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The defect structure of depleted zones in irradiated tungsten
THE
DEFECT
STRUCTURE L.
A.
OF DEPLETED
BEAVAN,t
R.
M.
ZONES
SCANLANt$
IN IRRADIATED
and D. N.
TUNGSTEN*
SEIDMANt
A quantitative field ion microscope study was made of the defect StruCtUr8 of two depleted zones detected in high purity ( < 1.6 - 1O-6 at.fr. impurity level) tungsten specimens irradiated i?a tiitzl under ultra-high v&cuum conditions at & specimen temperature of 18°K with 20 k8V W+ ions to a dose of N 1.10ie W+ ions cm-e. The irradiated specimens were examined by the pulse fiold evaporation technique at lt)‘K, hence their structure is ohamcteristic of this temperature. The depleted zone detected in tb8 (Ill) plane had a local vacant site concentration of N 3.7 at. */@and a self-interstitial atomconcentration (SIA) of N 0.92 at. ‘A, while the depleted zone detected in the (141) plane of a second specimen had values of - 10 and N 0.5 at. o/ofor these same quantities. The SIAs found locally were on the peripheral surfaces of the depleted zones. In addition to this large local imbahmce in point defect concentrations the depleted zones were elong&ted.along (011) directions. It was shown that each of these depleted zones was cm&ted by a single incident ion, and a comparison of the number of displaced atoms in each zone with the value predicted by the Kinchin-Pease model showed that this mod81 strongly overestimates the number of displacements created per incident ion. For the depleted zone detected in the (111) plene it was demonstrated that 23 of 25 SIAs found in the lattice around this zone could have been propagated away from it along (011) and (111) directions as focused replacement sequences. The measured distsnces of these SIAs away from the depleted zone along (011) and {i 11) directions were between 45-150 and 4585A, respectively. The upper and lower values of these distances were determined by a geometric sampling problem and not by the intrinsic range of focused replacement sequences. STRUCTURE
DES
DEFAUTS DES TUNGSTE~E
ZONES APPAUVRIES IRRADIE
DANS
LE
Au moyen du microscope a &mission d’ions, les auteurs ont effectu6 une etude quantitative de la structure des defauts de deux zones appauvries deteot6es dans des cjchantillons de tungstene de haute puretcj ( < 1,5 +lo-@ at. d’impurct6s) irradies in situ dans des conditions d’ultravide Bleve, a 18°K &veC des ions W+ de 20 keV jusqu’a une dose de 1 . lo** W+ ions crnea environ. Los bchantillons irradies ont Otn examines par la methode d’~vaporation par ohamp pulsti & 18”K, leur structure est done earact6ristique de cette temperature. L& zone appauvrie detectee dans 18 plan (111) present8 une concentration locale de sites vacanta de 8,7 at.% environ et une concentration d’atomes selfinterstitiels (SIA) de 0,92 at. o/0environ, alors que pour la zone appauvrie detect&e dans 18plan (141) d’un deuxieme Bchantillon, on obtient des valeurs de 10 et 0,5 at.% environ pour ces m6mes quantites. Les SIA trouvbs localement se trouvent SUPles surfaces peripheriques des zones appauvries. En plus de c8 dcSs6quilibrelooat important dans les concentrations des defauts ponetuels, 18szones appauvries sent disposbes 18 long des direotions (011). Les auteurs montrent que oh&curie de CBSzones est cr66e par un seul ion incident, et une comparaison du nombre d’atomes d8places dam ohaque zone WOO la vdeur pr8vue par la modele de Kinchin et Pease montre quo ce mod8le surestime fortement le nombre de deplacements ctiQs p&r chaque ion incident. Pour 18s zones appauvries detect6es dans 18 plan (11 l), 18s auteurs montrent que 23 des 25 SIA trouves dans le reseau amour de cette zone pourraient s’etre d6plactj.s a partir d’etle la long des dimctions (011) et (Ill) en st’quences de remplacement focalis8es. Les distances d8 oes SIA Q la zone, mesurees Ie long des directions (011) et (Ill) sent respeotivement de 45-150 et 45-85 A. Les v&leurs inferieures et superieurcs de ces distances ont et8 d6terminees par un calcul geomt?trique. DIE
STRUKTUR
V~RD~N~TER
ZONEN
IN
BESTR~LTEM
WOLFRA~~
Die Defektstruktur zweier verdtinnter Zonen, die durch in situ-Bestrahlung hochreiner Wolframproben (Verunreinigungskonzentration 5 1,5 . 10-6At.%) im Ultrahochvakunm bei 18°K mit 20 keV-Wolframionen (Dosis - I . lOie W+-Ionen/om*) erzeugt worden w&ren, wurde mit Bilfe quentitativer Feldionenmikroskopie bestimmt. Die bestrahlten Proban wurden bei 18°K mit der Method8 der Feldv~rdampfung uutersucht, d.h. die Struktnr der verdunnten Zonen ist fur dies8 Temperatur eharakteristisoh. Die auf der (1 ll)-Ebene gefundena verdiinnte Zone hatte sine lokale Leerstellenkonzentration von 8,7 At.% und eine Zwisohengitteratomkonzentration (SIA) von 0,92 At.%, wahrend die entsprechenden Gr658n der auf der (141).Ebene einer &nd8r8n Probe beobaohteten verdtinnten Zone 10 und 0,5 At.% waren. Die iokal bestimmten SIA-Wsrte gelten fur die peripheren Flachen der verdiinnten Zonen. Zusat,zlich zu diesem groGen lokalen Ungleichgewicht der Defektko~entr&tionen wurde eine Ausdehung der verdtinnten Zonen entl&ng (Oil)-Richtungen beobachtet. Es konnte gezeigt werden, da13 jede dieser verdmmten Zoncn durch ein einziges einfallendes Ion erzeugt wordon w&r. Ein Vergleich der Z&h1 der verlagerten Atome jeder Zone mit dem n&oh dem Kinchin-Pease-Model1 vorhergesagten Wert ergab, d&S dieses Mod811die Zshl der von einem einfallenden Ion erzeugten verlagerten Atome stark iiberschatzt. Fiir die auf der (Ill)-Eben8 gefundene Zone wurde gezeigt, da13 23 der 25 im umliegenden Gitter beobachteten Zwis~hengitte~tome ve~utli~h durch (01 l)- oder (11 l)-E~etzun~~t~~e aus dem Kernbereich der verdiinnten Zone wegtransportiert worden waren. Die Laufwege dieser Zwischengitter&tome entlang d8r (Oil)- und (Ill)-Richtungen lagen zwischen 45 und 150 A bzw. 45 und 85 A. Die oberen und unteren Grenzen dieser Reiohweiten wurden anhand eines geometrischen Modells bestimmt.
* Received April 26, 1971. This work was supported by the U.S. Atomic Energy Commissionunder Contract AT(30-l)-350450. Additional support was received from the Advanced Research Projects Agency through the use of the technical facilities of the Materials Science Center at Cornell University. t Cornell University, Department of Mrtterials Science and Engineering, Ithaca, New York 14850. $ NOW at: General Electric Research and Development Center, Schenectady, New York. ACTA
~~ETALLURGI~A,
VOL.
19, DECEMBER
1971
1339
ACTA
1340
METALLURGICA,
1. INT~QDUCTIQN
The concept
of a depleted
idea of a displacement by Brinkman.(ls2) heavy
metal
almost
from the
spike which was first described
energy of the incident displaces
the
zone evolved
A displacement
irradiated
with
spike occurs
metal
ions
when
the
atom
that
it
encounters.
Seeger’x) later pointed out that the existence of focused replacement
sequences would result in the transport of
self-interstitial
atoms
(SIAs)
away from the region
of the displacement
spike,
structure
a depleted
is called
The high local imbalance
and the resulting (or
of vacant
STAs in the region of a depleted
defect
diluted) lattice
zone.
sites and
zone also appears in
t,he ~~~rnputersimulated models of low energy collision events and
I< 2 keV]
described
by
‘CTineyard et aJ.(Q
the high energy
collision events programmed [ < 20 keV] by Beeler. c5) The physical reason for this
imbalance
in the local point defect concentrations
the fact that SIAs enjoy a mode of propagation from
the
displacement
spike,
whereas
does not as long as the temperature
is
away
a vacancy
is below the value
at which the vacant site is mobile. There have been a number of electron investigations
of depleted
with various types of energetic of this literature The electron
particles,
has been reviewed
microscope
resolving the individual
microscope
zones in metals irradiated and much
by Wilkens.c6)
is not at present capable of vacant lattice
sites or SIAs
in the depleted zone. and therefore the field ion microscope
(FIM)
with
suited for a detailed of point defects
its atomic
point defect
little
qualitative
quantitative
structure
metals were per-
and Galligan,“)
Hudson
These FIM investigations
of an essentially
zone.
with these prior investigations dissection
increments
specimens
were not’ employed.
that it is necessary
et oL(*)
have been
about
the
is that fine enough
to dissect
It will become a given atomic
one or two atoms at, a time, whereas
of the clear plane
all the above
experiment*s employed a field evaporation of about, one atomic layer.
1971
of the
depleted
and the existence
zones
along
of focused
(011)
replacement
sequences along (111) and (011) directions. 2. EXPERIMENTAL
TECHNIQUES
High purity W (9
> 4 * lo*, where .!J?is the resistance ratio R22930H/R4.2aK) specimens were irradiated with 20 keV W+ ions in a vacuum of (l-10) - lo-lo torr, and at a tip temperature irradiated
specimens
employing (e.g.
the
were
pulse
field
see Robertson
micrograph
and
(Tr)
then
of l@K.
examined
evaporation
SeidmanoO))
was taken between
T,
technique and
a FIM
each pulse with the
aid of an external image intensification semi-automated
The at
system, and a
35 mm ein& camera.
