RADIATION DAMAGE IN ROCK-FORMING MINERALS
by
ROBERT EARL SCOTT
B.S., Massachusetts Institute of Technology
(1976)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May,. 1977
Signature of Author...
I.............
Department of Earth and Planetary Sciences, May 1-2,
Certified
.
by..........
..
.
1977
.e.*...........
Thesis Supervisor
Accepted by..
.
-.-
w..,....r.-.ym...
Chairperson, Departmental Committee on Theses
J0N 9 1977
wTL
ACKNOWLEDGEMENTS
My utmost thanks to Dr. Robert L. Huguenin for his suggestion
of the topic, invaluable advice, great willingness, continued encouragement and considerable time he gave me.
My gratitude to Professor Roger G. Burns for taking me on as
one of his advisees during the absence of Professor Thomas B.
McCord.
Thanks are also due to Professor Robert L. Coble for his comments, suggestions, advice and efforts in providing me with invaluable information.
I am very grateful to the Remote Sensing Laboratory for providing me with financial support in the form of research assistantship.
My thanks are extended to Ms. Kristine L. Andersen for her
advice, enthusiasm and encouragement throughout my studies.
Finally, my utmost praise to my dear friends: Gary S. Isaacs,
Jean Harrison, Colin Gardinier and Adrian Middleton whose patience,
continuous encouragement and great understanding were immeasureable.
But my warmest and greatest thanks goes to my father, mother,
brother, sisters, my niece Sharon and God, without whom life would
have no meaning.
To all of the above individuals and to all whom I might have
omitted; I offer my sincere thanks.
To
My
cousin,
the late Leonard Charles Mosley
RADIATION DAMAGE IN ROCK-FORMING MINERALS
by
ROBERT EARL SCOTT
Submitted to the Department of Earth and Planetary Sciences
on May 12, 1977, in partial fulfillment of the requirements
for the Degree of Master of Science
ABSTRACT
The apparent absence of metal coatings, produced by solarwind sputtering, on lunar samples indicates that the solar wind
does not modify the soils to the extent predicted by laboratory
studies. This suggests that the sputtering efficiency of the solar wind is somehow decreased in the lunar enviroment.
The model for backward sputtering of metals and oxides has
been reviewed. The predicted sputtering yields of metals and oxides in comparison with the experimental yield values turns out
to differ by at least a factor of 3 or better. For example, the
predicted yield for Cu and Fe at 1.85keV are 0.014 and 0.035, respectively, and the experimental values are 0.03 and 0.009, respectively.
The sputtering yields of metals and oxides, obtained from
modified theories of sputtering by Sigmund and Kelly, are used in
conjunction with the solar wind plasma-lunar surface magnetic field
interaction model to estimate the sputtering rates. The predicted
order of enrichment of metals in lunar soils is in very good agreement with the order of enrichment determined from ESCA studies of
lunar samples.
The interaction of the lunar surface magnetic fields with
the solar-wind protons has been reviewed. The solar-wind protons
are predicted to be completely stood off at the Apollo 16 landing
site, and their mean kinetic energies are reduced at other sites.
At the Apollo 12 landing site, for example, the protons lose about
30-80% of their nominal (lkeV) incident kinetic energy. The loss
in proton energy by interaction with compressed magnetic fields
reduces substantially the sputtering efficiency of the solar wind.
The unexpected low abundances of metal surface coatings can now
possibly be explained.
THESIS SUPERVISOR: Roger G. Burns
TITLE: Professor of Geochemistry
-
5
TABLE OF CONTENTS
TITLE PAGE..............................................1
ACKNOWLEDGEMENTS........................................2
ABSTRACT...............................................4
-TABLE OF CONTENTS
...................................... 5
LIST OF FIGURES AND TABLES..............................7
INTRODUCTION...........................................15
I.
BACKWARD SPUTTERING OF METALS AND OXIDES BY
HYDROGEN IONS
...........................................16
A. Theory of Sputtering............................16
B. Sputtering Yields of Metals for Protons at
Normal Incidence...............................26
C. Variation of Sputtering Yield with Angle
of Incidence for Metals........................30
D. Velocity Distribution of Sputtered Atoms.......33
E. Sputtering Yields of Oxides for Protons
at Normal Incidence............................36
F. Variation of Sputtering Yield with Angle
of Incidence for Metal Oxides...................38
G. Velocity Distribution of Sputtered Molecules ...39
II.
SPUTTERING EFFECTS ON THE LUNAR SURFACE................41
A. Lunar Magnetic Field...........................41
B. Reduction of the Mean Kinetic Energy of
Solar-Wind Protons at the Lunar Surface
by Magnetic Field Interaction...................42
C. Fraction of Sputtered Atoms that Escape
.................................. 43
from the Moon
D. Fraction of Sputtered Molecules that
Escape from the Moon...........................45
III.
PREFERENTIAL SPUTTERING:
METHOD FOR PREDICTING
THE ORDER OF ENRICHMENT OF METALS......................46
IV.
SUMMARY................................................48
APPENDIX I..............................................51
APPENDIX II....................
........................ 68
REFERENCES.............................................72
TABLES.................................................74
6
FIGURES ......--.-----------------
LIST OF FIGURES AND TABLES
I.
FIGURES
Geometry of Sputtering Calaulation........ o.
1.
Factor a in Eq.(25) for protons and deuter on s
2.
incident on a heavy targe t .................. ...
.
2a. Variation of the sputteri ng yield with angle
of incidence for Ar+ ions incident on polycrystalline copper........
3.
Sputtering yields for H+ ions incident on
aluminum.................
.. ..
4.
Sputtering yields for H+ ions incident on
.. ..
aluminum................. . .. .........
5.
Sputtering yields for H+ ions incident on
.. ..
calcium..................
6.
Sputtering yields for H+ ions incident on
.. ..
calcium..................
on
Sputtering yields for H+ ions incident on
7.
.. ..
chromium................. ions..............
8.
Sputtering yields for H+ ions incident on
.. ..
chromium.................
Sputtering yields for H+
9.
copper...................
.
.
.
.
.
10.
Sputtering yields for H+ ions incident on
.....
.
copper......................
incident
on
Sputtering yields for H+ ions
11.
gold.........................
.. cident... ..........
12.
Sputtering yields for H+ ions incident on
..........
.............
gold.........................
Sputtering yields for H+ ions incident on
13.
.. . ..
iron.........................
14.
Sputtering yields for H+ ions incident on
.....
iron........................
15.
Sputtering yields for H+ ions incident on
...
magnesium....................
Sputtering yields for H+ ions incident on
16.
....
magnesium....................
Sputtering yields for 1+ ions incident on
17.
manganese....................
..........
18.
Sputtering yields for H+ ions incident on
manganese.....................
...
Sputtering yields for H+ ions incident on
19.
nickel......................
Sputtering yields for H+ ions incident on
20.
nickel.......................
21.
Sputtering yields for H+ ions
.. . ..
oxygen.......................
22.
Sputtering yields for H+ ions
. . . . . . . .
oxygen.......................
....
0
18
.
27
34
. 111
. 112
. 113
. 114
. 115
. 116
117
...
118
119
120
. 121
122
.
. 123
124
125
.126
127
.
128
.
.129
. 130
...
23.
24.
25.
'26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
Sputtering yields for H+ ions incident on
........
potassium.........
............
Sputtering yields for 11+ ions incident on
..........
potassium.........
on
.+
incident
ions
for
yields
Sputtering
..........
silver............
on
incident
ions
11+
for
Sputtering yields
.
silver............
Sputtering yields for H ions incident on
silicon.....:.....
Sputtering yields for H+ ions incident on
.. . ..
. ........
silicon........... .............
Sputtering yields for H+ ions incident on
..........
sodium............ f......
o...s. incide
on
incident
ions
....
.
...
H+
9..
...
for
.0......
Sputtering yields
..........
sodium............
Sputtering yields
..........
titanium..........
on
ions
incident
H+
Sputtering yields for
.. .... ... .... . .
. . . . .
titanium.......... for H+ ions incident on ..........
Sputtering yields for H+ ions incident on
.
zinc..............
Sputtering yields
zinc.............. .. . . . . . . . .. . . . . . .
Variation of the sputtering yield with angle
of incidence for H+ ions on aluminum.........
Variation of the sputtering yield with angle
of incidence for H+ ions on calcium..........
Variation of the sputtering yield with angle
of incidence for H+ ions on chromium.........
Variation of the sputtering yield with angle'
of incidence for H+ ions on copper...........
Variation of the sputtering yield with angle
of incidence for H+ ions on gold.............
Variation of the sputtering yield with angle
of incidence for H+ ions on iron.............
Variation of the sputtering yield with angle
of incidence for H+ ions on magnesium........
Variation of the sputtering yield with angle
of incidence for H+ ions on manganese......... ......
Variation of the sputtering yield with angle
of incidence for H+ ions on nickel............
Variation of the sputtering yield with angle
of incidence for H+ ions on potassium......... ......
Variation of the sputtering yield with angle
of incidence for H+ ions on silver............ ......
Variation of the sputtering yield with angle
of incidence for H+ ions on sodium............ ......
.
40.
.
41.
.
42.
43.
44.
45.
45a.
o.131
132
133
134
135
.
. 136
137
138
139
140
. 141
.
. 142
143
.
.
145
.
146
.
.147
.148
.. 149
150
.151
152
153
154
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
Variation of the sputtering yield with angle
of incidence for H+ ions on titanium.........
Variation of the sputtering yield with angle
of incidence for H+ ions on zinc.............
Velocity distribution of ejected atoms for
H+ ions incident on aluminum.................
Velocity distribution of ejected atoms for
H+ ions incident on calcium..................
Velocity distribution of ejected atoms for
H+ ions incident on chromium.................
Velocity distribution of ejected atoms for
H+ ions incident on copper...................
Velocity distribution of ejected atoms for
H+ ions incident on gold.....................
Velocity distribution of ejected atoms for
H+ ions incident on iron....................
Velocity distribution of ejected atoms for
H+ ions incident on magnesium...............
Velocity distribution of ejected atoms for
H+ ions incident on manganese...............
Velocity distribution of ejected atoms for
H+ ions incident on nickel..................
Velocity distribution of ejected atoms for
H+ ions incident on potassium...............
Velocity distribution of ejected atoms for
H+ ions incident on silicon.................
Velocity distribution of ejected atoms for
H+ ions incident on silver..................
Velocity distribution of ejected atoms for
H+ ions incident on sodium..................
Velocity distribution of ejected atoms for
H+ ions incident on titanium................
Velocity distribution of ejected atoms for
H+ ions incident on zinc....................
Sputtering yields for H1+ ions incident on
Al
64.
65.
66.
67.
68.
69.
2
0
3
-'--&--'-&
.
.
.
.
.
.
.
-*-'''''
.
.
.
-.
.
.
.
.
.
.
Sputtering yields for H+ ions incident on
CaO.......................................
Sputtering yields for H+ ions incident on
FeO.......................................
Sputtering yields for H+ ions incident on
'. . .' .' . .' ' ''. . .
Fe 20 3 . *---. . ' '' .
.
Sputtering yields for H+ ions incident on
Fe 304
.. .. . . . . . . . . . . . . . . . . .*. . . . . . . . . . . . . -Sputtering yields for 11+ ions incident on
MgO.......................................
Sputtering yields for H+ ions incident on
MnO........................................
.......
155
.......
156
.......
157
158
.......
159
.......
160
161
.......
162
.......
163
.......
164
.......
165
.......
166
.......
167
.......
168
.......
169
.......
170
.......
171
.
.
'......172
.......
173
174
.
175
.
176
.
......-- 177
178
.
70.
71.
72.
'
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
II.
Sputtering yields for H+ ions incident on
TiO............................................. ..
Variation of the sputtering yield with angle
of incidence for H+ ions on Al 0 o.............. ....
Variation of the sputtering yield with angle
of incidence for H+ ions on CaO.................
Variation of the sputtering yield with angle
.of incidence.for H+ ions on FeO................. ....
Variation of the sputtering yield with angle
of incidence for 11+ ions on Fe 0................
Variation of the sputtering yield with angle
of incidence for H+ ions on Fe 0............... ....
Variation of the sputtering yield with angle
of incidence for H+ ions on MgO.................. ....
Variation of the sputtering yield with angle
of incidence for H+ ions on MnO.................
Variation of the sputtering yield with angle
of incidence for H+ ions on TiO ................ .
Velocity distribution of ejected molecules
for H+ ions incident on A1 2 03------------------- Velocity distribution of ejected molecules
for H+ ions incident on CaO.................... ....
Velocity distribution of ejected molecules
for H+ ions incident on FeO..................... ...
Velocity distribution of ejected molecules
for H+ ions incident on Fe 2 0 3 ----- . -------------- - --Velocity distribution of ejected molecules
for H+ ions incident on Fe 30 4 . . . . . . . . . . . .. . . . . . .
Velocity distribution of ejected molecules
for H+ ions incident on MgO......................
Velocity distribution of ejected molecules
for H+ ions incident on MnO...................... ....
Velocity distribution of ejected molecules
for H+ ions incident on TiO2 ---------------. -----
.
1 70
180
181
182
183
184
185
186
.187
-188
189
.190
191
. 192
.193
194
.195
TABLES
1.
2.
3.
4.
5.
6.
Effective depth of origin of sputtered atoms.......
Reduced nuclear stopping cross section sn(E)
for Thomas-Fermi interaction.......................
Calculated a,2 , E* and U. for various targets......
Averages over the range distribution...............
Calculated <AX 2 >/<X> 2 and <Y 2>/<X> 2 for
various targets....................................
Calculated E7,
V , and E
for aluminum
.24
.25
.28
.31
.32
Ip
p
bombarded by H+ ions........................... ..... * 75
and E
for calcium
7.
Calculated ET'
8.
bombarded by H+ ions................................75
Calculated ET Vp, and E for chromium
9.
bombarded by H+ ions.................................76
Calculated ET VP , and E for copper
10.
11.
12.
13.
14.
V,
bombarded by H+ ions................................76
Calculated E , V , and E for gold
TP
P
. . . . . 77
bombarded by H+ ions.................
Calculated T, VP, and E for iron
P
p
bombarded by H+ ions................................77
Calculated Y , Vp, and E for manganese
bombarded by H+ ions................................78
Calculated E , V , and E for magnesium
p
p
bombarded by H+ ions................................78
Calculated T V , and E for nickel
16.
bombarded by H+ ions................................79
Calculated ET, Vp, and E for potassium
V Vp
p
bombarded by H+ ions................................79
Calculated NT'Vp' and Ep for silicon
17.
bombarded by H+ ions................................80
Calculated T V , and E for silver
18.
bombarded by H+ ions................................80
Calculated ET V , and E for sodium
19.
bombarded by H+ ions................................81
Calculated E , Vp, and E for titanium
20.
bombarded by H+ ions................................81
Calculated E , V , and E for zinc
20a.
bombarded by H+ ions.................................82
Calculated fT' Vp , and E for oxygen
15.
21.
22.
82
bombarded by H+ ions.......................... ...........
Sputtering yield of oxides for H+ and H+ ions
83
at normal incidence........................... .......
at
H+
ions
for
oxides
of
yield
Sputtering
83
normal incidence.............................. &........
.
28.
