
2kBTs
10
10
20
20
Incident Energy Eit [kJ/mol]
[kJ/mol]
IncidentEnergy
Energy EI
[kJ/mol]
Ei [kJ/mol]
Incident
(b)(b)
(a)(a)
Exchangerates
ratesof
of(a)
(a)normal
normal energy
energy and
and (b)
(b) tangential
tangential one of Ar molecules.
FIGURE8.8. Exchange
FIGURE
Trapping probability
probability
Trapping
Figures99show
showthe
therates
ratesofofthe
theAr
Armolecules
moleculestrapped
trapped on
on the
the Pt
Pt surface
surface for
for several
several incident
incident energies
energies at
at è0=30,
i=30, 45,
Figures
45,
60
degrees,
which
are
simulated
by
the
use
of
the
present
model.
With
increasing
the
incident
energy
and
decreasing
60 degrees, which are simulated by the use of the present model. With increasing the incident energy and decreasing
theincident
incidentangle,
angle,asasshown
shownininFig.
Fig.9(a),
9(a),the
thetrapping
trapping probability
probability decreases
decreases as
as reported
reported in
in many
many papers.
the
papers. Especially,
Especially,
these
results
also
agree
well
with
the
experimental
data
obtained
by
Mullins
et
al.(6)
If
the
trapping
probability
is
these results also agree well with the experimental data obtained
by
Mullins
et
al.(6)
If
the
trapping
probability
is
22è , and the power of cosine decreases with an increase in
dominated
only
by
the
normal
energy,
it
scales
with
E
cos
i
i
dominated only by the normal energy, it scales with ^cos ^ , and the power of cosine decreases with an increase
in
a7 èi, rather
cos0.7
contributionofofthe
thetangential
tangentialenergy
energytotothe
thetrapping
trappingprobability.
probability. The
The simulated
simulated data
data can
can scale
scale with
with E
EIi-cos
contribution
0I> rather
0.5
5
than
with
E
cos
è
given
by
Mullins
et
al.
We
think
that
this
scaling
of
our
data
agrees
with
the
experimental
i
than with Eicos°
0i igiven by Mullins et al. We think that this scaling of our data agrees with the experimental one
one
reasonably,because
becausethe
thedetection
detectionofofall
allmolecules
molecules scattered
scattered from
from the
the solid
solid surface
surface or
or all
all molecules
reasonably,
molecules adsorbed
adsorbed to
to that
that
verydifficult
difficultand
andthe
theexperimental
experimentaldata
datamay
mayinclude
include some
some error.
error.
isisvery
366
i 0.8
0.8
cd
0.66
§
I °w) 00.4
4
S
"EL
&0.2
0.2
H
0
0
1
i
•
TTsS =273
=273 K
K
0
θ i=30 degrees
0,-=30
degrees θ i=45 degrees
0f=45
degrees=6
de
rees
θ
degrees
^ i=60
° ^
-
A
D
AD
0
An D
o
A
o
A
D
A
n
n
_
g> 0.4
0.4
OH
-
g
0.2
°'
o
n
i
i
4
S
0^
2
I
00
i
TTs s==273
273KK •
—
θ i =30
0 0,=
30degrees
degrees .
A
0,θ- i==4 45
5 degrees
degrees_
n 0θ^i==6 60
0 degrees
degrees
_ n
6
0.6
1
°£
H
,
°.° o $
10
20
10
20
EEti [kJ/mol]
[kJ/mol]
i
0.8
i'*> 0.8
•f-H
n
i
11
i
Trapping Probability
Trapping Probability
1
1
^ DOA ,
A
0
10
20
10
20
0.7
0.7
£/cos
'
e
[kJ/mol]
E icos θti [kJ/mol]
(a) (a)
(b) (b)
FIGURE
11) atat7>273K
(b) ^cos°70.7
0t.
t, ,or
FIGURE 9.
9. Trapping
Trappingprobabilities
probabilitiesof
ofAr
Aron
onPt(l
Pt(111)
Ts=273Kasasfunction
functionofof(a)E
(a)E
i or (b) Eicos èi.
CONCLUDING
CONCLUDINGREMARKS
REMARKS
The
The Phantom
Phantom Particle
Particle model
model was
was applied
appliedtoto simulations
simulationsfor
forinteraction
interactionofofan
anAr
Armolecular
molecularbeam
beamwith
witha aPt(lll)
Pt(111)
surface.
The
validity
of
the
Phantom
Particle
model
as
a
solid
surface
was
clarified
by
comparing
the
surface. The validity of the Phantom Particle model as a solid surface was clarified by comparing thesimulation
simulation
results
results with
with the
the experimental
experimental ones,
ones, in
in which
which the
the same
same conditions
conditionsasasthe
theexperiments
experimentswere
wereused.
used. As
Asa aresult,
result,we
we
obtained
the
good
results
as
follows.
obtained the good results as follows.
1.
1. The
The calculated
calculated flux
flux distributions
distributions agreed
agreed well
wellquantitatively
quantitativelywith
withthe
theexperimental
experimentaldata
dataininthe
thewide
widerange
rangeofofthe
the
reflection
angle.
reflection angle.
2.
2. The
The TOP
TOF spectra
spectra at
at the
the specular
specular angle,
angle, especially
especiallythe
the width
widthofofthe
thespectra
spectraand
andchange
changeofofthe
thepeak
peakposition
position
depending
on
surface
temperature,
could
be
predicted
by
the
use
of
the
present
model.
depending on surface temperature, could be predicted by the use of the present model.
3.
3. The
The calculated
calculated average
average energy
energywas
wasclose
closetotothe
theexperimental
experimentalone
oneatatthe
thereflection
reflectionangle
anglelarger
largerthan
than3030degrees
degrees
whereas
at
the
small
angles
the
former
deviates
from
the
latter.
whereas at the small angles the former deviates from the latter.
4.
probabilities
with
4. The
The calculated
calculated trapping
trapping
probabilities agreed
agreed
with the
the experimental
experimentalones
onesexcept
exceptthe
thecalculated
calculatedresults
resultscould
could
07
05
scale
with
E^cos
0.7^ rather than with Z^cos 0.5^ given by Mullins et al.
scale with Eicos θi rather than with Eicos θi given by Mullins et al.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
The authors would like to acknowledge Professor A. E. Beylich and Dr. J. Blomer for their advice. The present
The authors would like to acknowledge Professor A. E. Beylich and Dr. J. Blömer for their advice. The present
study was supported by a grant -in-aid for Scientific Research (B) from the Japanese Ministry of Education, Science,
study was supported by a grant -in-aid for Scientific Research (B) from the Japanese Ministry of Education, Science,
Sports and Culture.
Sports and Culture.
REFERENCES
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1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
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Kittel, C., S.
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to solid
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ed.2375-2388
, John Wiley
& Sons, Inc., New York (1996).
Adelman,
A., and Doll,
J. D., state
J. Chem.
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Adelman,
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Doll, J.
J. Chem.
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Tully,
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Tully, J.C.,
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1975-1985.
Blomer,
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A.73
E.,(1980),
in the 20th
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Blömer,
J.,
and
Beylich,
A.
E.,
in
the
20th of Rarefied Gas Dynamics, ed. Ching Shem, Peking University Press, 1997, pp.
392-397.
392-397.
Hurst,
J. E., Wharton, L., Janda, K. C., and Auerbach, D. J., J. Chem. Phys. 78, 1559-1581 (1983).
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C., and Auerbach,
D. J.,
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78, 1559-1581
Mullins,
Rettner,L.,
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D. J., Chem.
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367