The field eva-
poration pulse width and height were adjusted so that each plane was dissected
one to two atoms at a time
(e.g. see Balluffi et oZ.(ii)). with
a
Vanguard
The cin& film was scanned
motion
analyzer
(see
Scanlan
et al.(12)for details concerning the data recording and analysis system).
All the analyses were performed
on
the enlarged negatives. Detailed infornlation tion,
the
concerning
ultra-high
vacuum
specimen
FIM,
the
metal ion source, and the measurement T,
have been reported
Scanlan
previously
et cL(~~)). In addition
preparasputtered
and control of
(Seidman et al. ;c13) it has been shown
(Seidman and Scanlan (lsl) that heating effects due to thermal
radiation,
ion
beam
gas and the thermoelastic evaporation
were
temperatures
negligible,
should
range
migration
of
SIAs
pulse
the
to T,
field
measured
rather
well.
was performed at 18°K
after the irradiation,
to the state of the depleted
the imaging
during
hence
correspond
Since, all the field evaporation immediately
heating,
effect
the results pertain
zone prior to any long and
vacancies
(Scanlan
et fl.J.(16)). 3. EXPERIMENTAL
RESULTS
defect
The main difficulty
in the field evaporation
The material presented
elongation
nature, and have given
information
of the depleted
zone.
of the FIM to the study of
clusters in irradiated
by Attardo
and Buswell.‘9)
is better
within and around a depleted
The previous applications formed
resolution
study of the spatial distribution
19,
directions,
in a
ion falls to a value such that it
every
VOL.
increment,
The first depleted
zone we consider
was detected
in a (111) plane on the incident beam side of the FIM tip
N 33 A
from
shows 20 different
the irradiated
surface.
FIM miorographs
Figure
1
of this depleted
zone taken at various stages of the dissection
process
whioh involved
the recording and analysis of a total of 4.4 * lo3 frames of film. (The examination of more than 7.5 * lo4 frames of film of unirradiated
control
here represents the results
specimens never revealed contrast effects of the type
of a quantitative study of two depleted zones in two different W specimens which were irradiated with
shown in Fig. 1.) The positions of the atoms and the vacant sites found in this plane are schematically
20 keV W+ ions at 18°K.
illustrated
Direct evidence is presented
for t,he existence of a local imbalance in the point defect concentration at the site of the depleted zone,
below each micrograph.
This depleted zone
extended through 50 successive (111) planes, and the tot,al number of atomic sites in t,he volume containing
BEAVA2;
et
DEPLETED
al.:
ZONES
IN
IRRADIATED
imbalance
1341
TUNQSTEN
between
the vacant
lattice
site and SIA
concentrations. Figure lattice
2 shows
a (111) projection
sites and SIA
positions
a depleted
analyzing
zone
of the vacant
(the
is given
The vacant lattice sites are denoted
procedure
for
in Section
4).
by open circles,
the SIAs by solid triangles and the multiple concentric circles imply t,hat more than one vacant site projected of projection
to the same atom position. reveals the 3 distinct
the depleted zone.
The direction
main branches
of elongation
3 branches was along the 3 different lying in the (111) plane.
lattice
This mode of
of the
(011) directions
An isometric drawing of this
depleted zone is shown in Fig. 3, where the thickness of each slab* is 4.56~(5atomiclayers),alld ary of each slab was determined
the bound-
by connecting
outer point defects on its periphery
the
by straight line
Figure 4 shows a series of 6 photographs
segments.
the ball model of this depleted indicate the positions
zone.
of
The large balls
of the vacant lattice sites, and
the small balls are SIAs.
It is clear from Figs. l-4
that the geometry of this depleted zone is not so regular that it could be approximatecl circular
cylinder,
or for
by a sphere or a right
that, mat,tcr
any
simple
geometric form. In t,he lattice of the specimen which contained depleted
zone there were 25 additional
were found
at appreciable
distances
this
SIAs which
from the zone.
The positions of these 25 SIAs are shown in Fig. 5, FIC~. 1, A series of 20 FIM micrographs (out of 4.4 * lo3 recorded) taken at various stages of the atom-by-atom dissection of the depleted zone detected in the (111) piene. The large solid black circles indicate SIAs, the open circles vacant lattice sites and the smaller solid black circles lattice atoms.
and their measured distances from the depleted
the most probable
crystallographic
directions
which these SIAs
were propagated
away from the depleted zone are also
1850.
completely
The
depleted
contained
within
zone
appeared
to
the periphery
be
of this
along
listed in Table 1. The numbers of the SIAs in Fig. 5 correspond
it was
zone
are listed in Table 1. In addition,
to the numbers in Table 1. A description
of the procedure
used to determine
graphic directions
is given in Appendices
these crystalloA and B.
(111) plane as no vacant sites were found on the atomic planes adjacent
directly to it. There were 172 vacant
sites within this 1850 at. vol. (!&) region. Tn addition, a total
of
17 SIAs
were found
in or immediately
adjacent to the depleted zone for a SIA concentration of -
0.92 at. %.
(unpublished accompan~~ng vation
It had been shown in this laboratory
work)
that
a possible
the appearance
of a vacant
contrast
effect
of a SIA is the obser-
lattice site immediately
prior to
the detection of the SIA. Since 12 of the SIAs observed in the (111) plane were preceded by a vacant
The second zone analyzed
was found
plane with its bottom surface ted side of the FIM intersecting depleted
specimen,
in the (141)
19d from the irradiaand its top surface
the surface of the specimen.
Since this
zone was so close to the irradiated
surface
we cannot be certain if it is a partial or a t,otal depleted zone. The dissection of this depleted zone involved the recording and analysis of 2.1 + 103 frames of film. A total of 85 vacant sites were found within a
lattice site we have taken the number of real vacant lattice sites to be 160. This latter correction implied
800 L& region, which meant that the vacancy concentration was - 10 at.%.? The number of SIAs found
that the concentration zone was - 8.7 at.%.
* With the except,ion of the third slab from t.he bottom, which is 10 atomic layers thick. 7 This based on a corrected value of 81 vacant sites (see Section 3.1 for the reason for the correction).
rather spongy
of vacant lattice sites in this Thus, the depleted zone had a
character,
and there was a large local
ACTA
1342
METALLURGICA,
VOL.
19,
19il I
PRbJECTldN
[iol] ,
/
\4-[oli)
---
i
ONTO
ll-
20
ONTO 50
/I 1
/
21-30
-~~
OF PLANES
50
FIG. 2. A series of (111) projections of the depleted zone detected in the (111) plane. The vacant lattice sites are indicated by open ciroles, the SIAs by solid black triangles and the multiple concentric circles imply that more than one vacant lattice site projected to the same atomic position. The zone in map 1 is elongated a.long [Toll, in map 2 along [TlO] and [iOl], in map 3 along [ilO] and in map 4 along [Toll. in or very
near this depleted
local
concentration
again
SIA
there was a rather
the SIA and the vacant
zone was 4, hence the
was N 0.5 at. %, and once large imbalance lattice
between
site concentrations.
Figure 6 shows a (141) projection symbols isometric
/(Ill)
drawing
of the depleted
photographic
views of a ball
zone, which was constructed
from the maps used to draw the projections
PLANE
in Fig. 6. This depleted zone exhibited DIRECTION
OF
along enough
the same
in Fig. 2, and Fig. ‘7 is an Finally, of this depleted zone.
Fig. 8 shows 5 different model
employing
as used previously
the
[lOi]
direction,
to be represented
presented
directionality
and it was not by any simple
regular
geometric
form. 4. DEPLETED
ZONE
In order to reconstruct
ANALYSIS
PROCEDURE
a depleted
dimensions the following procedure analyze the 35 mm cink film :
zone in three
was employed
to
1. First the x-y coordinates of the outermost ring of atoms on the plane were determined, and then the FIG. 3. An isometric drewing of the depleted zone detected in (111) plane constructed from the projection maps shown in Fig. 2.
coordinates of all the inner atoms were measured. The coordinates of each inner atom were always read
REAVAN
et al.:
DEPLETED
ZONES
IS
IRRADIATED
1343
TUNGSTES
FIG. 4. A series of 6 photographs of the ball model of the depleted zone constructed from the projection maps of Fig. 2. The large dark balls represent vacant lattice sites, and the smaller balls indicate SIAs. Photograph A was taken along the incident ion beam direction {- [2lI]}. Photographs B-E are perpendicular to the (111) plane. Photograph B w&s taken looking along the [ii21 direction, C along the [lTO] dire&ion, D looking toward the in&dent ion beam (- [211]1 and E along the [Oli] direction. Photograph P is an overhead view of the model taken looking almost along the [I 1I].
with
respect
to
the
remaining on the plane.
previously
measured
atoms
This practice eliminated
any
error due to film positioning between frames, and assured us that each atom was referenced with respect to at least 2 neighbor atoms (many atoms were measured multiply). 2. The x-y coordinates of the atoms in each plane were then plotted utilizing the multiple readings to insure that all atom
positions
were related
to t,he
same coordinate basis. occurred all coordinate
In cases were film slippage readings in that frame were
uniformly shifted to make multiple readings coincide. In no case was a vacant site attributed to a gap in atom coordinates, unless a vacant site was certified visually in the FIM micrograph. The identification of a bright spot as a SIA was determined dure which was previously bhis laboratory.
by a proce-
used (Scanlan et ut.(lQ)) in
ACTA
1344
TABLE
I. Distribution of SIAs found outside of depleted zone debected in a (111) plane SIA propagation direction and distance along
Distance from depleted zone 6)
Location by plane &W ____ -.
of SIA
METALLURGICA,
60 80 80 80 70 45
70 45 105 105
(121) (121) (141) (141) (141) (141) (141) (141) (141) (f41) (141) (X41)
-
[iil] (OTT] [Ofi] [oii] [Oii] [OTT]
70Foij 65 [ill] 60 [iii] 60 [111] 55 [iii] 55 [111] 45 [ill] 135 [ioi] 115 [roil x5 [ill] 85 [iii] 75 [iii] 70 [111] 70 [iii] 150 [roil 100 [ilO] 100 [IlO]
si: 60 60 55 5’ iz 130 100
ii2ij
:: 75 70 70 130 90 90
-.-obtained
in step 2 were then
fitted to a regular array of points by a best fit iteration Next, the array of lattice p,qsitions found
by this t.echnique was compared for t.he particular
to the ideal lattice
plane involved.
j In all cases the
lattice planes determined
expe~~e~tally
to be somewhat
from t‘he theoretical
tion.
distorted
The disto&ion
were found
was always found
were brought
the theoretical 4. Finally,
certainly
created
by
a single
incident
TN+
consists of making an upper
estimate of the number of primaries
associated
with
each depleted zone, and showing that the probability of each depleted zone being created by more than one This upper estimate is a simple geometric argument, based on the measured cross-sectional depicted
zone presented
depleted
zone detected
was Wf
situa-
area which the
to the ion beam.