Tabulation of the moments <AX 2 >/<X> 2 and
<Y 2 >/<X> 2 for oxides................................84
Molecular weight and binding energy of
metal oxides........................................85
Calculated ET V , and E for Al203
TP
p
bombarded by H+ ions................................86
Calculated E , V , and E for CaO
TP
p
. . . . . . 86
bombarded by H+ ions...
Calculated E , V , and E for FeO
p
. . . . . . 87
bombarded by H+ ions...............
Calculated ET' Vp, and E for Fe203
.
..
..
29.
bombarded by HI+ ions............... ...
Calculated ET' Vp, and E for Fe 3 04
bombarded by H+ ions...............
Calculated ET' Vp, and E for MgO
.
. .
.
30.
bombarded by H+ ions...............
Calculated ET' Vp, and E for MnO
. .
31.
23.
24.
25.
26.
.
27.
32.
33.
34.
35.
36.
37.
38.
39.
40.
.
..
.
87
. . 88
. .
.
.
. 88
.
. . . . . . 89
bombarded by H+ ions...............
Calculated ET V , and E for TiO
Tp
p2
bombarded by H+ ions................................89
Average chemical composition of lunar
surface regolith....................................90
Summary of lunar remanent magnetic field............91
The ratio of the solar-wind plasma pressure
to total magnetic field pressure....................92
Estimate of the sputtering rates at the
lunar surface.......................................93
Calculated F and F for aluminum
T
p
..................
bombarded by H+ ions.
95
Calculated F and F for calcium
T
p
. . -.- - 95
bombarded by H+ ions.
Calculated FT and F for chromium
T
p
. . . . . . 96
bombarded by H+ ions.
Calculated FT and F for copper
.
bombarded by H+ ions.................... .............
96
.
.
13
42.
Calculated FT and F for gold
T
pbombarded by H+ ions.
Calculated FT and F for iron
43.
bombarded by H+ ions.
Calculated FT and F for magnesium
41.
- -97
..............
.
46.
bombarded by H+ ions.
Calculated FT and Fp for manganese.
bombarded by H+ ions..........................
Calculated F and FP for nickel
T
bombarded by H+ ions.................. .9.....-....99
Calculated FT and F for potassiu
47.
bombarded by H+ ions....
Calculated FT and F for silicon
.
48.
bombarded by H+ ions....
Calculated FT and F for silver
.
49.
bombarded by H+ ions....
Calculated FT and F for sodium
50.
bombarded by H+ ions....
Calculated FT and F for titanium
44.
45.
52.
bombarded by H+ ions.
Calculated F and F for zinc
P
T
bombarded by H+ ions.
Calculated FT and F for oxygen
53.
bombarded by H+ ions............
Calculated FT and F for Al 203
51.
54.
55.
56.
.
-
.
-101
101
102
.-
.
bombarded by H+ ions.
Calculated FT Tand F P for CaO
.............
bombarded by H+ ions.........
Calculated F and F for FeO
P
T
bombarded by H+ ions.
Calculated FT and F for Fe 2 0 3
bombarded by H+ ions............
....
-----.--
102
....
103
-- - -. 103
-
.
-
-
.
-
-
-
-
-.-
-
104
104
.
14
57.
Calculated F T and Fp for Fe 304
bombarded by H+ ions. 0.
Calculated FT and F for MgO
.....
.58.
,
59.
60.
61.
62.
....
....
0
-
-
..
bombarded by H+ ions.
Calculated F and F for MnO
p
T
bombarded by'H+ ions.
Calculated FT and F for TiO2
105
.
.106
bombarded by H+ ions..........................
Sputtering rates at Moon under solar-wind
bombardment....................................
Comparison of AHs (M) and AHD (0) for some elements occuring in lunar soils.................. .....0 0109
.
.
INTRODUCTION
For many years the apparent absence of metal coatings, produced by solar-wind sputtering, on the lunar surface has been the
subject of controversy.
According to Hapke et al. [1975],
the
lunar fines are enriched in metallic Fe relative to the lunar
crystalline rocks.
The rocks typically have on the order of 0.1%
Fe, while the fines contain about 0.5% Fe, much of which is in the
superparamagnetic size range (<l00A).
Surfaces of many of the
grains in the fines are coated with an amorphous layer about 0.1
pm thick and are enriched in Fe.
ing evidence concerning the Fe.
However, there is some conflictBoth the fraction of grains con-
taining Fe and the degree of Fe enrichment are correlated with the
albedo.
The fines are deficient in oxygen relative to the crystal-
line rocks, although the extent to which this is due to the excess
Fe or due to a separate phenomenon is not clear.
This suggests
that the sputtering efficiency of the solar-wind protons is somehow decreased in the lunar enviroment.
In this thesis, sputtering yields of metal/oxide targets by
hydrogen ions are computed from modified theories of sputtering
by Sigmund [1969] and Kelly [1973], respectively.
The interaction
of solar-wind plasma with localized surface magnetic fields and
their effect on the sputtering efficiency of solar-wind protons
near the lunar surface is discussed.
The effects of sputtering on
thccomposition of lunar surface materials are discussed, and the
order of enrichment of metals in lunar surface materials is considered.
I.
BACKWARD SPUTTERING OF METALS.AND OXIDES BY HYDROGEN IONS
In the energy range leV to 2keV, very little experimental
data on the sputtering yield, S(atoms/ion), of metals and oxides
by hydrogen ions is available.
Grplund and Moore
[1960] used
electromagnetically analyzed ionic beams from a radiofrequency
source to study the sputtering yield for hydrogen ions normally
incident on Ag atoms at energies from 2 to 12keV.
KenKnight and
Wehner [1964) obtained sputtering yield data for hydrogen molecular ions normally incident on Be, Al, Ti, V, Fe, Co, Ni, Cu, Zr,
Mo, Pd, Ag, Ta, W, Re, Ir, Pt, and Au at 7keV by drilling holes
in thin target foils with magnetically separated hydrogen beams
(H+ and Ht).
Wehner et al. [1964a] obtained yield data for metals
(Cu, Fe) at 1.85keV and Oxides
(A12 0 3 , TiOl.,, FeO1 ,,, Fe2 03,
SiO 2 ) at %7.OkeV with the mass separation method.
The results for
protons can be inferred from the data provided by KenKnight and
Wehner [1964] and Wehner et al.
[1964a] since the hydrogen atoms
sputter independently.
It will be the object of the following section to review a
theoretical model for sputtering developed by Sigmund [1969].
We
will show that although the theory applies only to ions with masses much greater than that of hygrogen, an approximation can be
made that will alleviate this matter.
A. Theory of Sputtering
According to Sigmund [1969], the sputtering of a metal target
by energetic ions or recoil atoms is assumed to result from cas-
cades of atomic collisions.
The s'puttering is calculated under
the assumption of random slowing down in an infinite medium.
An
intergrodifferential equation for the yield is developed from the
general Boltzmann transport equation given by Eq.(l)
LGvx ,td
sv d x
G
x ,f,
V
where
v
G(xVi0
~
=magnitude
vo
N
da
Yt)d'v~dx
of arbitrary velocity vector
of an atom in a plane x=O at a time t=O,
density of target atoms
differential cross section [=da(;, 9', 9")
=k(i, V', 9")d 3 v'd 3 V",
Eaverage number of atoms moving at time t in
layer (x, dx) with velocity (v., d 3 V 0 ),
E velocity of atoms in a plane at time t,
E velocity of scattered particle,
E velocity of recoiling atom,
va/v.
The sputtering yield for backward sputtering of a metal target with
a plane surface at x=O (see fig.1) is then
(00
=
d0vv
(2
G (o,4
V,,t)
where the integration over dsv. extends over all v. with negative
x components large enough to overcome surface binding forces.
Multiplying Eq.(l) by dt and integrating over the interval (O,w)
we have
V'~~
~~~
tcc
C
-(
F -x(,v
18
dx
v
Ion
Target atom
(@o,dsv0 )
x
x=0
t=o
Fig. 1.
where
F
Geometry
1969].
of Sputtering calculation.
[From Sigmund,
Ct
= , G
x,0,)
t=t
E(xv 0 Iv.,
dcvx.E total number of atoms that penetrate
the plane x with a velocity (v,d 3 V)
during the development of the collision
cascade
G(
,Jt=o)- b(x)(-1. E one starting particle
and G(x,W4,oo)
0
since all starting particles have slowed down
below any finite velocity v0 .
If we consider only backward sputtering and introduce the
function
H L,;) =dv
with
vlFx49
no = vOX/v < 0
=
M 2 v2/2 > U(no)
H 2 E mass of the metal target atom
where U(n0 ) is the surface binding energy that, in general, depends
on the direction of ejection, characterized by the direction cosine
n o , Eq.(3) takes the following form
Introducing the function
= l-for
OM()
>O
= 0 for C<O
and satisfying the condition E.
=
M 2 v2/2 > U(no) and n.
=
vox/vo
< 0, Eq.(4) can be rewritten as
- b(x) OI-77) e(E-U()))-
x
N/d
( H~ysi
-IyA') -N(x,9")
(5
By introducing energy instead of velocity variables, we finally
obtain
0()
where E', T1',
NU do
HU,,2)-(xE,,'-
xE,2')
E" and a" are the energies and directional cosines
with respect to the x-axis of the scattered and recoiling particle
respectively.
The sputter yield is given by
S(EI)
=
H(x=0,E,9).
Expanding H in terms of the Legendre polynomials
21
(7
(Pk(nj)) we have
H(
H(y,E,-)
(23+1-)
,(x,
E) P(-g
(8
20
Multiplying Eq.(6) by P (I) and integrating over all possible
fl(n . 0) we find that
6(x) QE
)
[),
-
(x,E)l
(2L+0) N
[jH(x,%I) 1-
d-
-yP(co-."
where
(E)
)
H(X, E')
(9
Hjq (x, E"l)J
(-7)d- G(E-(3))
2
$'
(cos
P
(10
)
E laboratory scattering angle of scattered atom
$"Elaboratory scattering angle of recoiling atom.
integrate over all pos-
If we multiply Eq.(9) by xn(n=0,1,2,3,-..),
sible x, and introduce the moment integral
H,"(E) =
0u0
x" HI(x, E) dx
(11
we have
bao
(
-4
,AM
(E) +I-(U+1)
-P,(co
with
i*@o
')
H-'
E)
0
(E)
-
Pt(cm,
-J (2+1) N~fI
#4;
C (Hj"( E)
(12
CE")]
6t.x) x" dix
If we separate elastic from inelastic (electronic) collisions using
a method proposed by Li'ndhard et al. [1963], Eq.(12) becomes
E.
beQ,( E) -n
j(2
+ ,' (E
1) N
-' L
(21+ ) N S,(El
(E)
+ (A +
do- U , T ) [ H n (E )-P(..s
H
(E)
(1
(13
g(E-T)
0 ' )"(T)'T)
S E electronic stopping cross section,
d (E,Tr E differential cross section for elastic scattering,
(1-T/E) 1/2 + (1-M2/Ml) (T/E) (1-T/E)..../21
cos $'
cos $"E (T/Tm)1/2,
Tm
[4MiM 2 /(MI + M 2 ) 2 ]EE maximum recoil energy,
M Emass of ion.
where
For n=0 Eq.(13) yields
d (E,T) . ,(E I - P. tcos 1)i(E -T )
Qt( E) =(21-r )N
where it
(0.<.m.1)
is
With
assumed that Se(E)=O.
(14
HT)
do(ET): C.NE~~ T~'~
dT
,
the following expressions are given for the source terms
in Eq. (10)
Q.(E)
Q,(E)
L((I -,/
E)
(15a
1 1[-t+
(U, /E)]
(15b
S(E) =
[1 + 2U,/E -
QUC)
L - (u,/E-)3/Z + NO
-=
3
(0./E)a],
(15c
3 (15d
where we have used the identity U(no) = U./rO. For E<UO, the source
term takes on the following value
Q0(E)
and
0
=
0
andH
H(E) '= 0.
The following expressions for the leading terms of an asymptotic expansion, in powers of E, of the moment HO(E) is given below.
i
H' (E)
16a)
*
V
cu,'-
-2m
16c)
I/M
where
B( ,i)
+
E
4
E
m
-V(-m)
-8(1-4
-2/M
M) + 38t-m, Z. Zmi + Z
-
,cu,)
eNc
m
Beta function =
T( ) E Digamma function = d/d (lnF( ))
For m=O Eqs.(16a-16d) take the following form (see Appendix I)
H' (E)
4
,E)
4
4-'(1)
E
(7
(17a
E
C6 U011
2
( 7
(17c
-(E ) ,
with
where
T'(E)
C.
X.
a
(T'(l)
d/d(V(()),
= ivXa 2/2
= 24
= 0.219A.
=
=
72/6
(18
The moment HO(E) is the leading term at all energies E>>Uo
and it has the asymptotic form given by Eq.(17a).
is the integral of H0 (x,E) over all x'.
The moment HO(E)
It determines the number
of atoms penetrating a plane at an arbitrary position x with a
certain minimum energy when there is a homogeneous isotropic source
of recoiling atoms throughout an infinite medium.
Since Hi(E) is proportional to E, for elastic scattering, E
23
so that Eq.(17a) takes the form
in Eq.(17a) is replaced by v(E),
V
H (E)
(C)
(19
N C.U,
8'(0)
where v(E)/E is the fraction of the energy that is not lost to
ionization during the slowing down process.
Using the expression
/I.
dx F(x,
and Eqs. (8,11 and 18),
E,->
= v(E)
Eq. (19) can be rewritten as
4E
4-V2
~
t4
cu,
E.1)
Li0
U'
(20
where Ax = 3/4NCO is the expression for the effective depth of
origin of sputtered atoms.
The effective sputterind depth Ax is
given for a few metals and metal oxides in Table 1.
The sputtering yield of a metal target for normally incident
ions is given by
$(E)
where
S%(E)
EIAi-m>
C'~'"
= A oL N SCE)
E - Zr"
(21
is the elastic stopping power of
the ion, a is the factor that depends only on m and M 2 /Mj and
A =
(3/47r 2) (1/NCOUO).
If the energy of the impinging ion, E, is less than some limiting energy
24
Metal
AX(A)
Oxide
AX(A)
Ag
Au
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Ni
Si
Ti
Zn
15.4
3.9
2.1
26.7
5.8
4.8
5.3
48.1
23.9
5.7
42.7
4.7
17.9
9.1
5.8
Al203
CaO
Cr 2 03
FeO
Fe203
Fe304
MgO
MnO
TiO 2
10.4
12.4
8.0
7.2
7.9
8.0
11.6
7.7
9.8
Table
1.
Effective depth of origin of sputtered atoms.
E* =
with
I' , e 2
Z,
2_
a
-. Ma
X
= 1.309
a
=
(22
a2
0.219A
0
= Bohr raius = 0.529A
= 0.8853(Z 2 3 + Z /3)-1/2
a.
a 2
E
atomic number of ion
E atomic number of metal target atom
Z2
the elastic stopping power assumes the following form
Sn(E) = CTm.
(23
For E>E*, in the elastic collision region, Eq. (23) becomes
S,
where e =
(E)= 4--n Z, 2 e a
Ea
M /(MI+M
2 )]
S,,e
(24
[M2E/(M 1 +M 2 )]/EZ 1 Z 2e 2 /a 12] and sn(E) is the universal
function tabulated in Table 2.