For the
in the (111) plane this area
1.6 . lo-l3 cm2 and the total dose was N 1 * 1012
ion cm-2,
therefore
the maximum
number
W+ ions which hit this area was -0.16.
of
A similar
calculation for the depleted zone detected in the (141) plane showed
that
the
on its cross-sectional of estimating
the
maximum
number
srea was -~0.02. number
of
hits
This method
of primaries
with each depleted zone is an overestimate
associated because it
neglects the spread in the range of the incident ions. The additional
point which we wish to emphasize
very strongly is that each depleted zone was observed in a different specimen, depleted
and that, there were rrn other
zones found in these two specimens. examined
the density
in each casewas -
of depleted
each specimen.
zones was -
E’urthermore,
that the above
easily into coincidence
is strong
Hence,
we feel
evidence
that,
each depleted zone was only created by one incident ion.
experiwith
atom positions. the lattice
above procedure
planes
were positioned
another in the correct stacking obt,ain a final 3 dimensional
determined
by the
with respect to one sequence
model.
in order to
A ball model
consisting of only the vacancies
and SIAs which were
detected was then above information.
with the aid of the
constructed
5. DISCUSSION 5.1 P~o~b~~~~~ that each ~e~~~~~~zone uxxs created
by one ~nc~~e~~ ion Before proceeding with the main portion of the discussion we shall show that each depleted zone was * The amount of distortion varied inversely with the radius of the tip (Q-). For example, the shear for rr = 134 .& was 12” which decreased to 8’ when the specimen was field evaporated to an zy of = 158 A. For the second speoimen with ~~ = 320 8, the shear was only 6”.
in
of lattice
zone was perfect with
of the SIAs detected. information
1015 cm-3
the volume
examined around each depleted the exception
Since
IO-l7 cm3,
tq be a pure
shear,* so that the lattice points determined mentally
1971
The demonstration
the volume
3. The atom positions procedure.
almost ion.
19,
incident ion was small.
60 80 X0 80
i:::; (Ill) 1lllI
VOL.
FIQ. 5. An isometric drawing showing the relationship of the SIAs in the lattice to the depleted zone detected in the (111) plane. The numbers near the SIAs correspond to the numbers in Table 1. The direction of the incident ion beam (- [21i]) is almost normal to the plane of the page. The arrows from the depleted zone to the SIAs indicate the most probable propagation directiona.
BEAVAK
et al.:
DEPLETED
ZONES
IN
IRRADIATEI)
TfTSGSTES
1345
FIG. 6. Four (141) projections of the depleted zone detected in the (141) plane showing the elongation of this zone along a [lOI]. Vacant lattice sites are denoted by open circles and the SIAs hy solid black triangles.
The features of the depleted zones reported in Section 3 are in general qualitative agreement with many of the details of Beeler’s computer simulated model.c5) In this section we compare some of the details of the structure with Beeler’s model. The first point is that our measured defect concentrations are higher than those calculated by Beeler. The reason for this is due to the fact that he obtained his concentrations on the basis of a calculated volume
v-
(1411
PLANE
DIRECTiON
Of
FIG. 7. An isometric drawing of the depleted zone detected in the (141) plane constructed from the projection maps shown in Fig. 6. The top slab is 6 (141) atomic layers thick, and the other slabs are 5 layers in thickness.
of “collided atoms”.* This quantity cannot yet be experimentally determined, hence we used t.he procedure described in Section 3 to calculate the defect concentrations. Thus, our procedure. by definition, produced higher concentrations than those calculated by Beeler. The second point to note is that in Reeler’s model the elongation of the depleted zones along directions was caused by quasi-channeling? events. The present results indicate that such events are indeed possible. The models in Figs. 3 and 7 bear a, strong resemblance to Beeler’s (see Figs. 12-15 in his paper), although we note that his models are based on the stacking of (001) planes while our models have (111) and a (141) stacking sequence. %inally, the imbalance between the vacant site and SlA concentrations is directly attributable to the propagation of SIAs away from the region of the * Beelerls) refers to a collided atom as “an atom which received a nonzero energy transfer” as the result of a collision event. t Quasi-channeling refers to channeling of shorter range than t.he chtannsling that may occur along the (loo), (110) and (111) “tunnel-like cores”*in t!ha b.c.o. structure. Beeler states that quasi-channeling trajectories “exhibit intermittent low-index ohanneiing and are confined between two closely adjacent atom planes”.
ACTA
1346
METALLURGICA,
VOL.
19,
1971
z
i
FIG. 8. A series of 5 photographs of the ball model constructed from the projection maps of Fig. 6. The larger dark balls represent vacant latt,ice sites, and the small balls indicate SIAs. Photograph A was taken looking along the [Zll] direction, photograph B along the incident beam direction and photograph C looking along the incident beam direction. Photographs U and E aw overhead views of the dcplet’ed zone showing its geometry. Photograph E was t,aken looking along t,he [141].
depleted
zone by focused
Fig. 5 and Table in the lattice the
(111)
Twenty-three
around
the depleted
plane
propagation
replacement
1).
were in positions
along
(111)
and
(011)
sequences
(see
of the 25 SIAs zone detected consistent directions
in
with (see
incident ion are the amorphous solidmodelsof Pease.(ls)
In the present discussion
Kinchin-Pease the expression
Section 5.4).
amorphous
The concentration
of vacant sites determined
between
existing radiation
allows damage
theories and our results. The most commonly used models for the average number of displacements per
and
we will use the
solid model.
which yields
v(E) = E/2E,,
5.3 The concentration of defects in the depleted zones for a comparison
Harrison
and Seitz,(17) Snyder and Neufeld(l*) and Kinchin
(1)
where E is the energy of the primary particle initiating the depleted zone (20 keV in this case), E, the displacement threshold energy (50 eV(20*21)) and v(E) is the average number of displacements the initiating
particle.
Beeler,c5) among
produced
by
others,
has
et al.:
BEAVAN
point,ed
out
efficiency
that
(Ii,,)
the
DEPLETED
Kinchin-Pease
is a constant,
ZONES
displacement
and is given
by
the
expression h’,, Based
= v(E)/‘E = 1,‘(2E,).
011 a binary
model of a depleted
collision
(2)
computer
simulated
zone in W Beeler has shown that
the c~isplacement efficiency is energy dependent
and is
h’,,(E)
= 6.05(1 -- 0.04190 In E),
where E is in keV. the average
displacement
increasing E.
efficiency
The domina~lt
was the recombination
decreases
lattice
structure
with effect
with increasing E
of a SIA from one collision
with a vacancy
along &se-packed
from
directions
The Kin&in-Pease zone
(3)
Thus: Beeler’s model predicts that
which caused t,his decrease in Krr(E)
pleted
IRRADIATED
tion distances
another
collision
event
between 45 and 150 if were measured,
while for the (111) directions
propagation
between
found
45 and
model
on the average
Beelcr’s
model predicts
atoms per depleted zone.
predicts
that, each de-
200 displaced
atoms,
while
an average of 106 displaced The number of permanently
displaced atoms in Beeler’s model is determined
by the
size of the vacancy-SIA
region
employed
direct recombination
in his calculations.
site recombination Frpinsov
region
Beeler used a 30 atom (originally
described
rt ~1.@~)) for his O’K calculations>
by
and he
asserts that. the size of this region will increase as the temperature
We wish to emphasize upper
strongly
sampling problem.
is increased.
Furthermore,
Beeler states
events
region of t,he deplet,ed zone. of 106 displaced
which
have
lattice vibrations
been in the
Thus, the average value
atoms per depleted
zone is an upper
ourselves
that the extra bright
Kot,h of our deplet,ed zones contained value of200
obtained
less than the
on the basis of a Kinchin-Pease
and ih is clear that this model overestimates
considerably
the total
(for a discussion
number
of the defioiences
see Sigmund(z3)).
of displaced
atoms
of this model also
The 160 vacant sites in the depleted
replacement
purely a geometric the planes defined we couid
sequences problem. by [Oil]
not identify
propagation
the
along the (100) was Since no {loo> were in
and r3 (see Appendix
B)
/lOO? as a direction
of
for SIAs.
The computer
sinmlation
studies of radiation
by Erginsoy
near threshold energies focused replacement, sequences would
propagate
easiest
while (011) sequences energies.
in the
6. GENERAL which are of a philosophical some experiments experimental
REMARKS
nature, and also indicate
which now seem possible
with our
facilities.
1. The detailed
information
concerning
structure
here could not have been obt,ained if the
atomic layer.
was as coarse
increment
Hence, it is considered
all future research of this type employ dissection of a given plane. investigations
requirement
as one
mandatory
that,
atom-by-atom
for quantitative
FIM
of deplet,ed zones is that. the dose must,
be a low value if one is to associate each depleted zone with a single incident’ ion. Two depleted zones do not represent a distribution, but they do show that it is possible to obtain direct information
by FILM about the number
of displace-
by a single incident ion.
1. A direct determination displacements
per
incident
Thus, we
FIM experiments
:
of the average number of primary
could be obtained by performing here on N 25 depleted zones.
(111) plane could have been propagated along (011) and (111) directions. For the {Oil) directions propaga-
grounds.
In this section we wish to make a number of remarks
than 106, while the 81 vacant sites found in the second
B it is shown that the SIAs located in
:,lOO),
at higher
Thus, the existence of iOIl) focused replace-
ment sequences is possible on theoretical
suggest the following two additional
In Appendix
;I 11) and
would be established
zone detected in the (111) plane is 51 per cent greater
the (112), (111). (121), (141) and (i41) planes in the specimen containing the depleted zone detected in the
dam-
et uJ.(~~)showed that)
ments produced
zone is w 24 per cent smaller than 106.
Hence, the upper
values along the (111) and (011) in Mr. The absence of focused
2. An essential
lim& in his model.
by a
values ofthese distances are not necessarilythelimiting
field evaporation
depleted
are affected
spot contrast effects that we observe are due TaoSlAs
of indirect
recombination
1f .
Table
That is, that to date we have only
been able t.o satisfy
presented
by excited localized
distances
(see
t,hat the lower and
values for these distances
that, t,his 0°K number will be even smaller as a result
model.
85 L% were
age in K-Fe (b.c.c.)
of atoms.
E)rodu~~?d by a 20 ke?r pi+ ion should
contain
induced
I347
TUNGSTES
in the (112), (111) and fl41) planes.
given by
event
IN
of
energy
E
the analysis reported
2. A measurement of the relative temperature dependence of the size of the direct recombination region
could
be obtained
experiment described temperatures.
by simply
repeating
the
here at a series of irradiation
7.
SUMMARY
AND
CONCLUSIONS
1. A quantitative study was made of the defect structure of two depleted zones detected in W specimens irradiated at 18% to a dose of - I * fW ion cm-2 with 20 keV W+. The depleted zones were examined at 18°K by a pulse Beld evaporation technique that allowed the dissection of atomio planes one to two atoms at a time. Thus, the defects structure reported is characteristic of 18’K and the dose was low enough so that eaoh depleted zone wa8 created by a single incident ion. %. The depleted zone detected in the ( 1I1 ) plane had a rat,her irregular geometry which could not be described by any simple geometricform. It waselongated along t~he3 different (01 I) directions which he in the ( 111 f plane, The concentration of vacant lattice sites in the depleted zone was - 8.7 at.0/b, and the SIA concentration was - 0.92 at.%. The SIAs found locally were located on the peripl~eral surface of tnhe zone. 3. The depleted zone detc&ed in tfhe (142) had an irregular geometry which was elongated along the [lOi] direction. The vacant lattice site ~on~entration was N 10 at.%, and the SIA concentration was N 0.5 at. %. Once again the SIAs were found on the outer surface of the zone, 4. The results stated in 2 and 3 above are direct proof that a depleted zone has a large local imbalance in its point defect concentrations, and that SIBS are stable near the zone at a value of temperature which is below the start of long-range migration of SIAs. 5. The depleted zone detected in the (111) plane had 25 STAs in the surrounding lattice. It was shown that 12 of these 25 SIAs could have been propagat,ed from the zone along (111> directions, and 11 along (OII) directions. For the jOll> directions the p~opagat,ion distances were between 45 and 1508, while for the (111) directions these distances were between &5 and 85 A. The upper and lower limit in both cases was determine by a geometric sampling problem, and not, by the intrinsic range of focused replacement sequences. This result constitutes direct evidence fur the existence of focused replacement sequences. 6. The number of displaced atoms per depleted zone [16O for the one det,ected in the (111) and 81 for the one detected in the (141)] was considerably lower than t,he value of 200 predi~t~~d by the standard Kinchin-Pease model. Hence, this model overestimates strongly the number of defects prodnced by an incident, ion. ACKNOWLEDGEMENTS
We wish to thank Mr. B. F. Addis for the preparation of the high purity tungsten specimens, Professor
R. W. Ballu% for ~o~t,~~uo~lsencouragement and useful discussions, Dr. P. Petroff for useful discussions and Mr. R. Whitmarsh for technical assistance.
edited by A. SEZWER, D. SC~~iVIhcwEB, w, SCEIIAING and J. DIEHL, pp. 485-520. ~~~tl~~~(~ll&n~~ f 1970). 7. %I. J. ATTAR~W and J. &I. GALLIQA~~.Phys. Rm. Lett. 17, 191 (1966). 8. J. A. HUDSOX, B. 2. DFRY and B. RALPII, Phil. Mug. 81, 172 (1970). 9. J. T. BUBWELL. Phil, Mw. 22. 7X7 ifQ70‘1. rn. S. H. ROBERTS& and D, “NcW~~~I&~, J.‘s&&. fnsi~~n. 1, 1244 (i9SS). 11. R, W. BALLUBF’I,K. H. LIE, D. N. SEIDMAN and R. W, SIEGEL, in ~ra.ca&&s a+?d~?~~~r~~it~a~8 i?z &f&a&, edited by A. SEEDER,D. SCHUMACHER,W. SCHILCIXC; rendJ. DIE~F,, pp. 125-167. North-Holland (1970). 12. R. &%iM. SCANUN, D. L. STYRIS, D. N. SEIDMAX %nd D. G. AsT. Corn& X?nive&ty Materials Science &nteP Rspart No. 11.59(1969). 13. D. N. SEIDXAX, R. M. SCANL.W, D. L. STYRIS and J. M. BWHLEN, J. scient. In&mm. 2, 473 (1969). 14, R. 112. SC.~NLAPF,D. L. STYEWZ and D. N. SEIDMAN, Phil. &Wq$23,1439 (1971). 1.5. D. N. SEIUMAN and R. M. SCANLAX, Ph& Hag. 23, 1429 (1971). 16. R. M. SCANLAN, D. L. STYRW snd D. N. SEIDMAN, FW&. Mq. 25,1459 (X971). 17. w. HARRISON WX?F. SEITZ. PkW. B&v. 98. 1636 fl9&%. Ph&‘Rcv. $7, 1&% 18. 5%‘.8. SNYDER anti J. N&FE& (1955); J. NEUWLI> end W. 8. SNYUER, P&s. Rev. 99, 1326 (1955). 19. G. H. KINCHIN and R. S. PEASE. in Re;rmrts on Proarms in Physics, edited by A. C. ~TICXiANU, -Vol. 28, p. i. Tbo Physical Society ( 1956). 20. C. C. ROBERTS, Ph.l3. Thosis, Univcrsitg of North Caroline at ChtapeLHill (1968); C. G. ROBERTS. B&E dnb. Phys. Sot. 13, 255 (1968). 21. J. A. DICA!ARLO and J. T. STANXZY, Bzctl. Ant. Whys. Sac. 16, 317 (1971). 22. C. ER~IES~Y, 0. H. VINEYARD and A. ENQLERT, Hqp. Rev. 153, A595 (1964). 23. P. SIOMTIND,Ap@. Php. Lett. 14, 114 (19US). APPENDIX
A
The model employed for the tip was a hernisp~~~e of radius R. It was assumed that as the field evaporation process prooeeded the tip remained he~~sphe~cal, and that R increased uniformly. This model is shown in Fig. 9 where R, and R, represent the initial and final radii, respectively, It is seen that t,he center of each net plane shifts parallel to the surface of the plane by an amount* S as a result of the field evaporation process. The specimen in which a depleted zone was detected in the (Ill) plane had values of R, and R2 equal to 134 and 158A, respectively. The value of R, was measured when the last (111) plane in the depleted zone was imaged. The measured value of X in this
BEAVAN
et al.:
DEPLETED
ZONES
IN
IRRADIATED
,d’ HEMISPHERE APPROXIMATING
OF
HEMISPHERE
FINAL
(h k 1)
RADIUS R, IRRADIATED
PLANE
OBSERVED
CYLINDER OF (h k l, PLANES OBSERVED DURING EVAPORATION
OF
TIP
1349
TUNGSTEN
LAST (h k 1, OBSERVED
PLANE
SURFACE+ /
9. The model of the specimen used to calculate the depleted zone geometry and its relationship to the SIA’s in the lattice around it. The initial and final surfaces of the specimen were approximated by hemispheres of radii R, and R,, respectively. The quantity 0 is the angle between the [Ol I] and the normal to the (Ml) plane. The cylinder of (Ml) planes observed during field evaporat,ion was determined by the locations of (Ml) planes on the two hemispheres.
‘Fm.
case
was 48fi
which
differed
from
the
calculated
(112), (121), (141) and (i41)
value by less than 5 per cent. In addition, the measured
standard
and calculated
this Appendix
by less than considered
values of the direction 1”.
Hence,
the model
of S differed employed
was
011 stereogram
is to describe the (hkl)
determining
planes as shown on the
in Fig. 10.
The purpose
the methods
directions
along
of
used for
which
SIAs
to be a realistic one.
It should be noted that the bottom
end of the de-
pleted zone moved away from the central axis of the specimen process
during the course of the field evaporation (see
Fig. 5).
for the depleted which
This
displacement
zone detected
was less than
(111) plane studied.
one-half
was 14 L%
in the (111) the diameter
plane, of the
Hence, it was assumed for the
analysis of the SIA positions
presented
B that the (111) planes lay inside a cylinder whose axis was a [Ol l] direction. The same assumption was made for all the other
{hkl}
planes
examined
for
It should be noted that if R were a constant the field evaporation cylinders
containing
[Oil .I direction
process the {hkl)
then
SIh
OBSERVED
i
@
SIAs.
i !
during
the axis of the
planes
would
DEPLETED ZONE DETECTED PLANE
Relation of the position of the SIAs the depleted zone
lY 111
,N
(IllI
I’ ,’ /
_\
B
relative to
The 25 SlAs located outside of the depleted zone detected in the (111) plane were found in the (ill),
!