E
0.002
0.004
0.01
0.02
.0.04
0.1
0.2
Table
2.
sn(E)
E
0.120
0.154
0.211
0.261
0.311
0.372
0.403
0.4
1.0
2.0
4.0
10
20
40
sn(C)
0.405
0.356
0.291
0.214
0.128
0.0813
0.0493
Reduced nuclear stopping cross section sn(E) for
Thomas-Fermi interaction.
[From Sigmund, 1969].
Utilizing the expressions given by Eqs.(23 and 24),
Eq.(21) can be
written in its final form,
S(E)
=
(3/4rz)
eL T.
/U.2
(25
26
S(E)
-
04Zc)
. 4-n
Z, 2 e~za,
U.
[N\, /(M
(25
2
Expression (25) holds only for M 1 > M 2 .
ton sputtering Mi << M
E> E'
tMz)]sn(e)
In the case of pro-
This implies that expression (25) is in-
valid unless the parameter a is improved by a method described in
the next section.
B. Sputtering Yields of Metals for Protons at Normal Incidence
Before calculating the yield curves of metals, we have to
make a decision concerning the parameter a shown in figure 2 and
the surface binding condition.
Figure 2
shows a as a function of c for protons and deuterons.
The curves are rough estimates.
In order to improve a, we scaled
it to the sputtering yield value of Ag for normally incident H
at 2keV provided by Grolund and Moore [1960].
We found that a
better estimate of a is given by the following expression
a' = a/2.
For metals, the surface binding energy U. is equal to the
measured sublimation energy.
In Table 3, we have computed a 1 2 , E* and listed the sublimation energy (U0 ), the atomic number (Z2 ) and the mass (M2 ) of the
following metals:
Al, Ca, Cr, Cu, Au, Fe, Mg, Ni, K, Ag, Na, Ti
and Zn.
From Eq.(25) and the data provided by Fig.(2)
,
Tables 2 and
3, the yield curves were calculated for the metals listed in Table
3 (see Figures 3-34).
27
2.5
2.0-
DEUTERONS
~
a
1.0
0.5-
0.1
Fig. 2.
L.
-0
Factor a in Eq.(25) for protons and deuterons
[From Sigmund, 19691.
incident on a heavy target.
.28
(A)
Metal
al
Al
Ca
Cr
Cu
Au
Fe
Mg
Mn
Ni
K
Ag
Si
Na
Ti
Zn
0.1833
0.1619
0.1535
0.1450
0.1063
0.1498
0.1875
0.1516
0.1465
0.1644
0.1251
0.1795
0.1921
0.1575.
0.1435
Table
3.
2
E* (eV)
U0 (eV/atom)1
13.5
17.3
18.5
19.9
28.8
19.1
3.34
1.825
4.10
3.50
3.78
4.29
1.53
2.98
4.435
0.941
2.96
4.64
1.13
4.855
1.35
14.1
18.8
19.8
30.0
23.8
15.0
13.6
18.0
20.3
M2 (amu)
26
12
25
28
19
47
14
11
22
30
26.98154
40.08
51.996
63.546
196.9665
55.847
24.312
54.938
58.71
39.09
107.868
28.086
22.9898
47.9
65.38
Calculated a1 , E*, and U. for various targets.
2
1 From C. Kittel [19761
29
Grglund and Moore [1960] reports yield values for H+ ions
incident on Ag targets (see Fig. 26).
The predicted sputtering
yields are slightly larger than Grolund and Moore's reported values by a factor of %l.3.
The agreement with theory is surprising-
ly good.
KenKnight and Wehner [1964] reports yield data for light ions
(H+,H ) incident on Al, Au, Fe, Ni, and Ti at 7keV, and on Cu at
energies from 1 to 5keV.
The results for protons were deduced
from the data provided by KenKnight and Wehner [see Figs.(4, 10,
12, 14, 20, 26 and 30)].
The predicted sputtering yields differ from
KenKnight and Wehner's reported values by a factor which ranges
from 1.04 for Cu to 2.9 for Fe.
Wehner
[1964] reports yield values for H+ ions on Fe and Cu
targets at 1.85keV [see figs.(10,14)].
The predicted sputtering
yields in this case differ from the reported values by a factor of
2.1 for Cu and 3.9 for Fe.
The agreement between theoretical and experimental values at
low energies are not as good for Fe as it was in the case of Ag and
Cu.
This discrepancy can be explained as follows:
1) The assumption of random slowing down and of binary col-
lisions may break down at low energies.
There may be a small con-
tribution from focused collision sequences.
The quantitative ef-
fect on the sputtering yield will depend on the target.
2) The uncertainty of the low-energy cross section, as defined
30
by da = CodT/T, a fects the numerical factor in front of Eq.(20),
the value of C. (that may depend on the target), and the dependence
on U0 .
3) The surface binding condition U(ro) = U0 /n
affects the
numerical factor in front of Eq.(20); the value of U. is not known
from first principles but determines the magnitude of the yield.
4) The assumption of a plane surface may influence the magnitude of the yield.
So long as surface roughness is on a scale
that is small compared to the dimensions of the cascades, its effect on the sputtering yield will often average out.
Surface
roughness on a large scale, however, will tend to increase the
yield.
The quantitative effect depends on the geometry and can be
estimated when the shape of the surface is known.
5) The assumption of an infinite medium may also affect the
flux of low-energy recoils.[Sigmund, 1969]
There is no way of estimating the uncertainty in the theoretical sputtering yield values from the above points, but from comparison of both theoretical and experimental data one has to expect an uncertainty of at least a factor of 2 and in some cases
3.
C. Variation of Sputtering Yield with Angle of Incidence for
Metals
In Section I.B. we reported sputtering yield values for normally incident hydrogen ions.
It appears most reasonable to con-
sider the variation of the sputtering yield with the angle of in-
cidence.
According to Sigmund [1969], the dependence of the sputtering
yield S(E,n) on the angle of incidence, fl, can be estimated by the
following expression
(.7a)+1- ,YI
S
where S(E,1)
is
<1 7->
(_r
i)
(F.,
-.1/2
EX
2-&x->
](~26
-
)t-
-.
ZX
the yield for perpendicular incidence.
The moments
<X>, <AX 2 >, and <Y 2 > were. tabulated by Sigmund and Sanders [1967]
and are given in Table 4.
11 2/M
<X>
1/10
1/4
1/2
1
2
4
10
0.842
0.577
0.453
0.369
0.297
0.229
0.153
Table
/NC1
4.
<AX2>
<X>L
0.058
0.125
0.195
0.275
0.409
0.170
1.684
<Y2>_
<XY 2 >
<X>2
<X><Y4>
0.018
0.044
0.089
0.176
0.343
0.674
1.671
1.07
1.16
1.20
1.20
1.16
1.12
1.07
<AX 3 >
<X> -
0.007
0.021
0.043
0.079
0.135
0.221
0.345
Averages over the range distribution. M / M 2 '
[From Sigmund and anders,
dal=C E 1 2T 3 2 dT.
1967].
The values of <AX 2 >/<X> 2 and <Y 2 >/<X> 2 for M 2 /M1 > 10 were computed by fitting the best straight line of the form y=ax+b and
a power curve of the form y=axb, respectively, to the data points
given in Table 4 [see Table 5 and Appendix II].
Inserting the values of <AX 2 >/<X> 2 and <Y 2 >/<X> 2 into Eq.(26),
we obtain the variation of yield with q [see Figs.(35-47)].
cording to Sigmund [1969],
Ac-
the sputtering yield goes through a
32
Metal
<Ax2
26.8
Al
Ca
Cr
Cu
Au
Fe
Mg
Mn
Ni
K
Si
Ag
Na
Ti
Zn
Table
39.8
51.6
63.0
195.4
55.4
24.1
54.5
58.2
38.8
27.9
107.0
22.8
47.5
64.9
5.
4.363
6.437
8.320
10.139
31.263
8.926
3.932
8.782
9.373
6.277
4.538
17.159
3.725
7.666
10.442
2
2
2
4.409
6.505
8.397
10.218
31.098
9.005
3.972
8.861
9.452
6.344
4.587
17.201
3.761
7.740
10.521
Calculated <Ax 2 >/<x> 2 'and <Y 2 >/<x> 2 for various targets.
33
maximum at very oblique incidence and approaches zero for 0=90*.
This maximum cannot be explained on the basis of the assumption
of an infinite medium.
There will be a certain glancing angle at
which the repulsive action of the surface atoms is strong enough
to prevent the ions fr6m penetrating into the metal target, and
this angle will be a function of the structure of the target's
surface.
Dupp and Scharmann 11966],
Cheney and Pitkin [1965], and
Colombie [1964] reported values of the ratio S(E,n)/S(E,1) for
Ar+ ion incident on polycrystalline copper (see Fig. 2a).
The
agreement between theoretical prediction and experimental data is
quite good for 0<700.
D. Velocity Distribution of Sputtered Atoms
In a later section we will be conserned with the fraction of
To calculate
atoms that escape the Moon by natural sputtering.
this we need the velocity distribution of sputtered atoms.
The average energy ET transferred to a target atom by a collision with an energetic ion is given by the following expression
E
= [2M,
2 /(M+N7)
2
] E;
where Ei is the energy of the impinging ion.
(27
The number of atoms
ejected from the target, having a velocity between v and v+dv, is
given by the expression below
.dV
27X N
3tN2
V
.EP
[
MY1
KIEflP L- E
1
2E,] dv
(28
*/
THEORY
-PRESENT
-1
81r
of of
MOLC MANOV
(COS
-*--*
RL
/
t.
0
* DUPP of o./
2
-
O CHENEY 99at.
* COLOMB 'E
/
'
Fig. 2a.
/
O
Variation of the sputtering yield with angle of
incidence for Ar+ ions incident on polycrystalline
copper. Thick solid curve: Eq.(26): thin solid
curve:
1/cos 0. [From Sigmund , 1969].
where f is known as the Maxwell-Boltzmann distribution function
The most prob-
and Eb is the surface binding energy of the target.
able velocity, vp, of the recoil atoms can be obtained by finding
the velocity at which the function f has a maximum value.
It is
given by the equation
df/dv = 0.
From Eq. (28)
(29
we obtain
2n N n7_dv
r
I
2v rxp
tv
3
-AI
E-/ZE- 3
Ev22
exr(-3AA2 v2/4-r)3
0
Ex
2
- v2
_-3MZV2/4EJ
2i -- P2/
(3MZ/4
Ex(-3MzvZ/4%4'3
"
-- ) Z-v EXP [-M~v1/4E.t3:0
'-
Therefore
V
rA2(30
Z
Er= M-Lv,2 /3
In Tables 6-20, vp, E
and ET are tabulated for various targets.
The velocity distribution, df/dv, of the recoil atoms ejected
can be obtained by differentiating the Maxwell-Boltzmann distribution function f with respect to the velocity v.
the following equation,
It is given by
- 36
df
dv
E I
v
/
-
4E
2
/
Substitution of the values for M2,
EXr-3E
/zP1
(31
LEx
[-3Mzv/4~)
Eb abd ET into Eq. (31) gives us
the velocity distribution for various targets [see Figs.(48-62)].
Note that.the velocity.distribution of the sputtered atoms peak
heavily at very small velocities (3-9km/sec) in comparison with
the velocities of the incident protons [(l.4-4.4)x10 2 km/sec].
E. Sputtering Yields of Oxides for Protons at Normal Incidence
The sputtering behavior of oxides is different from that of
metals.
According to Kelly and Lam [1973],
the sputtering behavior
of oxides is in some cases "normal" in the sense of following Sigmund's theory of collisional sputtering.
In other cases the be-
havior is "abnormal", in that the collisional sputtering is
supplemented by thermal sputtering or by oxygen sputtering.
The collisional sputtering yield of oxides cannot be explained
by Sigmund's theory.
Instead, two approximations were used:
One
is to use Eq.(25) with the mean atomic weight of the oxide substituted; while the other is to use Eq.(25) in a form which is weighted
for the mole fractions of metal and oxygen,
where
+
X = L(A/E)]/{(A/E)
A E weighted percent
B E molecular weight
E E molecular weight
(100-A)/B],
of solute,
of solvent,
of solute.
The sputtering yields are tabulated with the aid of Figs.(3-34).
The results are shown in Figs.(63-70).
Wehner [1964] reports yield values for light ions (H+,H+)
incident on Al 2 0 3 ' TiO 2 , FeO, Fe 2 03 and Sio2 at 6-7keV [Table 21].
The results for protons were deduced from the data in Table 21
[see Table 22].
The predicted sputtering yields differ from
Wehner's reported values by a factor of 2 except in the case of
SiO 2 , which differs by a factor of 8.4.
This discrepancy may be
accounted for by oxygen sputterind and/or thermal sputtering.
Wehner et al. [1963] studied the effects of H+ bombardment
of Al 2 0 3, CuO, Cu 2 0, FeO, Fe 2 0 3 , and various rock powders at a
temperature of 300*C.
The results can be summarized as follows:
1) The surface of many materials, after sufficient bombardment, becomes covered with a brittle crust in which individual
dust particles become cemented together by sputtered atoms.
In
Al 2 0 3 only very little or very fragile crusting is observed.
The
crust is thicker in more loosely packed places or materials.
2) The surface layer of many compounds becomes enriched with
metal atoms.
Black CuO is first converted into red Cu 2 0 before
becoming covered with a very porous Cu layer.
The red Fe 2 03 con-
verts into Fe 3 0,, then to ferromagnetic FeO, and finally Fe metal
traces appear on the surface.
The reduction to a composition rich-
er in metal and the formation of a "metal black" causes a darkening
of the surface in most cases.
In the process of breaking up mol-
38
ecules under bombardment and of sputtering atoms back and forth,
oxygen atoms are more likely to escape from the surface than metal
atoms.
3) As previously note for metal oxides, whenever a crust is
formed it has a fibrous- structure with closely spaced needles and
spires and deep small holes all aligned in the direction of the
ion bombardment.
The predominance of microscopically very steep
walls is evidenced by the fact that the surface looks rather dark
when viewed in isotropic light, but becomes shiny when illuminated
and viewed from the same oblique angle.
Another effect of sputtering the oxides with hydrogen ions
is that water molecules can form by implantation of H+ and incipient formation of OH.
The water molecules can be driven from the
target by thermall y heating the oxide or bombarding it with ultraviolet radiation [R.L. Huguenin, personal communication].
F. Variation of Sputtering Yield with Angle of Incidence for
Metal Oxides
The procedure for estimating the dependence of the sputtering
yield, S(E,), on the angle of incidence q in the case of oxides
is quite similar to that used in the case of metals.
Recalling
Eq. (26) we have
E,7r
The necessary moments are tabulated in Table 23.
ZX~
Using the infor-
mation provided by Table 23 we obt'ained an estimate of the dependence of the sputtering yield on the angle of incidence [see Figs.
(71-78)] and we note thatfor heavier oxides
(Fe3 0 4) the difference
between S(E,q) for normal incidence and grazing incidence is small
in comparison with the lighter oxides (MgO,CaO).
G. Velocity Distribution of Sputtered Molecules
In a later section we will be concerned with the order of enrichment of oxides in the lunar material.
In order to calculate
the fraction of oxides which remain in the surface, we need to
calculate the escape velocity of oxides which are representative
of the lunar surface.