@
@
be a
exactly. APPENDIX
i
HERE
in Appendix
’
’ _.__ , m-4a--
/
,.
U
FIG. 10. A standard 011 stereogram showing the location of the (111) plane where the depleted zone was detected, and the planes in which SIAs were observed outside of the depleted zone.
1350
ACTA
METALLURGICA,
may have propagated away from the depleted zone. The directions considered were always low index directions along which focused replacement sequences could occur. The easiest SIAs to analyze were those found in the (111) plane unde~eath the depleted zone (SIAs Nos. 2-6 in Fig. 5) at distances between 45 and 80 A (Table 1). Since these SIAs lay within the cylinder of (111) planes whose axis was the [Oil] direction, it was clear that they could have only been driven away from the depleted zone along the [Oii] direction. Next we consider the analysis of the SIAs found in the (141) plane (SIA Nos. 16-22 in Fig. 5). Since the model chosen for the tip is a hemisphere we took the normal vectors to the (111) and (141) planes to be r1 = 5[111] and r, = 2[141], which only differ in magnitude by < 2 per cent. Therefore, ri and r2 are radii of a hemisphere, and have their origin at the center of the hemisphere. The vector r, from the center (or pole) of the (111) plane to the pole of the (141) plane, both of which are in the initial surface, -is r, (ra = r2 - I$ which is the [ill] vector. Since the cylinders containing these planes are parallel to the [Oil] direction the vector r, and [Oil] define the vertical (2li) plane which passes through the midpoints of all the (111) and (141) planes observed during the field evaporation process. Hence, any SIAs driven out of the depleted zone which were found in the (141) planes must have traveled along (h%Z)directions in the (21i) plane or (!&I) directions which were almost coplanar to the (2li) plane, The
VOL.
19,
1971 TABLE 2
Vertical Plane SIA on r3 (111) Defined plane to (~~2) by rs plfma and [Ol l] (W ;;;;j
None (217)
(121)
[232]
I%;
(741)
[735]
(671)
_.-
Low index directions in vertical plane
roi 1.1 [iiij
None None
None
Nearly Coplanar low index directions and offiet from
_ [iOf] 35-40 [iii]
7
[loll
20
[iii] _-
7
[iii] direction satisfies this condition, and any STA in the (141) plane at a depth which was within the length of the depleted zone along the [Oil] direction was most likely driven out along the [ill] direction (see SIA Nos. 18-22 in Fig. 5). The [lOi] is nearly coplanar with the (2li) plane, and the distance which the end of the vector parallel to the [iOi] would be away from the (21i) plane depends on the total distance traversed along this direction from its origin in the (111) plane. For SIA Nos. 16 and 17 the offset away from the vertical (2li) plane at the (141) plane is 40 and 35 A, respectively. Since the (141) planes were POA in width it is possible that these 2 SIAs were propagated along the [TOT] direction from the outside edge of the depleted zone to the inside edge of the (141) plane. The SIAs on the other planes were analyzed in a similar manner. The results of these analyses are shown in Table 2 where the parameters discussed above are listed.
DEFECT
STRUCTURE L.
A.
OF DEPLETED
BEAVAN,t
R.
M.
ZONES
SCANLANt$
IN IRRADIATED
and D. N.
TUNGSTEN*
SEIDMANt
A quantitative field ion microscope study was made of the defect StruCtUr8 of two depleted zones detected in high purity ( < 1.6 - 1O-6 at.fr. impurity level) tungsten specimens irradiated i?a tiitzl under ultra-high v&cuum conditions at & specimen temperature of 18°K with 20 k8V W+ ions to a dose of N 1.10ie W+ ions cm-e. The irradiated specimens were examined by the pulse fiold evaporation technique at lt)‘K, hence their structure is ohamcteristic of this temperature. The depleted zone detected in tb8 (Ill) plane had a local vacant site concentration of N 3.7 at. */@and a self-interstitial atomconcentration (SIA) of N 0.92 at. ‘A, while the depleted zone detected in the (141) plane of a second specimen had values of - 10 and N 0.5 at. o/ofor these same quantities. The SIAs found locally were on the peripheral surfaces of the depleted zones. In addition to this large local imbahmce in point defect concentrations the depleted zones were elong&ted.along (011) directions. It was shown that each of these depleted zones was cm&ted by a single incident ion, and a comparison of the number of displaced atoms in each zone with the value predicted by the Kinchin-Pease model showed that this mod81 strongly overestimates the number of displacements created per incident ion. For the depleted zone detected in the (111) plene it was demonstrated that 23 of 25 SIAs found in the lattice around this zone could have been propagated away from it along (011) and (111) directions as focused replacement sequences. The measured distsnces of these SIAs away from the depleted zone along (011) and {i 11) directions were between 45-150 and 4585A, respectively. The upper and lower values of these distances were determined by a geometric sampling problem and not by the intrinsic range of focused replacement sequences. STRUCTURE
DES
DEFAUTS DES TUNGSTE~E
ZONES APPAUVRIES IRRADIE
DANS
LE
Au moyen du microscope a &mission d’ions, les auteurs ont effectu6 une etude quantitative de la structure des defauts de deux zones appauvries deteot6es dans des cjchantillons de tungstene de haute puretcj ( < 1,5 +lo-@ at. d’impurct6s) irradies in situ dans des conditions d’ultravide Bleve, a 18°K &veC des ions W+ de 20 keV jusqu’a une dose de 1 . lo** W+ ions crnea environ. Los bchantillons irradies ont Otn examines par la methode d’~vaporation par ohamp pulsti & 18”K, leur structure est done earact6ristique de cette temperature. L& zone appauvrie detectee dans 18 plan (111) present8 une concentration locale de sites vacanta de 8,7 at.% environ et une concentration d’atomes selfinterstitiels (SIA) de 0,92 at. o/0environ, alors que pour la zone appauvrie detect&e dans 18plan (141) d’un deuxieme Bchantillon, on obtient des valeurs de 10 et 0,5 at.% environ pour ces m6mes quantites. Les SIA trouvbs localement se trouvent SUPles surfaces peripheriques des zones appauvries. En plus de c8 dcSs6quilibrelooat important dans les concentrations des defauts ponetuels, 18szones appauvries sent disposbes 18 long des direotions (011). Les auteurs montrent que oh&curie de CBSzones est cr66e par un seul ion incident, et une comparaison du nombre d’atomes d8places dam ohaque zone WOO la vdeur pr8vue par la modele de Kinchin et Pease montre quo ce mod8le surestime fortement le nombre de deplacements ctiQs p&r chaque ion incident. Pour 18s zones appauvries detect6es dans 18 plan (11 l), 18s auteurs montrent que 23 des 25 SIA trouves dans le reseau amour de cette zone pourraient s’etre d6plactj.s a partir d’etle la long des dimctions (011) et (Ill) en st’quences de remplacement focalis8es. Les distances d8 oes SIA Q la zone, mesurees Ie long des directions (011) et (Ill) sent respeotivement de 45-150 et 45-85 A. Les v&leurs inferieures et superieurcs de ces distances ont et8 d6terminees par un calcul geomt?trique. DIE
STRUKTUR
V~RD~N~TER
ZONEN
IN
BESTR~LTEM
WOLFRA~~
Die Defektstruktur zweier verdtinnter Zonen, die durch in situ-Bestrahlung hochreiner Wolframproben (Verunreinigungskonzentration 5 1,5 . 10-6At.%) im Ultrahochvakunm bei 18°K mit 20 keV-Wolframionen (Dosis - I . lOie W+-Ionen/om*) erzeugt worden w&ren, wurde mit Bilfe quentitativer Feldionenmikroskopie bestimmt. Die bestrahlten Proban wurden bei 18°K mit der Method8 der Feldv~rdampfung uutersucht, d.h. die Struktnr der verdunnten Zonen ist fur dies8 Temperatur eharakteristisoh. Die auf der (1 ll)-Ebene gefundena verdiinnte Zone hatte sine lokale Leerstellenkonzentration von 8,7 At.% und eine Zwisohengitteratomkonzentration (SIA) von 0,92 At.%, wahrend die entsprechenden Gr658n der auf der (141).Ebene einer &nd8r8n Probe beobaohteten verdtinnten Zone 10 und 0,5 At.% waren. Die iokal bestimmten SIA-Wsrte gelten fur die peripheren Flachen der verdiinnten Zonen. Zusat,zlich zu diesem groGen lokalen Ungleichgewicht der Defektko~entr&tionen wurde eine Ausdehung der verdtinnten Zonen entl&ng (Oil)-Richtungen beobachtet. Es konnte gezeigt werden, da13 jede dieser verdmmten Zoncn durch ein einziges einfallendes Ion erzeugt wordon w&r. Ein Vergleich der Z&h1 der verlagerten Atome jeder Zone mit dem n&oh dem Kinchin-Pease-Model1 vorhergesagten Wert ergab, d&S dieses Mod811die Zshl der von einem einfallenden Ion erzeugten verlagerten Atome stark iiberschatzt. Fiir die auf der (Ill)-Eben8 gefundene Zone wurde gezeigt, da13 23 der 25 im umliegenden Gitter beobachteten Zwis~hengitte~tome ve~utli~h durch (01 l)- oder (11 l)-E~etzun~~t~~e aus dem Kernbereich der verdiinnten Zone wegtransportiert worden waren. Die Laufwege dieser Zwischengitter&tome entlang d8r (Oil)- und (Ill)-Richtungen lagen zwischen 45 und 150 A bzw. 45 und 85 A. Die oberen und unteren Grenzen dieser Reiohweiten wurden anhand eines geometrischen Modells bestimmt.
* Received April 26, 1971. This work was supported by the U.S. Atomic Energy Commissionunder Contract AT(30-l)-350450. Additional support was received from the Advanced Research Projects Agency through the use of the technical facilities of the Materials Science Center at Cornell University. t Cornell University, Department of Mrtterials Science and Engineering, Ithaca, New York 14850. $ NOW at: General Electric Research and Development Center, Schenectady, New York. ACTA
~~ETALLURGI~A,
VOL.
19, DECEMBER
1971
1339
ACTA
1340
METALLURGICA,
1. INT~QDUCTIQN
The concept
of a depleted
idea of a displacement by Brinkman.(ls2) heavy
metal
almost
from the
spike which was first described
energy of the incident displaces
the
zone evolved
A displacement
irradiated
with
spike occurs
metal
ions
when
the
atom
that
it
encounters.
Seeger’x) later pointed out that the existence of focused replacement
sequences would result in the transport of
self-interstitial
atoms
(SIAs)
away from the region
of the displacement
spike,
structure
a depleted
is called
The high local imbalance
and the resulting (or
of vacant
STAs in the region of a depleted
defect
diluted) lattice
zone.
sites and
zone also appears in
t,he ~~~rnputersimulated models of low energy collision events and
I< 2 keV]
described
by
‘CTineyard et aJ.(Q
the high energy
collision events programmed [ < 20 keV] by Beeler. c5) The physical reason for this
imbalance
in the local point defect concentrations
the fact that SIAs enjoy a mode of propagation from
the
displacement
spike,
whereas
does not as long as the temperature
is
away
a vacancy
is below the value
at which the vacant site is mobile. There have been a number of electron investigations
of depleted
with various types of energetic of this literature The electron
particles,
has been reviewed
microscope
resolving the individual
microscope
zones in metals irradiated and much
by Wilkens.c6)
is not at present capable of vacant lattice
sites or SIAs
in the depleted zone. and therefore the field ion microscope
(FIM)
with
suited for a detailed of point defects
its atomic
point defect
little
qualitative
quantitative
structure
metals were per-
and Galligan,“)
Hudson
These FIM investigations
of an essentially
zone.
with these prior investigations dissection
increments
specimens
were not’ employed.
that it is necessary
et oL(*)
have been
about
the
is that fine enough
to dissect
It will become a given atomic
one or two atoms at, a time, whereas
of the clear plane
all the above
experiment*s employed a field evaporation of about, one atomic layer.
1971
of the
depleted
and the existence
zones
along
of focused
(011)
replacement
sequences along (111) and (011) directions. 2. EXPERIMENTAL
TECHNIQUES
High purity W (9
> 4 * lo*, where .!J?is the resistance ratio R22930H/R4.2aK) specimens were irradiated with 20 keV W+ ions in a vacuum of (l-10) - lo-lo torr, and at a tip temperature irradiated
specimens
employing (e.g.
the
were
pulse
field
see Robertson
micrograph
and
(Tr)
then
of l@K.
examined
evaporation
SeidmanoO))
was taken between
T,
technique and
a FIM
each pulse with the
aid of an external image intensification semi-automated
The at
system, and a
35 mm ein& camera.
The field eva-
poration pulse width and height were adjusted so that each plane was dissected
one to two atoms at a time
(e.g. see Balluffi et oZ.(ii)). with
a
Vanguard
The cin& film was scanned
motion
analyzer
(see
Scanlan
et al.(12)for details concerning the data recording and analysis system).
All the analyses were performed
on
the enlarged negatives. Detailed infornlation tion,
the
concerning
ultra-high
vacuum
specimen
FIM,
the
metal ion source, and the measurement T,
have been reported
Scanlan
previously
et cL(~~)). In addition
preparasputtered
and control of
(Seidman et al. ;c13) it has been shown
(Seidman and Scanlan (lsl) that heating effects due to thermal
radiation,
ion
beam
gas and the thermoelastic evaporation
were
temperatures
negligible,
should
range
migration
of
SIAs
pulse
the
to T,
field
measured
rather
well.
was performed at 18°K
after the irradiation,
to the state of the depleted
the imaging
during
hence
correspond
Since, all the field evaporation immediately
heating,
effect
the results pertain
zone prior to any long and
vacancies
(Scanlan
et fl.J.(16)). 3. EXPERIMENTAL
RESULTS
defect
The main difficulty
in the field evaporation
The material presented
elongation
nature, and have given
information
of the depleted
zone.
of the FIM to the study of
clusters in irradiated
by Attardo
and Buswell.‘9)
is better
within and around a depleted
The previous applications formed
resolution
study of the spatial distribution
19,
directions,
in a
ion falls to a value such that it
every
VOL.
increment,
The first depleted
zone we consider
was detected
in a (111) plane on the incident beam side of the FIM tip
N 33 A
from
shows 20 different
the irradiated
surface.
FIM miorographs
Figure
1
of this depleted
zone taken at various stages of the dissection
process
whioh involved
the recording and analysis of a total of 4.4 * lo3 frames of film. (The examination of more than 7.5 * lo4 frames of film of unirradiated
control
here represents the results
specimens never revealed contrast effects of the type
of a quantitative study of two depleted zones in two different W specimens which were irradiated with
shown in Fig. 1.) The positions of the atoms and the vacant sites found in this plane are schematically
20 keV W+ ions at 18°K.
illustrated
Direct evidence is presented
for t,he existence of a local imbalance in the point defect concentration at the site of the depleted zone,
below each micrograph.
This depleted zone
extended through 50 successive (111) planes, and the tot,al number of atomic sites in t,he volume containing
BEAVA2;
et
DEPLETED
al.:
ZONES
IN
IRRADIATED
imbalance
1341
TUNQSTEN
between
the vacant
lattice
site and SIA
concentrations. Figure lattice
2 shows
a (111) projection
sites and SIA
positions
a depleted
analyzing
zone
of the vacant
(the
is given
The vacant lattice sites are denoted
procedure
for
in Section
4).
by open circles,
the SIAs by solid triangles and the multiple concentric circles imply t,hat more than one vacant site projected of projection
to the same atom position. reveals the 3 distinct
the depleted zone.
The direction
main branches
of elongation
3 branches was along the 3 different lying in the (111) plane.
lattice
This mode of
of the
(011) directions
An isometric drawing of this
depleted zone is shown in Fig. 3, where the thickness of each slab* is 4.56~(5atomiclayers),alld ary of each slab was determined
the bound-
by connecting
outer point defects on its periphery
the
by straight line
Figure 4 shows a series of 6 photographs
segments.
the ball model of this depleted indicate the positions
zone.
of
The large balls
of the vacant lattice sites, and
the small balls are SIAs.
It is clear from Figs. l-4
that the geometry of this depleted zone is not so regular that it could be approximatecl circular
cylinder,
or for
by a sphere or a right
that, mat,tcr
any
simple
geometric form. In t,he lattice of the specimen which contained depleted
zone there were 25 additional
were found
at appreciable
distances
this
SIAs which
from the zone.
The positions of these 25 SIAs are shown in Fig. 5, FIC~. 1, A series of 20 FIM micrographs (out of 4.4 * lo3 recorded) taken at various stages of the atom-by-atom dissection of the depleted zone detected in the (111) piene. The large solid black circles indicate SIAs, the open circles vacant lattice sites and the smaller solid black circles lattice atoms.
and their measured distances from the depleted
the most probable
crystallographic
directions
which these SIAs
were propagated
away from the depleted zone are also
1850.
completely
The
depleted
contained
within
zone
appeared
to
the periphery
be
of this
along
listed in Table 1. The numbers of the SIAs in Fig. 5 correspond
it was
zone
are listed in Table 1. In addition,
to the numbers in Table 1. A description
of the procedure
used to determine
graphic directions
is given in Appendices
these crystalloA and B.
(111) plane as no vacant sites were found on the atomic planes adjacent
directly to it. There were 172 vacant
sites within this 1850 at. vol. (!&) region. Tn addition, a total
of
17 SIAs
were found
in or immediately
adjacent to the depleted zone for a SIA concentration of -
0.92 at. %.
(unpublished accompan~~ng vation
It had been shown in this laboratory
work)
that
a possible
the appearance
of a vacant
contrast
effect
of a SIA is the obser-
lattice site immediately
prior to
the detection of the SIA. Since 12 of the SIAs observed in the (111) plane were preceded by a vacant
The second zone analyzed
was found
plane with its bottom surface ted side of the FIM intersecting depleted
specimen,
in the (141)
19d from the irradiaand its top surface
the surface of the specimen.
Since this
zone was so close to the irradiated
surface
we cannot be certain if it is a partial or a t,otal depleted zone. The dissection of this depleted zone involved the recording and analysis of 2.1 + 103 frames of film. A total of 85 vacant sites were found within a
lattice site we have taken the number of real vacant lattice sites to be 160. This latter correction implied
800 L& region, which meant that the vacancy concentration was - 10 at.%.? The number of SIAs found
that the concentration zone was - 8.7 at.%.
* With the except,ion of the third slab from t.he bottom, which is 10 atomic layers thick. 7 This based on a corrected value of 81 vacant sites (see Section 3.1 for the reason for the correction).
rather spongy
of vacant lattice sites in this Thus, the depleted zone had a
character,
and there was a large local
ACTA
1342
METALLURGICA,
VOL.
19,
19il I
PRbJECTldN
[iol] ,
/
\4-[oli)
---
i
ONTO
ll-
20
ONTO 50
/I 1
/
21-30
-~~
OF PLANES
50
FIG. 2. A series of (111) projections of the depleted zone detected in the (111) plane. The vacant lattice sites are indicated by open ciroles, the SIAs by solid black triangles and the multiple concentric circles imply that more than one vacant lattice site projected to the same atomic position. The zone in map 1 is elongated a.long [Toll, in map 2 along [TlO] and [iOl], in map 3 along [ilO] and in map 4 along [Toll. in or very
near this depleted
local
concentration
again
SIA
there was a rather
the SIA and the vacant
zone was 4, hence the
was N 0.5 at. %, and once large imbalance lattice
between
site concentrations.