Utilizing the information provided by Table 24 and Eqs.(27
and 30) we are able to compute v., Ep as well as ET for metal oxides (see Tables 25-32).
Substitution of the values for M 2, Eb
and ET into Eq.(31) yields the velocity distributions Isee Figs.
(79-86)].
Note that at E =lkeV the velocity distribution of the
sputtered molecules peaks heavily at v=(1-2km/sec) for the heavier
oxides and at v=(3-4km/sec) for the lighter ones.
Statistically
more light than heavy molecules should be given sufficient energy
to escape the solid during sputtering, therefore MgO would be
sputtered in preference to Fe 3 0 .
The collisional sputtering
model indicates that the major oxides should be enriched in proportion to their molecular weights and predicts the following order of enrichment:
Fe 3 0 4 >Fe 2o 3 >Al 2 0 3 >TiO 2 >FeO>MnO>CaO>MgO. As we
40
will discuss in a later section, the actual order of enrichment
observed is Al 2 0 3 >FeO>CaO>MgO>TiO2 for Lunar Maria and Al 20 3 >CaO>
MgO>FeO>TiO 2 for Lunar Highlands
[Taylor, 1975]
(see Table 33).
There is no explanation, at the writing of this thesis, for the
discrepancy in the ordering of TiO 2 '
II.
SPUTTERING EFFECTS ON THE LUNAR SURFACE
The lunar surface is continually bombarded by intense solar
radiation.
The surface is unprotected by an atmosphere or strong
magnetic field; thus solar illumination is unattenuated at all wavelengths and high energy protons and other ions are allowed to reach
the surface.
Laboratory studies of the interaction of the solar
wind with the surface indicate that the optical properties and composition of the soil should have been greatly modified.
One of
the predicted modifications is that the soil particles should be
coated with metallic Fe, produced by solar-wind sputtering.
When
lunar samples were returned to the earth, metal coatings were not
found.
The apparent absence of metal coatings indicates that the
solar wind does not modify the soils to the predicted extent.
In Section B, I will show that the solar-wind protons are
reduced in energy by interaction with surface magnetic fields; thus
their sputtering efficiency is greatly reduced.
If this is true,
then the observed low abundances of metal surface coatings can be
at least in part explained.
A. Lunar Magnetic Field
The magnetic fields associated with the electrical currents
produced by electromagnetic excitation of the Moon were measured
at the Apollo landing sites.
Steady remanent magnetic fields were
measured on the lunar surface at the Apollo 12, 14, 15 and 16
landing sites by a surface magnetometer.
Table 34 gives the mag-
nitudes of the remanent fields at these sites.
Lin et al.
[1976] were able to measure lunar surface magnetic
fields down to a spatial scale of 7km by the electron reflection
method.
%5*S
The area'observed extends from 150 E to 500 E longitude at
latitude.
The field strengths.range up to bl0 2y, averaged
over the resolution element (see Table 34).
B. Reduction of the Mean Kinetic Energy of Solar-Wind Protons
at the Lunar Surface by Magnetic Field Interaction
According to Scott [1976],
the streaming solar-wind plasma
has a magnetic field associated with it, which exerts a magnetic
'pressure' on the remanent magnetic fields associated with the
lunar surface.
This pressure acts to compress the surface field.
If the local surface field is strong enough, it can stop the wind
before it reaches the surface, i.e. a bow shock is formed.
A
weaker field would not stop the wind, but would reduce its incident
energy at the surface.
In order to determine to what extent the protons are slowed
by the magnetic field compression, it is necessary to determine
the strengths of the local remanent fields.
Steady remanent fields
have been measured at nine surface sites during the Apollo 12, 14,
15 and 16 missions and also in the region located at
%50S
latitude,
15 0 E-50 0 E longitude.
The ratio of the plasma pressure to the total magnetic pressure is expressed as
n mv 2 /(Bt2 /8r)
(33
st
p p s
AB is the total surface compressed field,
=
where Bst
=B
S+
B S H steady remanent field,
and
B
E B A- (B E+BS),
BA = total surface field,
BE E extralunar field measured by Explorer 35,
vs E solar wind velocity (4.376x102 km/sec),
= proton density,
p .
m E proton mass.
n
The values for
<l implies that the steady remanent field is
compressed to the stagnation magnitude required to stand off the
solar wind.
>l implies that the steady remanent field is not com-
pressed to the stagnation magnitude required to stand off the solarwind plasma (see Table 35).
The compressed remanent field reduces the mean energy and.
velocity of the protons at one site by as much as 459eV and l.1x10 2
km/sec, respectively.
Such reduction i'
incident proton energies
would substantially reduce the sputterin,<efficiency of the protons.
In order to arrive at a reliable estimate of the sputtering
rates on the lunar surface, the flux, incident energy of the proton and the sputtering yields of lunar soils have to be known.
Assuming a flux of 4x10 8 protons/cm 2 sec [Formisano and Moreno,
1971] and using the data in Table 35 and Figs.(3-34 and 63-70), an
estimate of the sputtering rates on the lunar surface is obtained
(see Table 36).
C. Fraction of Sputtered Atoms that Escape from the Moon
In order to obtain' an estimate of the amount of material lost
from the Moon (metal coatings, oxides), we have to compute the
44
fraction of sputtered atoms/molecules with velocities greater than
the lunar escape velocity (ve=2.4km/sec).
The fraction of sputtered atoms with velocities greater than
the lunar escape velocity can be determined by integrating fdv from
It is given by the equation
v=ve to v=+m.
F
Zn
M
EXFv
Mv/4E
E-6/2V,
3
] dv
x
(34
This gives
F-f
V
v-
t,2
-v
Fr
E
3/zz
./2
S/.P3,)
-X r [-) M
v
v./45,
-A e IL-3/2.]d
4Ex e xt [-3 Ej,/zE,3 dV
f
2
v
(I-
, [-IM-zv3/41.
3z dv)
(35
The change of variable v = [(C+l)/ 2 ]ve converts Eq.(35) to
FT
E xP
C-
Eb/2fT1 ( I-
(2 3
-,)-m
)-n
Eq.(36) may be approximated by the following expression
FT E P
with
and
(
/-23-1
(E3a
2
Ak ,,~
(36
y = 3 M 2 /ET
Xk E Gaussian arguments
Ak E Gaussian weights
1(
[
[-Y((N- -)v) 2 /4]
Because velocities of the sputtered atoms depend on their
masses as well as the surface binding energy of the target being
45
bombarded, larger fractions of the- lighter species will escape the
lunar surface.
According to Cassidy and Hapke [1975], the probable
fraction of sputtered atoms lost, Fp
is assumed to be 0.5FT since
it is'assumed that half of the atoms will have a velocity component
in the downward directi.on (see Tables 37-52).
D. Fraction of Sputtered Molecules that Escape from the Moon
The fraction of sputtered molecules with velocities greater
than the lunar escape velocity were calculated (see Tables 53-60).
Comparison of the fraction FT for metal oxides and their corresponding metals indicates that FT is a strong function of Eb as
well as M2.
This suggests that there would be some preferential
retention of heavy oxides with high binding energies.
The pre-
dicted order of enrichment using surface binding energies as well
as molecular weights is: Fe20 3>Fe304>Al2 0 3>FeO>MnO>TiO 2 >CaO>MgO.
This order tends to be in better agreement with the order observed.
III.
PREFERENTIAL SPUTTERING:
OF ENRICHMENT OF METALS
METHOD FOR PREDICTING THE ORDER
The escape rate (amount of material lost by the Moon) may be
estimated by multiplying the sputtering yield of metals/oxides by
the probable fraction lost, Fp (see Table 61).
The order of enrichment of metals in the lunar surface material, however, can be best explained by a thermodynamic model
proposed by Pillinger et al. [1976].
According to Pillinger et al.
[1976], the transfer of momen-
tum concept is a good initial working hypothesis for the prediction
of the order of enrichment, but because it does not take into consideration the nature of the bonding between atoms, it cannot completely explain preferential sputtering either for lunar materials
or two element compounds.
They found that preferential sputtering
will occur to give a metal when: AH s(M) [sublimation energy of the
metal] > AHD(O)/y (the heat of dissociation/oxygen atom) or when
AH (M)/[AHD(0)/y] > 1.
The values of AH (M),
AHD(0)/y and
AH5 (M)/[ HD(0)/y] are given in Table 62.
The thermodynamic model explains much more satisfactorily the
data obtained from the lunar samples.
Of the major elements onlp'
iron would be converted to metal; titanium by virtue of its conversion to lower oxides, e.g. Ti 2 03' would also be enriched relative to oxygen.
The calculated preferential sputtering factors
gives the order of enrichment: Fe>Ti>Si>Al>Ca>Mg which agrees with
the order of enrichment observed during surface analysis by ESCA
{Housley and Grant, 1975] and our predicted order of enrichment
47
(see Table 61).
48
IV.
SUMMARY
The model for backward sputtering of metals/oxides as pro-
posed by Sigmund [1969] and Kelly [1973], respectively, has been
reviewed.
Sigmund's theory is valid only for M,>M 2 .
In order to apply
Sigmund's theory to proton sputtering (M<<M2), we have therefore
had to consider an approximation.
The quantity a, which depends
only on M 2 /M1 , was improved by substituting experimental S values
into the analytical S deduced by Sigmund [1969].
The predicted sputtering yields of metals/oxides, in comparison with the experimental yield values, turns out to differ by at
least a factor of 3 or better.
For example, the predicted values
for Cu and Fe at 1.85keV are 0.014 and 0.035, repsectively, and
the experimental values are 0.03 and 0.009, respectively.
The sputtering yields of metals/oxides, obtained from modified theories of sputtering by Sigmund and Kelly, are used in conjunction with the solar wind plasma- lunar surface magnetic field
interaction model to estimate the sputtering rates at the lunar
surface.
The interaction of the lunar surface magnetic fields with
the solar-wind protons has been reviewed.
According to the mag-
netic compression model, the streaming solar-wind plasma has a
magnetic field associated 'with it, which exerts a magnetic 'pressure' on the remanent magnetic fields associated with the lunar
surface.
This pressure compresses the surface field.
If the lo-
cal surface field is strong enough, it can stop the wind before
49
it reaches the surface, i.e. a bow shock is formed.
A weaker
field would not stop the solar wind, but would reduce its incident
energy at the surface.
The solar-wind protons are predicted to be completely stoodoff at the Apollo 16 landing site, and their mean kinetic energies
reduced at other sites.
At the Apollo 12 landing site, for exam-
ple, the protons lose about 30-80% of their nominal (lkeV) incident energies [Scott, 1976].
The loss in proton energy by interaction with compressed
magnetic fields can have a substantial effect on the sputtering
efficiency of the solar wind.
When high energy solar-wind ions
impact lunar soil, the kinetic energy is converted to thermal energy.
Since the protons are small (%10- 9 cm.)
in comparison to
grains in the lunar soil, the thermal energy is confined to a region of atomic dimensions, and dissociation (sputtering) occurs.
The number of atoms dissociated per incident ion (sputtering yield)
is simply dependent on the ion energy.
Sputtering rates fall off precipitously with reductions in
incident ion energies.
From the data of Wehner [1963] and others
it appears that a minimum ion energy of near 20-50eV is required
for sputtering to occur.
The loss of 30-80% in the ion energy at
the Apollo 12 landing site should reduce substantially the sputtering efficiency.
Sputtering efficiencies at other regions of
the Moon will similarly be low; thus the unexpected low abundances
of metal surface coatings predicted to have been produced by sput-
50
tering can now be possibly explained.
Laboratory work is needed to determine the dependence of
sputtering yield on incident ion energies for lunar-like soils,
in order to test the proposed interaction model.
APPENDIX I
Solutions of the Integral Equation- Governing the Sputtering Yield
of Polycrystalline Targets
In Section I.A. we analyzed the integral equation
that determines the number of atoms that have sufficient energy to
overcome the surface binding forces of the target.
The solutions
given were asymptotically exact in the limit of high ion energy.
In this section the above integral equation will be analyzed with
the aid of a method proposed by Robinson [1963;1968].
The average number of atoms moving in a layer (x,dx) at time
t with velocity (',dsv3)
is represented by the function
G(x,to 1 ,t)d
3 vodx
(I.1
The number of atoms with velocity (*O,dsv3)
penetrating the layer
x in a time interval dt is given by
G
(x,.V, t) CO v. IVI it
(1.2
v0 y = the x-component of vo.
where
The sputtering yield for backward sputtering of a solid with
a plane surface at x=O is given by
sJ
d'v.
v.
j
d CG
oG,,,
(1.3
where the integration over d vo extends over all v. with negative
x-components large enough to overcome surface binding forces.
In an isotropic and homogeneous target, the function
52
will satisfy the Boltzmann's equation
G(x, *ov,t)
0
-{
G(x,
-
v.,
N
G(x/ v.t4
7)
da
[ G (f,,.
(I.4
After
Consider a particle initially at x=O moving at t=O.
The proba-
a time t=6t, it may or may not have made a collision.
bility of making or not making a collision is given by
-
.,0,
G
votdG
V ',t) + G
,
(I.
- N E~t
+ [ (
5
where the first term on the right-hand side of Eq.(I.5) expresses
the probability of making a collision and the second term is the
probability for not making a collision.
Let
v,
G(bt) = G (x -7)v$t
-6t)
V,
and
x-vSt ,=t
%=
Therfore
a
and since
'bCi
)
d G(
s
.
G
G(bt)
bc
-
[dy/Idb43 = -- )v
G '(Sht)
-'r
dQ
d d bt
bG
d
v
IV /dt1- L d-/Cdtl
,
v
b
d
2G
dbt
-a
c=,
/d
(
t]
_bG
Ga
(1.7
The Taylor series expansion for G(6t) is
G
)
G (o)
+j
()b
+
G(")
2!
(bU 2 4-
__t_
ct
ItP
=
-
6
or
G~--vs,9,7
=G(x,5
4st
,
)t
(
v
) be
+
-
+
(1.8
Substituting Eq. (I.8) into Eq. (I.5) we have
G
-, )
(x ,
_&efd
=
x,
,-,
)
_.(,.
)t
-&
(1.9
b
+-(
I
sv
Jt)
-
t
do)
[
Ck
$t
x
j
[GLx,,,t )-(v
[ (,
-)
t+ 3
zit
x
+ GLx
(I.10
zt
2)x
fda GLx/,V6 4,t) + wvbt2
NV ilt
de
(.y
b3x-
E.)
+
-4
Neglecting the last term on the right-hand side of Eq. (I.10) we
obtain
(v
S.
'ax
+,5
= Wv
)t
t
-
d-
t
[G(x,",N,0zt
+
G(x-
,,v",
t
3
f/ dera G(x,va, v,t)
vt
and
te
Now we inrc
t
c
t ) - G ( -, 4-,,-",. t ) 3 (i. 11
G( x'
Now we introduce the function
F
where
F( x,VD,
X,v.7
V) I vo I d V,
Gcx,749
dv
t
(I
[2
is the total number of atoms that pen-
etrate the plane x with a velocity (vo,,dsv.).
F(x,-*ov)
satisfies
54
by integration over t.
an equation that follows from Eq. (.4)
Rewriting Eq. (I.4)
-
G(xVVt
1
V b4.
vt)-
jzX,V
NJ4
cvovt
-&
iultiplying through by dt and integrating we have
t/G[
) a-
4, 0 ta
6x,
-G
x.'