Figure 6 shows a (141) projection symbols isometric
/(Ill)
drawing
of the depleted
photographic
views of a ball
zone, which was constructed
from the maps used to draw the projections
PLANE
in Fig. 6. This depleted zone exhibited DIRECTION
OF
along enough
the same
in Fig. 2, and Fig. ‘7 is an Finally, of this depleted zone.
Fig. 8 shows 5 different model
employing
as used previously
the
[lOi]
direction,
to be represented
presented
directionality
and it was not by any simple
regular
geometric
form. 4. DEPLETED
ZONE
In order to reconstruct
ANALYSIS
PROCEDURE
a depleted
dimensions the following procedure analyze the 35 mm cink film :
zone in three
was employed
to
1. First the x-y coordinates of the outermost ring of atoms on the plane were determined, and then the FIG. 3. An isometric drewing of the depleted zone detected in (111) plane constructed from the projection maps shown in Fig. 2.
coordinates of all the inner atoms were measured. The coordinates of each inner atom were always read
REAVAN
et al.:
DEPLETED
ZONES
IS
IRRADIATED
1343
TUNGSTES
FIG. 4. A series of 6 photographs of the ball model of the depleted zone constructed from the projection maps of Fig. 2. The large dark balls represent vacant lattice sites, and the smaller balls indicate SIAs. Photograph A was taken along the incident ion beam direction {- [2lI]}. Photographs B-E are perpendicular to the (111) plane. Photograph B w&s taken looking along the [ii21 direction, C along the [lTO] dire&ion, D looking toward the in&dent ion beam (- [211]1 and E along the [Oli] direction. Photograph P is an overhead view of the model taken looking almost along the [I 1I].
with
respect
to
the
remaining on the plane.
previously
measured
atoms
This practice eliminated
any
error due to film positioning between frames, and assured us that each atom was referenced with respect to at least 2 neighbor atoms (many atoms were measured multiply). 2. The x-y coordinates of the atoms in each plane were then plotted utilizing the multiple readings to insure that all atom
positions
were related
to t,he
same coordinate basis. occurred all coordinate
In cases were film slippage readings in that frame were
uniformly shifted to make multiple readings coincide. In no case was a vacant site attributed to a gap in atom coordinates, unless a vacant site was certified visually in the FIM micrograph. The identification of a bright spot as a SIA was determined dure which was previously bhis laboratory.
by a proce-
used (Scanlan et ut.(lQ)) in
ACTA
1344
TABLE
I. Distribution of SIAs found outside of depleted zone debected in a (111) plane SIA propagation direction and distance along
Distance from depleted zone 6)
Location by plane &W ____ -.
of SIA
METALLURGICA,
60 80 80 80 70 45
70 45 105 105
(121) (121) (141) (141) (141) (141) (141) (141) (141) (f41) (141) (X41)
-
[iil] (OTT] [Ofi] [oii] [Oii] [OTT]
70Foij 65 [ill] 60 [iii] 60 [111] 55 [iii] 55 [111] 45 [ill] 135 [ioi] 115 [roil x5 [ill] 85 [iii] 75 [iii] 70 [111] 70 [iii] 150 [roil 100 [ilO] 100 [IlO]
si: 60 60 55 5’ iz 130 100
ii2ij
:: 75 70 70 130 90 90
-.-obtained
in step 2 were then
fitted to a regular array of points by a best fit iteration Next, the array of lattice p,qsitions found
by this t.echnique was compared for t.he particular
to the ideal lattice
plane involved.
j In all cases the
lattice planes determined
expe~~e~tally
to be somewhat
from t‘he theoretical
tion.
distorted
The disto&ion
were found
was always found
were brought
the theoretical 4. Finally,
certainly
created
by
a single
incident
TN+
consists of making an upper
estimate of the number of primaries
associated
with
each depleted zone, and showing that the probability of each depleted zone being created by more than one This upper estimate is a simple geometric argument, based on the measured cross-sectional depicted
zone presented
depleted
zone detected
was Wf
situa-
area which the
to the ion beam.
For the
in the (111) plane this area
1.6 . lo-l3 cm2 and the total dose was N 1 * 1012
ion cm-2,
therefore
the maximum
number
W+ ions which hit this area was -0.16.
of
A similar
calculation for the depleted zone detected in the (141) plane showed
that
the
on its cross-sectional of estimating
the
maximum
number
srea was -~0.02. number
of
hits
This method
of primaries
with each depleted zone is an overestimate
associated because it
neglects the spread in the range of the incident ions. The additional
point which we wish to emphasize
very strongly is that each depleted zone was observed in a different specimen, depleted
and that, there were rrn other
zones found in these two specimens. examined
the density
in each casewas -
of depleted
each specimen.
zones was -
E’urthermore,
that the above
easily into coincidence
is strong
Hence,
we feel
evidence
that,
each depleted zone was only created by one incident ion.
experiwith
atom positions. the lattice
above procedure
planes
were positioned
another in the correct stacking obt,ain a final 3 dimensional
determined
by the
with respect to one sequence
model.
in order to
A ball model
consisting of only the vacancies
and SIAs which were
detected was then above information.
with the aid of the
constructed
5. DISCUSSION 5.1 P~o~b~~~~~ that each ~e~~~~~~zone uxxs created
by one ~nc~~e~~ ion Before proceeding with the main portion of the discussion we shall show that each depleted zone was * The amount of distortion varied inversely with the radius of the tip (Q-). For example, the shear for rr = 134 .& was 12” which decreased to 8’ when the specimen was field evaporated to an zy of = 158 A. For the second speoimen with ~~ = 320 8, the shear was only 6”.
in
of lattice
zone was perfect with
of the SIAs detected. information
1015 cm-3
the volume
examined around each depleted the exception
Since
IO-l7 cm3,
tq be a pure
shear,* so that the lattice points determined mentally
1971
The demonstration
the volume
3. The atom positions procedure.
almost ion.
19,
incident ion was small.
60 80 X0 80
i:::; (Ill) 1lllI
VOL.
FIQ. 5. An isometric drawing showing the relationship of the SIAs in the lattice to the depleted zone detected in the (111) plane. The numbers near the SIAs correspond to the numbers in Table 1. The direction of the incident ion beam (- [21i]) is almost normal to the plane of the page. The arrows from the depleted zone to the SIAs indicate the most probable propagation directiona.
BEAVAK
et al.:
DEPLETED
ZONES
IN
IRRADIATEI)
TfTSGSTES
1345
FIG. 6. Four (141) projections of the depleted zone detected in the (141) plane showing the elongation of this zone along a [lOI]. Vacant lattice sites are denoted by open circles and the SIAs hy solid black triangles.
The features of the depleted zones reported in Section 3 are in general qualitative agreement with many of the details of Beeler’s computer simulated model.c5) In this section we compare some of the details of the structure with Beeler’s model. The first point is that our measured defect concentrations are higher than those calculated by Beeler. The reason for this is due to the fact that he obtained his concentrations on the basis of a calculated volume
v-
(1411
PLANE
DIRECTiON
Of
FIG. 7. An isometric drawing of the depleted zone detected in the (141) plane constructed from the projection maps shown in Fig. 6. The top slab is 6 (141) atomic layers thick, and the other slabs are 5 layers in thickness.
of “collided atoms”.* This quantity cannot yet be experimentally determined, hence we used t.he procedure described in Section 3 to calculate the defect concentrations. Thus, our procedure. by definition, produced higher concentrations than those calculated by Beeler. The second point to note is that in Reeler’s model the elongation of the depleted zones along
ACTA
1346
METALLURGICA,
VOL.
19,
1971
z
i
FIG. 8. A series of 5 photographs of the ball model constructed from the projection maps of Fig. 6. The larger dark balls represent vacant latt,ice sites, and the small balls indicate SIAs. Photograph A was taken looking along the [Zll] direction, photograph B along the incident beam direction and photograph C looking along the incident beam direction. Photographs U and E aw overhead views of the dcplet’ed zone showing its geometry. Photograph E was t,aken looking along t,he [141].
depleted
zone by focused
Fig. 5 and Table in the lattice the
(111)
Twenty-three
around
the depleted
plane
propagation
replacement
1).
were in positions
along
(111)
and
(011)
sequences
(see
of the 25 SIAs zone detected consistent directions
in
with (see
incident ion are the amorphous solidmodelsof Pease.(ls)
In the present discussion
Kinchin-Pease the expression
Section 5.4).
amorphous
The concentration
of vacant sites determined
between
existing radiation
allows damage
theories and our results. The most commonly used models for the average number of displacements per
and
we will use the
solid model.
which yields
v(E) = E/2E,,
5.3 The concentration of defects in the depleted zones for a comparison
Harrison
and Seitz,(17) Snyder and Neufeld(l*) and Kinchin
(1)
where E is the energy of the primary particle initiating the depleted zone (20 keV in this case), E, the displacement threshold energy (50 eV(20*21)) and v(E) is the average number of displacements the initiating
particle.
Beeler,c5) among
produced
by
others,
has
et al.:
BEAVAN
point,ed
out
efficiency
that
(Ii,,)
the
DEPLETED
Kinchin-Pease
is a constant,
ZONES
displacement
and is given
by
the
expression h’,, Based
= v(E)/‘E = 1,‘(2E,).
011 a binary
model of a depleted
collision
(2)
computer
simulated
zone in W Beeler has shown that
the c~isplacement efficiency is energy dependent
and is
h’,,(E)
= 6.05(1 -- 0.04190 In E),
where E is in keV. the average
displacement
increasing E.
efficiency
The domina~lt
was the recombination
decreases
lattice
structure
with effect
with increasing E
of a SIA from one collision
with a vacancy
along &se-packed
from
directions
The Kin&in-Pease zone
(3)
Thus: Beeler’s model predicts that
which caused t,his decrease in Krr(E)
pleted
IRRADIATED
tion distances
another
collision
event
between 45 and 150 if were measured,
while for the (111) directions
propagation
between
found
45 and
model
on the average
Beelcr’s
model predicts
atoms per depleted zone.
predicts
that, each de-
200 displaced
atoms,
while
an average of 106 displaced The number of permanently
displaced atoms in Beeler’s model is determined
by the
size of the vacancy-SIA
region
employed
direct recombination
in his calculations.
site recombination Frpinsov
region
Beeler used a 30 atom (originally
described
rt ~1.@~)) for his O’K calculations>
by
and he
asserts that. the size of this region will increase as the temperature
We wish to emphasize upper
strongly
sampling problem.
is increased.