-
t)
Utilizing expression (1.12),
- x P
- IVTh = WNf<1C.h
V
(-A t-0)
-- )
(1.13
t) it]
-fGx
t0
Eq. (I.13) assumes the form
CO
GOA 'tVO IVit)
G,
d
Fxv,)
=
p-
, V
\,AI)
-
(1.14
,A
Nfda
I
-F (x,
rF(4')
.Flx,
).
-
.
jO
(1.15
where we have made the assumption that
(1.16
represents one starting particle, and
G
since at t=
Lx,
C, oa )
-\,
= 0
(1.17
all atoms have slowed down below any finite velocity
t
55
yoConsidering only backward sputtering and introducing the
function
(1.18
H (xv1-=d'v,Iv0 j 1~(xC,7)
where
T19 = Vo /V
_ 0,
(1.19
= M2 v2/2 >_ U(no)
E
= mass of target atom,
surface binding energy.
E
U(no)
M2
H(xi) represents the sputtering yield of a target atom for the
case that the source is at x=0 and the sputtered surface in the
plane x.
.L
Recalling Eq. (I.15)
b~)(-v"
=L<d
E(x;,)
-7)~
;x7,)
[
- F~x,A4,9'
(1.20
and multiplying it by 1vOXI, integrating over to we have
S b( C -
v.x
dAv . - -
.
( x ,U
'
$ )
d
.
*I
X
*
(v-v) d'v.
N
IV~I b
)
J'v
-
)
-'
de
d'v.
1
(1.21
N-x
(1.22
3v,
--
-
[tv., I{(F~
x
v,C
= Nfd-
-
F(x,4,v')
EN(x,v)
-
Fxva,')
-il x,-
Ix
-
I-I
('~(4$"'~)
I
(1I.
23
Introducing the function
9(U)
=
1 for (>O
=
0 for C<0
and satisfying the condition given by expression (1.19), Eq.(I.23)
can be rewritten as
(1.24
In a random medium H(x,9 ) is a function of x, v, and
1,
the
directional cosine, but not on the azimuth of v with respect to
the x-axis.
Introduction of energy, E, instead of velocity vari-
ables, we have
- &x;)y
(-)G E- (7)))
E9
(1.25
N do-
where E',
I', E" and
( Yx,E,1))
H('x/E',3'
-
HxE",,)so)]
" are the energies and directional cosines
with respect to the x-axis of the scattered and recoiling particle,
respectively.
The sputter yield is given by
S(E,'I)
= H(x=O,E,j).
(1.26
Expanding II interms of Legendre polynomials we have
57
2o
HA(xIE) Pt( )
(2.-i+l)
H ( x,/*El ) -= E
(1.27
where Pk (q) are Legendre polynomials.
Eq.(I.25) is multiplied by P (1) and integrate over a with
the condition rjs.0.
I
I
0 (E - L)( )) F
J-
b6tx)
(-9) O( E
-u-r)
N dJcr[j
-Ui
)-
Pg
{21
(T
- )Q
N
=
-
J-
-211:g,E') P)
(x,E Pft')Ld
H.(E" Pfl)Plt/'ijdbw
)
E)
HCx,
(2
e')
(1.29
]
Using the folowing relation between the P (ri) ' s
(72-+0 ) P'L(9)) = (AL+0 P.,(g
+P.,y)
(1.30
the following equation is obtained.
-
5(x)
+
=
N
0(- ) G ( E -
IH_,
2A+ I
dcr [(2-I)
-
..
JulI
(( )
u()) P)) d')
(x, Ell Pj
)) Pkvy)) d
AtIH
(x,E)
=
(1.31
I
c.x,
E I P
ri)P
Hjx,
HL -A, E") P.4ly ) PgLg;0)'A')
E'
)
P
'
I-y
Using the following relations
PL )(-)
2
(1.32
~IfrI
(1.32
the above equation becomes
) - (
-k)-rG (-1)) 0 t E-0UL0 )?A
)H
rNJd d (21T1(
ye
C21+
-(Il
H
~
V~p
- H(.~cV)
(ZAI)
-Sty-
-) (
do-
i -
x,'PL-O))
(,(+
)
I
Z(L'
(A,
IHL..
M E')P>t(')(
- H (-x, E")
(1.33
b~d
d
(-?)G(E-0(7))Pt))dr) N
9.H..I ()t, S)I
,
E)+t9 A L-..,(xE)
IPL(
I
) d-)
(1.34
Pi->) c) ]
Using the relation
J
j1=0
e
8
(1.35
9=,3, 5,.
Eq. (I,34) has the final form
bux) QJ(E) -
AH,_, ()L,E) + (1+\) Hj.,
- (21+0) NI
d4-
CMk.(x,
Ix;,
EFl
E)- P (cob 0') HL(AE')
- P(cOc
where
Qj(E)
2z
(-)d?
GUE -U(7)) ) PS(t0))
(1.37
(1.36
0")
59
and
laboratory scattering angle of scattered atom,
E laboratory scattering angle of recoiling atom.
Introducing the moment
,o kp~,~) ck
H (E)
(1.38
multiplying Eq. (I.36) by xn and integrating we have
Q((E)
00@
(n
QEJ) L
x *
d -
26x) x
/0e[
(x,
n ~0d.i
x"
4
00
g(o
x Ec)dx--
i
Pe CoA)
,E"
x
(,)
d
-
n
"M.(,E)d
'
'H I(;K,E
x*
C0
(1C+* xH
x.
g(,e)d
x
& (0
E)
i(
Y,"~~
IXl
Ot,E)
'.(coso,)
dx-
(1.40
/0o
With
5(.x)
X" d-x=ba
we have
- {.J.
6,4Q,()
(E
+
9-+)
H"2 EI = (7.M+ N
de L. H" (E) -
(1.41
-
H (E') PI.(coso') - H;(E") Pczosp")]
The terms which include the elastic and inelastic (electronic)
collisions can be separated by using the method given by Lindhard
et al. [1963].
Sn',
This yields
QJ(E)
-
n
[l H2
(E)+
(3.+I)
I
(E)] =(2JL+)
,_(E) d
+(21+' N
g"E
dE
C
(1.42)
dur (ET)
H(E)
-
(E-T'1 P((os') - HICT) Pf(cm #")l
Tao
where S (E) is the electronic stopping cross section, da(E,T) is
the differential cross section for elastic scattering, T is the
recoil energy, and
cos $' = (l-T/t) 1/2 + [(1-M 2 /M ) (T/E)(l-T/E)
cos $" = (T/Tm) 1/2
Tm = YE
(1.43
2
Y = 4M 1M 2 /(M+M 2 )
M
E mass of incident ion
1/2]/2
For n=O Eq.(I.41) becomes
Q (E)
d<r(E,T)[I*(E)-
= (2R_+ 1) N
P,(c*')HCE-T) - P(c*>#") HO CT))
(1.44
An especially useful approximation of da (Thomas-Fermi cross
section) is the power approximation, where
do = CE-mT-l-m dT
and m is a number between 0 and 1. Eq. (I.44) becomes
Q(E) - (2 L+1)
I CE
/
7dT
E
Hmt)
C
- P ((t- r/E))7
+-
(1.45
x H',.(E-r) - P,((T/Tv,)")
for M =M2
we have
H(T))
61
Q,(E)
d
z= (21+0)NCE'
[
T/T''''
( E
t
>IL)
-T/s
-
-P
t4*
(r
-T)-
H*(T)]
((rT/E)')
where we assumed Se (E)=.
Now we proceed to solve the integral given by Eq.(I.44).
We
use the procedure which has been described by Robinson [1965;1968].
Rewriting Eq. (1.44) we have
Q IE~ (21t
~ crz(j
di.T~
-
PH~iT/I")
--
r-
-
F ((-TI E-02) A0CT I
Let's consider the case for Z=O.
The above equation takes the fol-
lowing form
Q,(.E:-
odvtE T) [ R' tE)-- VA (E-'-
m'
T
where we have made use of the relation
PO(e) = 1.
With the Thomas-Fermis cross section approximated by the power approximation
da (ET)= CNE-mT--mdT
(1.46
we have
E
Q(E~Ct%
0
HO(E)
jdT
E-:-I)
(1..47
the integral of H0 (x,E) over all x; i.e. determines the number of atoms penetrating a
plane at an arbitrary position x with a certain minimum energy, when there is a homogeneous isotropic source of recoiling atoms throughout an infinite medium.
= 0 for
E>UO
1 for U 0 <E<2U0
HO(E)
(1.48
With m fixed Robinson calcu-
U0 being the surface binding energy.
lated the asymptotic solution
H* (E) ~(.
with
3 -i.
2w.
for U>>2UO
(1.49
(r)=2 (Z" -1)1*
where C=l at m=-l (hard-sphere scattering),
E=(12/7r2 )ln2=0.84 at
m=0 and (=0 at m=l.
If m in Eq.(I.49) is a function of E [m=m(E)],
H.(E) is nonlinear over most of the energy range.
the function
For fixed m we
have
6E
T.
j
U.
E
I
CE'
l
dE
E''
CE
C
)T~~
i
.CE'(' t lT
,...i(f~)
i-rE
__
-
T dT
8
~(~rvh)
-
art,
where
I
UO
E
~ E
u.
(1.50
-r
j
is the elastic stopping power.
increases with m.
From Eq.(I.50) we see that 6E/E
In the keV region and below where m<0.5, 6E/E
vill always be <<1 for E>>U..
((m)
This shows that m in the expression
cannot be determined by Eq.(I.50).
Therefore we replace Ea.
(1.50) by
m = m(2UO).
If
m[m(2U 0 )] is
=
(1.51
inserted into Eq.(I.49), HO(E) becomes
It is possible to obtain Eq.(I.49) if the power
linear for EI>>2U0 .
m in the cross section, Eq.(I.50) is allowed to vary from step to
step.
First we consider one single step
m(E)
= mo for 2U 0 <E<U 1
m
where m >mO and E>>2U0 .
l
(1.52
E>U 1
For E<E 1 we can utilize the exact solution
given by Robinson [1965;1968].
.~
for
For m=mo
fa.,-inZ.
NC(
2n'
(c20,
\./
:(sd
(I5
(1.53
where
CSt
k~s
,m
r
a
-
-t
(1.54
Z
1.-(.,-rt
and a is some arbitrary real number > 1.
(1.55
B(s,l-m) and Bl/2(s,1-m)
are the Beta and incomplete-Beta functions, respectively.
The
integrand in Eq. (I.53) has singularities at roots si of the equa-
64
-2<s
tion F(s.,m)=0 and so=l, -l<s <0
'1etc.
2
With
F(s. ,n0 ) = 0
we have
r
r-(5)
(-
m)
r (s -
-
I
mn,
/r (-m,>
r (s -n.
(1.57
Using Sterling's formula we have
F (Z)
~ e-z z
h
r - I
Li
(zu1''l
+
1al
+
2
639
1
eSIa
r-Ws)-M
~ e-
(2rt I
e
F ( i-rr()
e
I"
-
I
SI-S
($-r ..
s (sS-
f
+I
't-m)
2(5rn)I
( I +t
- i; 3
+
I
-
518 40 %-m
( ,,qr [I,-,
127S-tI- II I
120-M)
(S- rm)
[I
m)
-
i-S
-+
lZ(5-r"~
+1
(i -ni
(2n), I Z
5le8900-r'*
28s (I-nr)f
t Ift - T")
O-M)
(q0z
S-5
$59
+1
- I/
(.'-mI
(s-r)
1
Zs4sB3ZO
(I-r") - 112
(2:r
r
51z1
5(8OZ3
(s-rn)
I
2 2I-M) I
[
t
+ IZ(S-M>
(1.58
(
-
")-
C'-
-.>0
65
For s 0 =1 we have from Eq.(I.58) that
e
-1
4-]
(2s)"t[1
The poles of the function
is one root of Eq.(I.57).
so that s=
k(s,mo) in Eq.(I.53) are cancelled by the poles of the denominator
so that the integrand is regular outside the real axis.
The path
of integration C, (Fig.A.1) can be transformed to C 2 that encloses
the real axis for s<l in the positive direction.
residue
C2
C,
Fig. A.l
theorem ($
fozidz = 2 i
H, (E)
where
REs
f(a)
we have
A-, (E/2u)C(/Nc)
(1.59
Utilizing the
66
H,(\ 1=
00
A
5;
"'I,
-V(S; -m.)
V(x>
;
-- .W
E
4
2u.)
NC
- (1.60
-x
o
(1.61
- "(SO
For i=0, s=l Eq. (I.60) takes the folowing form
(,
(i--m.) [8iI,
(±2'
+ k u-rn.)
l -m.>o
-
-6('j -m. 0)]
5
E i
\20.) Nc
(I)
'f~
t*I -n~) W CI
-
H-2"
(
t-en.)- M )
I -2'"
2
\0INc
r-(
r 0
[w
(-n.)
-en.
1
-+(0
I
i/- 2
4/z - 2' M
4ru -en, -Y~)
For m=O, i.e. E<E1,
II
(E
20. sc
we obtain (using L'Hopital's Rule)
In2
H'* (E)
2'4-( )
Now we wish to
calculate T'(1).
[ -4--t( )ci t
-_
I
E
NCU.
(1.62
We have
= t -A
['4q,1)3j
dt
S=O
I_
67
0o
kni£
Eq.(I.62) takes the form
He'
31n2/T/z [E/Ncau,]
(1.63
Eq.(I.63) differs from Eq.(17a) by a factor of 1/41n2.
The
difference occurs because in our analysis of the integral equation
using Robinson's method, we solved the equation for E>2U 0 .
otherhand Sigmund solved the equation for E>U 0 .
On the
APPENDIX II
CURVE FITTING
.A. Linear Least Square Fit
In Section I.C., the values of <AX 2 >/<X> 2 and <Y 2 >/<X> 2 were
computed by the method of least squares for M 2 / 1 1>l0, since Sigmund
and Sanders [1967] only computed values for 0.l<M 2 /M <10.
In this
section we will explain the technique of linear regression by the
method of least squares.
First we will illustrate the simplest kind of least squares
fit, that which is often called a simple linear regression.
We
will fit a straight line
y = ao + a x
to the data points in Table 4.
as a function of M 2 /M .
(II.1
The moment <AX 2 >/<X> 2 is plotted
The least sauares coefficients are de-
termined from the set of N data points (x ,y.)
manner.
in the following
The function to be minimized is:
I(kxv)
y~
-Y;3 2(11.2
21.Ea.+
L
a, x -.
(11.3
Differentiating, we obtain the two normal equations
or
2 (a.+a, x - yi)
=0
2 (a.+ a, x;
x; =o
(II.4
(11.5
69
±o
I
a(
de + a
2:
2:X;
(11.6
y
(11.7
Using Cramer's rule
IT: XY
Z iJ
dl
=
(11.8
N
02
Finally, we obtain the expressions for the least squares coefficiand v.:
ents in terms of sums of the x.
LI
1
a4
X.. -~
...
a,
x
zx
x.
N
where
Y
=
(11.9
(II.10
M 2 /M.
y = <AX 2 >/<X> 2 .
The quality of the least squares fit to the data points provided is given by the expression
r2
1
NLN
~~NZ~
~Z[~(jZ
(11. 11
70
The value of r 2 will lie between 0~and 1.
The closer r2 is to 1,
the better the fit.
Least-squaring the data provided by Table 4 we find that
a o =O.15955, a1=0.08686 and r 2 =0.99800.
II. Power Curve Fi-t
We wil fit a power curve
y = aoxai
to the data points in Table 4.
a function of M 2 /M1 .
(ao>0)
(11.12
The moment <Y 2 >/<X> 2 is plotted as
By writing Eq. (II.12) as
lny = allnx + lnao
(11.13
the problem can be solved as a linear regression problem.
Using
the same procedure of Section I we find that
(11.14
a,
C3,
where
EP
-t4(2
n
a
:IA)(II.15
x = M 2 /Ml
y = <Y2>/<X>2
and
r =
(II.16
71
Fitting a power curve to the data boints provided by Table 4 find
that ao=0.17381, a =0.98330 and r 2 =0.99997.
Applications Programs, 1975].
[Hewlett-Packard HP-25
72
REFERENCES
1.
Cassidy, W., and B. Hapke, Effects of darkening on surfaces
of airless bodies, Science, 172, 716-718, 1971.
2.
Cheney, K.B., and E.T. Pitkin, J. Appl. Phys.,
3.
Colombie', N., Thesis, University of Toulouse, 1964
lished).
4.
Dyal, P., C.W. Parkin, and W.D. Daily, Surface magnetometer
experiments: Internal properties and lunar field interactions
with the solar plasma, Proc.Lunar Sci. Conf. 3rd., 2287-2307,
1972.
5.
Dupp, G. and A. Scharmann, Z. Physik, 194, 448, 1966.
6.
Formisano, V.,
365, 1971.
7.
GrOlund, F., and W.J. Moore, Sputtering of silver by light
ions with energies from 2 to 12keV, The Journal of Chemical
Physics, 32, 1540-1545, 1960.
8.
Hapke, B., W. Cassidy and E. Wells, Effects of vapor-phase
deposition processes on the optical, chemical, and magnetic
properties of the lunar regolith, The Moon, 13, 339-353, 1975.
9.
Housley, R.M. and R.M. Grant, ESCA studies of lunar surface
chemistry, Proc. Sixth Lunar Sci. Conf., 3269-3275, 1975.
10.
Kelly, R. and N.Q. Lam, The sputtering of oxides part I: A
survey of the experimental results, Radiation Effects, 19,
39-47, 1973.
11.
KenKnight, C.E. and G.K. Wehner, Sputtering of metals by hydrogen ions, Journal of Applied Physics, 35, 322-326, 1964.
12.
Kittel, C., Introduction to Solid State Physics, John Wiley
& Sons, Inc., New York, 1976, p.78.
13.
Lin, R.P., K.A. Anderson, R.E. McGuire, and J.E. McCoy, Fine
scale lunar surface magnetic fields detected by the electron
reflection method, Lunar Science VII: Revised Abstracts of
Papers Presented at the Seventh Lunar Science Conference, 492494, 1976.
14.
Lindhard, J., V. Nielsen, M. Scharff, and P.V. Thomsen, Integral equations governing radiation effects (Notes on atomic
collisions, II), Matematisk-fysiske Meddelelser udgivet af
Det Kongelige Danske Videnskabernes Selskab, Bind 33, 1-42,
1963.
36, 3542, 1965.
(unpub-
and G. Moreno, Rivista del Nuovo Cimento, 1,
73
15.
Lindhard, J., M. Scharff and H.E. Schiott, Range consepts and
heavy ion ranges (Notes on atomic collisions, II), Matematiskfysiske Meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab, Bind 33, nr. 14, 1-42, 1963.
16.
Molchanov, V.A. and V.G. Tel'kovskii, Dolk. Akad. Nauk SSSR,
136, 801, 1961 [English transl.:
Soviet Physics - Doklady,
6, 137, 1961].
17.
Robinson, M.T., The influence of the scattering law on the
radiation damage displacement cascade, Philosophical Magazine,
12, 741-765, 1965.
18.
Robinson, M.T., The influence of the scattering law on the
radiation damage displacement cascade. II, Philosophical
Magazine, 17, 639-642, 1968.
19.
Rol, P.K., J.M. Fluit, and J. Kistemaker, Physica, 26, 1000,
1960.
20.
Scott, R.E., Thesis, Massachusetts Institute of Technology,
1976 (unpublished).
21.
Sigmund, P. and J.B. Sanders, in Proceedings of the International Conference on "Application of Ion Beams to Semiconductor Technology," edited by P. Glotin (Editions Ophrys, Paris,
1967), p.228.
22.
Sigmund, P., Theory of sputtering.I. Sputtering yield of amorphous and polycrystalline targets, Physical Review, 184,
383-416, 1969.
23.
Taylor, R.S., Lunar Science:
Press, Inc., New York, 1975.
24.
Wehner, G.K., Sputtering effects on the moon's surface, General Mills Third Quarterly Status Report Covering Period
25 October 1963 to 24 January 1964 (unpublished).
25.
Wehner, G.K., D.L. Rosenberg and C.E. KenKnight, Investigation of sputtering effects on the moon's surface, General
Mills Fourth Quarterly Status Report Covering Period 25 January 1964a to 24 April 1964a (unpublished).
A Post-Apollo View, Pergamon
74
TABLES
75
Energy of Incident H+ (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table
Vp(km/sec)
E p(eV)
69.4
62.5
55.5
48.6
41.7
37.7,
27.8
20.8
13.9
6.9
3.5
0.7
0.1
18.2
.17.3
16.3
15.2
14.1
12.9
11.5
10.0
8.1
5.8
4.1
1.8
0.6
46.3
41.7
37.0
32.4
27.8
23.1
18.5
13.9
9.3
4.6
2.3
0.5
0.05
6. Calculated ETI Vp, and Ep for aluminum bombarded by H
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table
ET(eV)
T
7.
Calculated ET
ET (eV)
47.9
43.1
38.3
33.5
28.7
23.9
19.1
14.4
9.5
4.7
2.4
0.5
0.05
Vp, and E
V (km/sec)
p
12.4
11.8
11.1
10.4
9.6
8.8
7.8
6.8
5.5
3.9
2.8
1.2
0.4
E (eV)
p
31.9
28.7
25.5
22.3
19.1
16.0
12.8
9.6
6.4
3.2
1.6
0.3
0.03
for calcium bombarded by H
.76
Energy of Incident H (eV)
ET (eV)
Vp(km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
37.4.
33.6
29.8
26.1
22.4
18.7
14.9
11.2
7.5
3.7
1.9
0.4
0.04
9.6
9.1
8.6
8.0
7.4
6.8
6.1
5.3
4.3
3.0
2.1
0.9
0.3
24.922.4
19.9
17.4
Table
8.
Calculated
V , and E
m ,r
14.9
12.5
10.0
7.5
5.0
2.5
1.3
0.3
0.03
for chromium bombarded by H
Energy of Incident H (eV)
ET (eV)
Vp(km/sec)
Ep(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
30.7
27.7
24.6
21.5
18.4
15.4
12.3
9.2
6.1
3.1
1.5
0.3
0.03
7.9
7.5
7.1
6.6
6.1
5.6
5.0
4.3
3.5
2.5
1.8
0.8
0.2
20.5
18.5
16.4
14.4
12.3
10.3
8.2
6.2
4.1
2.1
1.0
0.2
0.02
Table
9.
Calculated E , Vp, and E p for copper bombarded by H
77
Energy of Incident H (eV)
ET (eV)
V p(km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
10.1
9.1
8.1
7.1
6.1
5.1
4.1
3.0
2.0
1.0
0.5
0.1
0.01
2.6
2.4
2.3
2.2
2.0
1.8
1.61.4
1.2
0.8
0.6
0.3
0.1
6.8
6.1
5.4
4.7
4.1
3.4
2.7
2.0
1.4
0.7
0.3
0.1
0.01
Table 10.
Calculated ET'
p
and E
p
for gold bombarded by H
Energy of Incident H (eV)
_f(eV)
ZT
V p(km/sec)
Ep(eV)
1000
900
800
700
600
.500'
400
300
200
100
50
10
1
34.8
31.3
27.9
24.4
20.9
17..4
13.9
10.4
7.0
3.5'
1.7
0.3
0.04
8.9
8.5
8.0
7.5
6.9
6.3
5.7
4.9
4.0
2.8
2.0
0.9
0.3
23.2
20.9
18.6
16.3
13.9
11.6
9.3
7.0
4.6
2.3
1.2
0.2
0.03
Table 11.
Calculated ETo' V
1
and E for iron bombarded by H
p
78
Energy of Incident H (eV)
ET(eV)
V p(km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
35.4
31.8
28.3
24.7
21.2
17.7
14.2
10.6
7.1
3.5
1.8
0.4
0.04
9.1
8.6
8.1
7.6
7.1
6.4
5.8
5.0
4.1
2.9
2.0
0.9
2.9
23.6'
21.2
18.9
16.5
Table 12.
Calculated
T
Energy of Incident H+ (eV)
1000
900
800
700
600
500
400
300
200
100
50
Table 13.
NT.
Vp,
14.2
11.8
9.4
7.1
4.7
2.4
1.2
0.2
0.03
and E for manganese bombarded by H
P
E (eV)
Vp (km/sec)
Ep (eV)
76.4
68.8
61.2
53.5
45.9
38.2
30.6
22.9
15.3
7.6
3.8
0.8
0.1
20.1
19.1
18.0
16.8
15.6
51.0
45.9
40.8
35.7
30.6
25.5
20.4
15.3
10.2
5.1
2.6
0.5
0.1
14.2
12.7
11.0
9.0
6.4
4.5
2.0
0.6
Calculated E , Vp, and E
P
for magnesium bombarded by H
.79
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
Table 14.
Ep (eV)
33.2
29.9
26.5
23.2
19.9
16.6
13.3
10.0
6.6
3.3
1.7
0.3
0.03
8.5
8.1
7.6
7.1
6.6
6.0
5.44.7
3.8
2.7
1.9
0.9
0.3
22.1
E*
T
(eV)
49.0
44.1
39.2
34.3
29.4
24.5
19.6
14.7
9.8
4.9
2.5
0.5
0.05
1000
900
800
700
600
500
400
300
200
100
50
10
1
Calculated
Vp (km/sec)
(eV)
Vp, and E
Calculated ET
Energy of Incident H (eV)
Table 15.
NT
ET
E
,'Vp,
and E
19.9
17.7
15.5
13.3
11.1
8.9
6.6
4.4
2.2
1.1
0.2
0.02
for nickel bombarded by H
Vp (km/sec)
Ep (eV)
12.7
12.1
11.4
10.6
9.8
9.0
8.0
7.0
5.7
4.0
2.8
1.3
0.4
32.7
29.4
26.1
22.9
19.6
16.3
13.1
9.8
6.5
3.3
1.6
0.3
0.04
for potassium bombarded by H
80
E (eV)
NT.
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 16.
Vp (km/sec)
17.5
.16.6
15.7
14.6
13.6
12.4
11.1
9.6
7.8
5.5
3.9
1.8
0.6
66.9
60.2
53.5
46.8
40.1
33.4
26.8
20.1,
13.4
6.7
3.3
0.7
0.07
44.6
40.3
35.7
31.2
26.8
22.3
17.8
13.4
8.9
4.5
2.2
0.5
0.1
and E for silicon bombarded by H
Calculated ETV
Vp,
p
Energy of Incident H (eV)
ET (eV)
Vp (km/sec)
1000
900
800
700
600
500
400
300
200
100
50
10
1
18.3
16.5
14.7
12.8
11.0
9.2
7.3
5.5
3.7
1.8
0.9
0.2
0.02
4.7.4.4
4.2
3.9
3.6
3.3
3.0
2.6
2.1
1.5
1.0
0.5
0.1
Table 17.
E (eV)
Calculated E , V , and E
T
P
p
E (eV)
p
12.2
11.0
9.8
8.6
7.3
6.1
4.9
3.7
2.5
1.2
0.6
0.1
0.01
for silver bombarded by H
Energy of Incident H (eV)
E (eV)
T
VP (km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
80.5
72.4
64.4
56.3
48.3
40.2.
32.2
24.1
16.1
8.0
4.0
0.8
0.1
21.2
-20.1
19.0
17.8
16.4
15.0
13.4
11.6
9.5
6.7
4.7
2.1
0.7
53.7
48.3
42.9
Table 18.
Calculated ET'
Vp
and E
ET(eV)
ZT
vP (km/sec)
1000
900
800
700
600
500
400
300
200
100
50
10
1
40.4
36.3
32.3
28.3
24.2
20.2
16.1
12.1
8.1
4.0
2.0
0.4
0.04
10.4
9.9
9.3
8.7
8.1
7.4
6.6
5.7
4.7
3.3
2.3
1.0
0.3
Calculated ET
V,
32.2
26.8
21.5
16.1
10.7
5.4
2.7
0.5
0.1
for sodium bombarded by H
Energy of Incident H (eV)
Table 19.
37.6
E (eV)
p
26.9
24.2
21.5
18.8
16.2
13.5
10.8
8.1
5.4
2.7
1.4
0.3
0.03
titanium bombarded by H
and E for
f
p
.82
Energy of Incident H (eV)
E (eV)
T.
v p(km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
29.9
26.9
23.9
20.9
17.9
15.0
12.0
9.0
6.0
3.0
1.5
0.3
0.03
7.7
7.3
6.9
6.4
5.9
5.4
4.9
4.2
3.4
2.4
1.7
0.8
0.2
19.9~
17.9
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
1.0
0.2
0.02
Table
20.
Calculated
TIV
1
and E for zinc bombarded by H+
p
Energy of Incident H (eV)
ET (eV)
v p(km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
111.5
100.4
89.2
78.1
66.9
55.7
44.6
33.5
22.3
11.2
5.6
1.1
0.1
30.0
28.4
26.8
25.1
23.2
21.1
18.9
16.4
13.3
9.5
6.7
3.0
0.9
74.4
66.9
59.5
52.1
44.6
37.2
29.7
22.3
14.9
7.4
3.7
0.7
0.1
Table 20a.
Calculated ET
Vp, and E
for oxygen bombarded by H
f
-83
Oxide
keV
10
3S H+
2
3
FeO
7.0
7.0
6.0
6.5
6.5
10.5
11.8
7.5
7.5
12.7
15.0
17.1
12.9
10.6
20.4
Fe 2 03
Sio 2
7.0
7.5
9.4
83.0
12.8
92.0
Al203
TiOx
Table 21.
keV
Al20
7.0
7.0
6.0
6.5
6.5
0.005
0.006
0.004
0.004
0.006
0.010
0.010
0.013
0.011
0.011
7.0
7.5
0.005
0.042
0.013
0.005
FeOx
Fe 2 03
SiO 2
Table 22.
x=1.86
beam shift
x=1.86
uniformity (?)
Sputtering yield of oxides for H+ and H+ ions at normal
incidence. [From Wehner, 1964].
Oxide
TiOx
Comment
10 3 s H+
SH+(Eq.
32
)
Sputtering yield of oxides for H+ at normal incidence.
* Values for SH+ deduced from data given in Table 21.
Oxide
M2 /M
<AX2>/<X>2
<y 2 >/<X> 2
Al203
101.2
16.227
16.278
Cao
55.6
8.964
9.043
FeO
71.3
11.461
11.538
Fe 2 0 3
158.4
25.366
25.304
Fe 3 O4
229.7
36.740
36.462
MgO
40.0
6.468
6.536
MnO
70.4
11.317
11.394
TiO2
79.3
12.735
12.808
Table 23.
2
2
2
Tabulation of the moments <AX 2 >/<X> and <Y >/<X>
for oxides.
85
Table 24.
Qxide
M 2 (amu)
Eb (eV)
Al 20
101.96.
10.0'
CaO
56.08
8.4
FeO
71.85
13.1
Fe2 0
159.69
14.3
Fe 30 4
231.54
13.8
3
MgO
40.31
7.9'
MnO
70.94
10.6
TiO 2
79.9
10.31
Molecular weight and binding energy of metal oxides.
-From Kelly and Lam 11973].
86
Energy of Incident H+(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 25.
E T(eV)
ET
V p(km/sec)
E p(eV)
19.4
17.4
4.9
4.7
4.4
4.1
3.8
3.5
3.1
2.7
2.2
1.6
1.1
0.5
0.2
12.9
23.3
11.6
9.1
7.8
6.5
5.2
3.9
2.6
1.3
0.7
0.1
0.02
15.5
13.6
11.6
9.7
7.8
5.8
3.9
1.9
1.0
0.2
0.01
Calculated KT, Vp r and E
p
for Al 203 bombarded by H+
Energy of Incident H (eV)
ET (eV)
V p(km/sec)
E p(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
34.7
31.2
27.8
24.3
20.8
17.3
13.9
10.4
6.9
3.5
1.7
0.3
0.04
8.9
8.5
8.0
7.5
6.9
6.3
5.6
4.9
4.0
2.8
2.0
0.9
0.3
23.1
20.8
18.5
16.2
13.9
11.6
9.3
6.9
4.6
2.3
1.2
0.2
0.03
Table 26.
Calculated ET
,
and E
for CaO bombarded by H+
p f
87
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 27.
ET(eV)
V (km/sec)
Ep (eV)
27.3
24.6
21.8
19.1
16.4
13.6.
10.9
8.2
5.5
2.7
1.4
0.3
0.03
7.0
6.6
6.3
5.8
5.4
4.9
4.4
3.8
3.1
2.2
1.6
0.7
0.2
18.2
16.4
14.6
12.7
10.9
9.1
7.3
5.5
3.6
1.8
0.9
0.2
0.02
NT
Calculated T, Vp, and E
p
for FeO bombarded by H
Energy of Incident H (eV)
ET (eV)
vp (km/sec)
1000
900
800
700
600
500
400
300
200
100
50
10
1
12.5
11.2
10.0
8.7
7.5
6.2
5.0
3.7
2.5
1.2
0.6
0.1
0.01
3.1
3.0
2.8
2.7
2.5
2.2
2.0
1.7
1.4
1.0
0.7
0.3
0.1
Table 28.
Calculated
T
Vp, and E
E (eV)
p
8.3
7.5
6.7
5.8
5.0
4.2
3.3
2.5
1.7
0.8
0.4
0.1
0.01
H
for Fe203 bombarded by
88
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 29.
Calculated T T
Energy of Incident H+ (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 30.
Calculated ET'
ET (eV)
v P(km/sec)
E p(eV)
8.6
7.8
6.9
6.0
5.2
4.3
3.5
2.6
1.7
0.9
2.2
2.1
2.0
1.8
1.7
1.5
5.8
5.2
0.4
0.5
0.1
0.01
0.2
0.1
V , and E
1.4
1.2
1.0
0.7
4.6
4.0
3.5
2.9
2.3
1.8
1.2
0.6
0.3
0.1
0.01
for Fe 30 bombarded by H+
4
E (eV)
Vp (km/sec)
Ep (eV)
47.6
42.8
38.1
33.3
12.3
11.7
11.0
10.3
9.6
8.7
7.8
6.8
5.5
3.9
2.8
1.2
0.4
31.8
28.6
25.4
22.2
19.0
15.9
12.7
9.5
6.4
3.2
1.6
0.3
0.03
28.6
23.8
19.0
14.3
9.5
4.8
2.4
0.5
0.05
bombarded by H+
, and Ep for MgO
Energy of Incident H (eV)
ET (eV)
Vp (km/sec)
E (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
27.6
24.9
22.1
19.3
16.6
13.811.1
8.3
5.5
2.8
1.4
0.3
0.03
7.1
6.7
6.3
5.9
5.5
5.0
4.4
3.9
3.2
2.2
1.6
0.7
0.2
18.4
16.6
14.7
12.9
11.1
9.2
7.4
5.5
3.7
1.8
0.9
0.2
0.02
Table 31.
Calculated ETr V , and E
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table
32.
for MnO bombarded by H
E*
ST (eV)
v p(km/sec)
E (eV)
24.6
22.1
19.7
17.2
14.8
12.3
9.8
7.4
4.9
2.5
1.2
0.2
0.03
6.3
6.0
5.6
5.3
4.9
4.5
4.0
3.4
2.8
2.0
1.4
0.6
0.2
16 .4
14 .8
13 .1
11 .5
9 .8
8 .2
6 .6
4 .9
3 .3
1 .6
0 .8
0 .2
0 .02
by H+
Calculated ET, V , and Ep for TiO2 bombarded
90
Oxide
Maria
(wt %)
Highlands
(wt %)
SiO2
45.4
45.5
TiO2
3.9
0.6
Al2 0 3
14.9
24.0
FeO
14.1
5.9
MgO
9.2
7.5
CaO
11.8
15.9
0.6
0.6
Na20
K 20
Table 33.
----
Average chemical composition of Lunar Surface
[From Taylor, 1975].
Regolith.
91
Coordinates .
Site
Apollo 12
Apollo 14
Site A
Site C'
Apollo 15
Apollo 16
ALSEP
Site 2
5
Site
Site 13
FRPS
Taylor Crater
Alfraganus Crater
M. Tranquilitatis
Toricelli R
Capella CA
Capella D
Gutenberg G
M. Fecunditatis
Table 34.
Field
Magnitude(y)
23. 40 W
38
3.20 S
2.60S
26.1 0 N
17. 20 W
15.5 0 W
3.70 E
103
43
3
8.90S
15.5 0 E
15. 50 E
15.5 0 E
15. 50 E
15. 50 E
4.50 S
5.0*S
5.0*S
234
189
112
327
113
20
83
86
30
85
75
43
100
3.20 S
9.0*S
9.1 0 S
8.9 0 S
9.0*S
16. 0*E
19
.
00 E
26. 50 E
29.0 0 E
36.0*E
39. 00 E
40. 50 E
42. 5*E
6.0*S
6.5*S
6.50 S
6.0*S
6.0*S
Summary of Lunar remanent magnetic field.
et al., 1972 and Lin et al., 19761.
From [Dyal
Final Velocity
of H+(km/sec)
Site
Apollo 12
Apollo 14
Site A
Site C'
Apollo 15
Apollo 16
ALSEP
Site 2
Site 5
Site 13
FRPS
Taylor Crater
Alfraganus Crater
M. Tranquilitatis
Toricelli R
Capella CA
Capella D
Gutenberg G
M. Fecunditatis
.Final Energy
of H+(eV)
2.788
351.9
641.3
0.380
2.178
348.300
-561.8
323.1
438.7
1635.0
540.7
997.1
0.074
0.113
0.321
0.038
0.315
10.070
0.584
0.544
4.464
0.557
0.716
2.178
0.403
-1560.0
-1233.0
-639.0
-2221.0
-674.4
417.0
-370.5
-401.9
387.2
-391.6
-276.9
323.1
-535.2
12600.0
7872.0
2115.0
25560.0
2171.0
900.6
711.0
836.9
776.4
794.4
397.1
540.7
1484.0
Table 35. The ratio of solar-wind plasma pressure to total magnetic field pressure.
Oxide
Site
Apollo
12
Apollo 14
Site C'
(Gutenberg
A1 2 0 3
CaO
FeO
MgO
MnO
TiO 2
[Sputtering Rate at Moon]
A/year
Atoms/cm 2 year
0.91 x 1015
WV
1.61
"V
0.72
"V
1.33
"V
0.81
0.83
3.0
5.3
2.4
4.4
2.7
2.8
Metal
[Sputtering Rate at
Atoms/cm2 year
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
0.69 x 1015
It
1.14
t
0.43
it
0.41
t
"
0.40
2.18
1.61
0.58
2.17
0.51
0.38
"V
Vt
"t
"
A1 2 0 3
CaO
FeO
MgO
MnO
TiO 2
0.91 x 1015
if
1.60
it
0.73
WV
1.33
'I
0.81
it
0.84
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
0.69 x 1015
"V
1.11
"t
0.42
"
0.44
t
0.40
2.15
"
1.59
WV
0.57
"
2.13
WV
0.51
if
0.37
A1 2 0 3
CaO
FeO
MgO
MnO
TiO2
0.85 x105
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
0.72
1.19
0.45
0.32
0.43
2.27
1.64
0.61
2.24
0.52
0.40
Moon]
A/year
2.3
3.8
1.4
1.4
1.3
7.2
5.3
1.9
7.2
1.7
1.3
2.3
3.7
1.4
1.5
1.3
7.1
5.3
1.9
7.1
1.7
1.2
iV
Apollo 15
1.59
0.67
1.29
0.76
0.75
"V
"V
WV
"V
"V
2.8
5.3
2.2
4.3
2.5
2.5
x1015
"V
"V
"
"
"
"
"V
"V
WV
"V
2.4
3.9
1.5
1.1
1.4
7.5
5.5
2.0
7.5
1.7
1.3
Site
Oxide
Taylor Crater
A1 2 0 3
CaO
FeO
MgO
MnO
TiO2
[Sputtering Rate at Moon]
A/year
Atoms/cm2 year
0.86 x 1015
it
1.59
0.68
"
1.30
"
0.78
0.77
2.9
5.3
2.3
4.3
2.6
2.6
Metal
Al
Ca
Cr
Cu
Fe
Al 03
Ca8
FeO
MgO
MnO
TiO2
0.89 x 1015
it
1.59
it
0.71
1.31
0.76
0.79
2.9
5.3
2.4
4.3
2.6
2.6
0.72 x 1015
f
1.16
I
1.5
0.35
if
1.2
0.42
it
1.4
7.4
5.5
2.23
1.64
""
Mn
Na
0.61
"
2.21
0.52
0.39
"
Al
Ca
Cr
Cu
Fe
2.4
3.9
0.45
K
Mg
Si
Ti
Toricelli R
[Sputtering Rate at0 Moon]
A/year
Atoms/cm 2 year
0.71
1.16
0.44
"
"
2.0
7.3
1.7
1.3
x
1015
"
2.4
3.8
"
1.5
0.38
"
1.3
0.41
"
K
Mg
2.22
"
1.61
"
1.4
7.4
5.4
Mn
Na
Si
0.59
2.18
0.52
0.38
"
Ti
Table 36. Estimate of the sputtering rates at the lunar surface.
"
2.0
7.3
"
1.7
"
1.3
95
FT
Energy of Incident H (eV)
0.929
0.921
0.912
0.899
0.883
0.871
0.830
0.778
0.685
0.463
0.207
0.0002
0
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 37.
Calculated FT.
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 38.
and F
F
p
0.465
0.461
0.456
0.450
0.442
0.436
0.415
0.389
0.343
0.232
0.104
0.0001
0
for aluminum bombarded by H
FT
F
p
0.940
0.933
0.924
0.913
0.900
0.879
0.849
0.802
0.711
0.488
0.349
0.0002
0
0.470
0.467
0.462
0.457
0.450
0.440
0.425
0.401
0.356
0.244
0.175
0.0001
0
Calculated FT, and Fp for calcium bombarded by H
Energy of Incident H+ (eV)
FT
0.837
0.822
0.802
0.776
0.742
0.698
0.635
0.542
0.392
0.144
0.018
0
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 39.
Calculated FT', and F
Energy of Incident H (eV)
Table 4 0.
Calculated FT,
for chromium bombarded by H+
FT
1000
900
800
700
600
500
400
300
200
100
50
0.827
0.808
0.786
0.758
0.722
0.674
0.606
0.507
0.351
0.113
0.055
T
F
p
0.419
0.411
0.401
0.388
0.371
0.349
0.318
0.271
0.196
0.072
0.009
0
0
F
p
0.414
0.404
0.393
0.379
0.361
0.337
0.303
0.254
0.176
0.057
0.028
0
and F for copper bombarded by H+
p
Energy of Incident H+(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 41.
Calculated FT, and F
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table
42.
FT
0.363
0.319
0.272
0.219
0.164
0.109
0.058
0.020
0.002
0
0
0.182
0.160
0.136
0.110
0.082
0.055
0.029
0.010
0.001
0
0
for gold bombarded by H+
FT
0.820
0.801
0.779
0.750
0.714
0.666
0.599
0.500
0.336
0.111
0.010
0
0
Calculated FT, and Fp for iron bombarded by
F
p
0.410
0.401
0.390
0.375
0.357
0.333
0.300
0.250
0.168
0.056
0.005
0
0
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 43.
0.969
0.966
0.961
0.956
0.948
0.939
0.923
0.898
0.849
0.714
0.497
0.021
0
0.485
0.483
0.481
0.478
0.474
0.470
0.462
0.449
0.425
0.357
0.249
0.011
0
Calculated FT, and Fp for magnesium bombarded by H
Energy of Incident H+ (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 44 .
FT
FT
0.870
0.856
0.839
0.817
0.788
0.750
0.694
0.610
0.467
0.202
0.035
0
0.435
0.428
0.420
0.409
0.394
0.375
0.347
0.305
0.234
0.101
0.018
0
Calculated F , and F for manganese bombarded by H+
T
P
.99
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 45.
0.806
0.786
0.762
0.731
0.693
0.642
0.571
0.469
0.314
0.090
0.008
0
0
F
p
0.403
0.393
0.381
0.366
0.347
0.321
0.286
0.235
0.157
0.045
0.004
0
0
Calculated FT, and F for nickel bombarded by H
T
p
Energy of Incident H+(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 46.
FT
FM
0.970
0.966
0.958
0.952
0.944
0.932
0.914
0.883
0.823
0.655
0.397
0.030
F
p
0.485
0.483
0.479
0.476
0.472
0.466
0.457
0.442
0.412
0.328
0.199
0.015
0
Calculated FT, and Fp for potassium bombarded by H
100
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 47.
0.899
0.889
0.875
0.859
0.837
0.808
0.766
0.699
0.582
0.335
0.033
0
F
p
0.450
0.445
0.438
0.430
0.419
0.404
0.383
0.350
0.291
0.168
0.017
0
Calculated FT' and F for silicon bombarded by H+
T'
.
p
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 48 .
FT
FT
0.719
0.690
0.655
0.612
0.558
0.489
0.400
0.282
0.138
0.026
0.0001
0
F
p
0.360
0.345
0.328
0.306
0.279
0.245
0.200
0.141
0.069
0.013
0.00005
0
Calculated FT, and F for silver bombarded by H +
T '?
p
101
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 49.
0.978
0.976
0.973
0.968
0.964
0.955
0.945
0.927
0.890
0.785
0.603
0.058
F
p
0.489
0.488
0.487
0.484
0.482
0.478
0.473
0.464
0.445
0.393
0.302
0.029
Calculated FT' T and F for sodium bombarded by H
.
p
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 50.
FT
FT
0.827
0.810
0.788
0.761
0.727
0.680
0.616
0.521
0.371
0.130
0.015
0
0
0.414
0.405
0.394
0.381
0.364
0.340
0.308
0.261
0.186
0.065
0.008
0
0
Calculated FT, Tand F for titanium bombarded byH+
p
102
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 51.
Calculated FT, and F
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 52.
FT
0.915
0.905
0.892
0.876
0.854
0.824
0.780
0.709
0.579
0.300
0.073
0.458
0.453
0.446
0.438
0.427
0.412
0.390
0.355
0.290
0.150
0.037
0
for zinc bombarded by H
FT
0.966
0.962
0.956
0.950
0.942
0.931
0.915
0.888
0.836
0.697
0.481
0.026
0
0.483
0.481
0.478
0.475
0.471
0.466
0.458
0.444
0.418
0.349
0.241
0.013
0
Calculated FT, T and'Fp for oxygen bombarded by H+
103
Energy of Incident H+(eV)
1000
900
800
700
600
500
400
300
200
100
Table 53.
Calculated FT, and F
Energy of Incident H (eV)
1000
900
800
700
600
.500
400
300
200
100
50
10
1
Table 54.
FT
0.428
0.388
0.343
0.292
0.236
0.174
0.111.
0.051
0.011
F.
p
0.214
0.194
0.172
0.146
0.118
0.087
0.056
0.026
0.006
for Al203 bombarded by H
FT
0.686
0.657
0.623
0.581
0.531
0.466
0.383
0.276
0.142
0.019
0.0003
0
0
Calculated FT, Tand Fp for CaO bombarded by H
0.343
0.329
0.312
0.291
0.266
0.233
0.192
0.138
0.071
0.010
0.00015
0
0
104
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 55.
Calculated FT, and F
Energy of Incident H (eV)
1000
900
800
700
600
.500
400
300
200
100
Table 56.
Calculated FT, and F
FT
0.474
0.435
0.391
0.341
0.284
0.220
0.149.
0.078
0.021
0.0004
0
0.23.7
0.218
0.196
0.171
0.142
0.110
0.075
0.039
0.011
0.0002
0
for FeO bombarded by H+
FT
F
0.138
0.110
0.082
0.056
0.034
0.017
0.006
0.001
0
0.069
0.055
0.041
0.028
0.017
0.009
0.003
0.0005
0
0
0
0
0
p
for Fe203 bombarded by H+
105
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
Table 57.
Calculated FT'. and F
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 58.
Calculated FT, and F
FT
Fp
0.046
0.032
0.020
0.011
0.005
0.002
0.001
0.0003
0.023
0.016
0.010
0.006
0.003
0.001
0.0005
0.00015
0
0
0
for Fe304 bombarded by H
FT
Fp
0.776
0.754
0.727
0.694
0.653
0.599
0.526
0.423
0.272
0.072
0.005
0
0
0.388
0.377
0.364
0.347
0.327
0.300
0.263
0.212
0.136
0.036
0.0025
0
0
for MgO bombarded by H +
106
Energy of Incident H +(eV)
1000
900
800
700
600
500
400
300
200
100
50
10
1
Table 59.
0.547
0.511
0.469
0.420
0.362
0.294
0.215
0.127
0.043
0.002
0
0
0
0.274
0.256
0.235
0.210
0.181
0.147
0.108
0.064
0.022
0.001
0
0
0
Calculated F Ty and Fp for MnO bombarded by H
Energy of Incident H (eV)
1000
900
800
700
600
500
400
300
200
100
50
10
Table 60.
FT
Calculated FT, and F
FT
F
0.514
0.476
0.433
0.383
0.325
0.257
0.175
0.095
0.030
0.001
0
0.257
0.238
0.217
0.192
0.163
0.129
0.088
0.048
0.015
0.0005
0
for TiO2 bombarded by H
p
Site
Apollo
Oxide
12
[Loss
Rate]
Atoms/cm2 year
Al2O 3
CaO
FeO
MgO
MnO
TiO2
x 1015
A1203
CaO
FeO
MgO
MnO
TiO2
.09 x 1015
I
.40
t
.09
I"
.42
i"
.13
i"
.12
"t
It
it
It
"
to
0
A/year
.40
.48
.37
.98
.52
.48
Metal
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
[Loss Rate]
Atoms/cm2 year
A/year
.31 x 1015
1t
.52
.16
.15
.15
.03
.77
.23
If
.05
it
.22
is
.14
to
Apollo 14
Site C'
(Gutenberg
.30
.31
.30
.34
.44
.40
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
.30
.49
.15
.15
.14
.01
.75
.22
.27
.21
.13
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
.33
.49
.19
.13
.18
.10
.80
.27
.10
.23
.17
it
It
"I
It
"t
it
"t
"t
ifl
it
"I
"t
"t
It
"I
it"t
it
1.00
1.64
0.50
0.51
0.46
3.34
2.49
0.72
0.91
0.69
0.43
it
Apollo 15
A1 2 0 3
CaO
FeO
MgO
MnO
TiO2
.18 x 1015
f
.55
.16
i,
.50
.21
.19
.60
.81
.53
.66
.69
.64
It
IV
it
it
1.11
1.86
0.63
0.44
0.59
3.66
2.64
0.88
3.64
0.77
0.55
Site
Oxide
Taylor Crater
A1 2 0 3
CaO
FeO
MgO
MnO
TiO 2
Toricelli R
Al203
CaO
FeO
[Loss Rate]
Atoms/cm2 year .
x105
"
"
"I
"I
x
10
it
to
MgO
it
MnO
of
TiO2
it
15
[Loss Rate]
Atoms/cm2 year
A/year
Metal
0.55
1.13
0.49
1.63
0.66
0.61
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti*
. 33 x 1015
Al
Ca
Cr
Cu
Fe
K
Mg
Mn
Na
Si
Ti
.32 x 1015
11
.53
of
.18
of
.15
",
.16
it
"t
.06
"I
0.49
1.62
0.45
1.56
0.58
0.55
Table 61. Sputtering rates at Moon under solar-wind bombarment.
.55
.19
.14
.17
.08
.79
.26
.08
.23
.16
.77
.25
.06
.23
.15
"
"
"
"
'-'
"
"I
",
A/year
1.10
1.81
0.63
.0.47
0.55
3.59
2.62
0.87
3.57
0.77
0.52
109
AH D(0)/y
Oxide
AH (M)
Al203
76
134
0.57
CaO
36
151
0.24
FeO
84
64
1.31
MgO
33
145
0.23
Si0 2
87
104
0.84
TiO 2
106
114
0.93
Ti 2 03
106
123
0.86
Ti3 0
106
117
0.91
Table 62.
AHs (M)/[AHD(O)/y]
Comparison of AH (M) and AHD (0) for some elements
IFrom Pillinger et al., 1976].
occuring in lunar soils.
110
FIGURES
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10 X 10 TO THE CENTIMETER
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18 X 25 CM.
46 1510
Fig. 5.
. . *. -
.'
..
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--
...
INU.S.A
MADE
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Sputtering yields for H+ ions
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from Eq. (25)].
_
4
44
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1
5
1
-t44
I
-
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{
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f
7
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F g.
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Sputtering yields for H ions
incident on calcium [calculated
6.
Eq. (2 5)]
*from
-
- w
.~~
. .......
77
..
T>
i t
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Fig.
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q
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7 .~7 7
4
F
IL-
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. ... ..
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-t
on chromium [calculat-
ed from Eq.(25)].
.--
.
Sputtering yields for H+ ions
7incident
I7__
U
_.
*
-
I(k
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IL
. -1
1
1
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.. ..
--
Sputtering yields for H~ ions
incident on chromium [calculated
o
Eq. (25]
t--
i
- ---
-(.2454).
77
---- --
7-
--
I
a
00
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Fig.
9.
Sputtering yields for H+ ions
and Wehner
k'' FKenKnight
7777j
incident on copper
from Eq.(25)].
- ---
----
-
---
-
-
[calculated
AWehner
-
-
-
-
S ....
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-7
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.
yields for H+. ions
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2
---
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Fig. 10
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11.
Sputtering yields for H+ ions
incident on gold [calculated
from Eq. (25)].
*KenKnight and Wehner
I I
*
i.
v!..-
II____
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t .t : , Wi-i
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7-
[calculated
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ions
(25)1]
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H
for
yields
Sputtering
12.
"Fig.
.
7r
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. .. . . . . .
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7
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Fig. 13. Sputtering yields for f+ ions
incident on iron [calculated
from Eq. (25)].
*Kenknight and Wehner
AWehner
I
-I
-
tt
t ..1 .I
t
14r1
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77
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t
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+
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-
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_
I
-
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I
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-
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717
7
....
4
-
-7.
-4-
Sputtering yields for H+ ions
Fig. 14.
incident on iron [calculated
* -from Eq.(25)].
-KenKnight and Wehner
AWehner
--
-
-
_
-
-
-
.j
--
-
--
t
--
-
77
-
--....
K
-
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1
----
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t
.77
.
..
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7
7
--
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.
.
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1
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.
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7
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-
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5
6...7.0
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8
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7
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-
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;___
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:q
Fig.
15.
Sputtering yields for H+ ions
incident on magnesium [calculated from Eq. (25)].
-
~~
.
.. .
7<P7
I
e
-
1
. ..
.
. .
.. .
. . . ._
_
t
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-
. . ..
._
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_
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--
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7_.
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tM
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MAUL IN
U
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7 7-.
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*
.
Fig.
.
.
7
. .
. . .
.
.
....
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.1
16.
- 7.-
for H+
Sputtering yields
71
.2
..
.
_
71r"
~1t
It
77
...
..
.
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-
ions
incident on magnesium [calculated from Ec.(25)].
-7
.1
611
..
CI
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.
.
. I I.
....
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0
tit~~;
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22
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->..
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H
Sputtering yields for
ions
ed from Eq.(25)].
-
q
_
_
7=
77
t
t8i-
_
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1
-f-7
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7
--
74
0-
h7
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l7
777
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7
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0 -7 1-I_
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------
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KEUFFEL &
-
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7- -
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1
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t IT1
1 7T
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-
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-7
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Sputtering yields for H+ ions
on manganese [calcuIincident
N lated from Eg. (25)1].
T JT ' TFig. 18.
TT7
7777
9+
1U
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LDJ.
MADE N U S A
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f rH i n
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CO.
18 x
U
46 IblO
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MADE IN U S A
I.
-
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.. .....
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5 1-
Fig.
7
*
ions
Sputtering yields for H
19.
incident on nickel
[calculated
from Eq. (25)].
*KenKnight
__
and
Wehner
t-
-------------------------
------
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--
--
--
-
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477
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46 1510
7_77 77.77
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7
7
7
~----ig.
20.
*-
i-
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Sputtering yields frH
--
incident on nickel
-
[calculat-
----- -ed from Eq. (25)].
*KenKnight and Wehner
4
4
ti
I
= 7...
...
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7
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IL~t#-
V,~
18X
46 1510
25 CM.
- tFig---7t-
7-
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Fig
-
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.
.
Sputtering yields for H+ ions
on oxygen [calculated
.-.. -v from Eq. (25) ].
21.
-incident
..
.
--
-
177
*-
....... . .i .
717i..
.. ...
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t
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.
.... .
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....
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77
---
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+.
..
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~~ ~ ~~ - ~ -7 ~. ~ ~ ~ ~ ~ ~ ~ -.
IiI-I.IiiIi1
17
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10
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KEUFFEL & ESSER CO.
18 X 25 CM.
461510
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...
I ......
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. . ...:.V
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.:
. 2..
I
'I
fht77t+
~
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Thi
T
t - -
nt
-77
.
. . .
T
ig. 22.
Sputtering yields for H + ions
incident on oxygen [calculated
from Eq.(25)].
..iii......_._
_.
I~.
i-
.-----
~
~
--------
--
_
-
1-41
os2~~-4--7
--
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i
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f ....
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....
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I *-
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,--~-I-------------
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* 1
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K~k
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x
In
n I 5~I
ir
'
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& ESSER CO. MADE IN
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-r
o
r
A-i-
1--
I-
I
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Fig. 23. Sputtering yields for HI ions
i
incident on potassium [calculat-ed from Eq. (25)].
-A
u.Jv
77-.
--
71-7-
-
-
--
-
-
7.
-
-
.
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1---
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17
15
0
...
.
q:
.
T
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7
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w
w.
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1
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0-4-
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10
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777
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A
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.
4b 1olu
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. .~ .
, .
inc924nt on potssium [acuj
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from
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.
.
Eq. (25)].
. .
. .
.
.
. .
. .
.
. .
. .
.
. .
. ..
tt
7V7
4
*
.._
__....
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'S
.
. .
. ..-
.. ..
|L/Ark
& ESSER CO.
46-1510
18 x 25 CM.
10 X 10 TO THE CENTIMETER
KEUFFEL
INUS A
MADC
I
f*.ii:;*
.-
-~~~~;1
,..
7-
'.
.
I ..
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I
44,
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Fig. 25. Sputtering yields for H+ ions
incident on silver [calculated
from Eq.(25)].
flGrolund and Moore
It
7-71~
- 7-
-..-.
..
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7 -
--
T"t
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T-
w
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4
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10
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Ho-- KEUFFEL & ESSER CO. MADEIN USA.
46-1510
18 X 25 CM.
.... .....
_.
K
r.1i
Th
__
7~7
7-
717
..
...
__-_-_-__-_-__-_4
H
Sputtering yields for H
26.
-;Fig.
incident on silver
S7ed
.
-
---
-
- -
_7 - 7 .
. .
-
..
.
.
LW~~7 __.l
1~i
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7
.
7
WJ.,
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;
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b
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ions
[calculat-
from Eq.(25)].
-__--__
*z-~
-
-
EGrolund and Moore
7
U
.... .
.____
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t
,:
10 X 10 TO THE CENTIMETER
KEUFFEL & ESSER CO. MADEIN U.SA.
46 1510
18 X 25 CM
I~~7
T~7-
777-7--------Fig. ...... ...2.Spu
._....
te.n
yield
-
..or
H.on
*---------------------------------------incident on silicon [calculated
....
fromnEg (25)].
... ... .. . .
-777
7
_
7
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7
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07777--
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5L-706
7K
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. .... ......
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7 - . --.
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18 X 25 CM.
10 X 10 TO THE CENTIMETER
46 1510
KEUFFEL & ESSER CO. MADEIN U.S A.
..
-
.ig
Variation of the sp uttering
yield with angle of incidence
for H ions on aluminum [calculated from Eq.(26)].
Clt . . ..C *C.
35.
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Sputtering yields for H ions
incident on MnO [calculated
r17from
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Variation of the sputtering
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for H ions on Al 0
[calcu-
..
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7 777
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Variation of the sputtering
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from Eq.(26)].
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Variation of the sputtering
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for
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Variation of the sputtering
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2
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4
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7
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Variation of the sputtering
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Variation of the sputtering
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Fig. 7 --Velocity distribution of
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ions incident on A10 3
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Velocity distribution of
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Velocity distribution of
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Velocity distribution of
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1
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2
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Velocity distribution of
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AEi=200eV
AEi=400eV
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