Furthermore,
Beeler states
events
region of t,he deplet,ed zone. of 106 displaced
which
have
lattice vibrations
been in the
Thus, the average value
atoms per depleted
zone is an upper
ourselves
that the extra bright
Kot,h of our deplet,ed zones contained value of200
obtained
less than the
on the basis of a Kinchin-Pease
and ih is clear that this model overestimates
considerably
the total
(for a discussion
number
of the defioiences
see Sigmund(z3)).
of displaced
atoms
of this model also
The 160 vacant sites in the depleted
replacement
purely a geometric the planes defined we couid
sequences problem. by [Oil]
not identify
propagation
the
along the (100) was Since no {loo> were in
and r3 (see Appendix
B)
/lOO? as a direction
of
for SIAs.
The computer
sinmlation
studies of radiation
by Erginsoy
near threshold energies focused replacement, sequences would
propagate
easiest
while (011) sequences energies.
in the
6. GENERAL which are of a philosophical some experiments experimental
REMARKS
nature, and also indicate
which now seem possible
with our
facilities.
1. The detailed
information
concerning
structure
here could not have been obt,ained if the
atomic layer.
was as coarse
increment
Hence, it is considered
all future research of this type employ dissection of a given plane. investigations
requirement
as one
mandatory
that,
atom-by-atom
for quantitative
FIM
of deplet,ed zones is that. the dose must,
be a low value if one is to associate each depleted zone with a single incident’ ion. Two depleted zones do not represent a distribution, but they do show that it is possible to obtain direct information
by FILM about the number
of displace-
by a single incident ion.
1. A direct determination displacements
per
incident
Thus, we
FIM experiments
:
of the average number of primary
could be obtained by performing here on N 25 depleted zones.
(111) plane could have been propagated along (011) and (111) directions. For the {Oil) directions propaga-
grounds.
In this section we wish to make a number of remarks
than 106, while the 81 vacant sites found in the second
B it is shown that the SIAs located in
:,lOO),
at higher
Thus, the existence of iOIl) focused replace-
ment sequences is possible on theoretical
suggest the following two additional
In Appendix
;I 11) and
would be established
zone detected in the (111) plane is 51 per cent greater
the (112), (111). (121), (141) and (i41) planes in the specimen containing the depleted zone detected in the
dam-
et uJ.(~~)showed that)
ments produced
zone is w 24 per cent smaller than 106.
Hence, the upper
values along the (111) and (011) in Mr. The absence of focused
2. An essential
lim& in his model.
by a
values ofthese distances are not necessarilythelimiting
field evaporation
depleted
are affected
spot contrast effects that we observe are due TaoSlAs
of indirect
recombination
1f .
Table
That is, that to date we have only
been able t.o satisfy
presented
by excited localized
distances
(see
t,hat the lower and
values for these distances
that, t,his 0°K number will be even smaller as a result
model.
85 L% were
age in K-Fe (b.c.c.)
of atoms.
E)rodu~~?d by a 20 ke?r pi+ ion should
contain
induced
I347
TUNGSTES
in the (112), (111) and fl41) planes.
given by
event
IN
of
energy
E
the analysis reported
2. A measurement of the relative temperature dependence of the size of the direct recombination region
could
be obtained
experiment described temperatures.
by simply
repeating
the
here at a series of irradiation
7.
SUMMARY
AND
CONCLUSIONS
1. A quantitative study was made of the defect structure of two depleted zones detected in W specimens irradiated at 18% to a dose of - I * fW ion cm-2 with 20 keV W+. The depleted zones were examined at 18°K by a pulse Beld evaporation technique that allowed the dissection of atomio planes one to two atoms at a time. Thus, the defects structure reported is characteristic of 18’K and the dose was low enough so that eaoh depleted zone wa8 created by a single incident ion. %. The depleted zone detected in the ( 1I1 ) plane had a rat,her irregular geometry which could not be described by any simple geometricform. It waselongated along t~he3 different (01 I) directions which he in the ( 111 f plane, The concentration of vacant lattice sites in the depleted zone was - 8.7 at.0/b, and the SIA concentration was - 0.92 at.%. The SIAs found locally were located on the peripl~eral surface of tnhe zone. 3. The depleted zone detc&ed in tfhe (142) had an irregular geometry which was elongated along the [lOi] direction. The vacant lattice site ~on~entration was N 10 at.%, and the SIA concentration was N 0.5 at. %. Once again the SIAs were found on the outer surface of the zone, 4. The results stated in 2 and 3 above are direct proof that a depleted zone has a large local imbalance in its point defect concentrations, and that SIBS are stable near the zone at a value of temperature which is below the start of long-range migration of SIAs. 5. The depleted zone detected in the (111) plane had 25 STAs in the surrounding lattice. It was shown that 12 of these 25 SIAs could have been propagat,ed from the zone along (111> directions, and 11 along (OII) directions. For the jOll> directions the p~opagat,ion distances were between 45 and 1508, while for the (111) directions these distances were between &5 and 85 A. The upper and lower limit in both cases was determine by a geometric sampling problem, and not, by the intrinsic range of focused replacement sequences. This result constitutes direct evidence fur the existence of focused replacement sequences. 6. The number of displaced atoms per depleted zone [16O for the one det,ected in the (111) and 81 for the one detected in the (141)] was considerably lower than t,he value of 200 predi~t~~d by the standard Kinchin-Pease model. Hence, this model overestimates strongly the number of defects prodnced by an incident, ion. ACKNOWLEDGEMENTS
We wish to thank Mr. B. F. Addis for the preparation of the high purity tungsten specimens, Professor
R. W. Ballu% for ~o~t,~~uo~lsencouragement and useful discussions, Dr. P. Petroff for useful discussions and Mr. R. Whitmarsh for technical assistance.
edited by A. SEZWER, D. SC~~iVIhcwEB, w, SCEIIAING and J. DIEHL, pp. 485-520. ~~~tl~~~(~ll&n~~ f 1970). 7. %I. J. ATTAR~W and J. &I. GALLIQA~~.Phys. Rm. Lett. 17, 191 (1966). 8. J. A. HUDSOX, B. 2. DFRY and B. RALPII, Phil. Mug. 81, 172 (1970). 9. J. T. BUBWELL. Phil, Mw. 22. 7X7 ifQ70‘1. rn. S. H. ROBERTS& and D, “NcW~~~I&~, J.‘s&&. fnsi~~n. 1, 1244 (i9SS). 11. R, W. BALLUBF’I,K. H. LIE, D. N. SEIDMAN and R. W, SIEGEL, in ~ra.ca&&s a+?d~?~~~r~~it~a~8 i?z &f&a&, edited by A. SEEDER,D. SCHUMACHER,W. SCHILCIXC; rendJ. DIE~F,, pp. 125-167. North-Holland (1970). 12. R. &%iM. SCANUN, D. L. STYRIS, D. N. SEIDMAX %nd D. G. AsT. Corn& X?nive&ty Materials Science &nteP Rspart No. 11.59(1969). 13. D. N. SEIDXAX, R. M. SCANL.W, D. L. STYRIS and J. M. BWHLEN, J. scient. In&mm. 2, 473 (1969). 14, R. 112. SC.~NLAPF,D. L. STYEWZ and D. N. SEIDMAN, Phil. &Wq$23,1439 (1971). 1.5. D. N. SEIUMAN and R. M. SCANLAX, Ph& Hag. 23, 1429 (1971). 16. R. M. SCANLAN, D. L. STYRW snd D. N. SEIDMAN, FW&. Mq. 25,1459 (X971). 17. w. HARRISON WX?F. SEITZ. PkW. B&v. 98. 1636 fl9&%. Ph&‘Rcv. $7, 1&% 18. 5%‘.8. SNYDER anti J. N&FE& (1955); J. NEUWLI> end W. 8. SNYUER, P&s. Rev. 99, 1326 (1955). 19. G. H. KINCHIN and R. S. PEASE. in Re;rmrts on Proarms in Physics, edited by A. C. ~TICXiANU, -Vol. 28, p. i. Tbo Physical Society ( 1956). 20. C. C. ROBERTS, Ph.l3. Thosis, Univcrsitg of North Caroline at ChtapeLHill (1968); C. G. ROBERTS. B&E dnb. Phys. Sot. 13, 255 (1968). 21. J. A. DICA!ARLO and J. T. STANXZY, Bzctl. Ant. Whys. Sac. 16, 317 (1971). 22. C. ER~IES~Y, 0. H. VINEYARD and A. ENQLERT, Hqp. Rev. 153, A595 (1964). 23. P. SIOMTIND,Ap@. Php. Lett. 14, 114 (19US). APPENDIX
A
The model employed for the tip was a hernisp~~~e of radius R. It was assumed that as the field evaporation process prooeeded the tip remained he~~sphe~cal, and that R increased uniformly. This model is shown in Fig. 9 where R, and R, represent the initial and final radii, respectively, It is seen that t,he center of each net plane shifts parallel to the surface of the plane by an amount* S as a result of the field evaporation process. The specimen in which a depleted zone was detected in the (Ill) plane had values of R, and R2 equal to 134 and 158A, respectively. The value of R, was measured when the last (111) plane in the depleted zone was imaged. The measured value of X in this
BEAVAN
et al.:
DEPLETED
ZONES
IN
IRRADIATED
,d’ HEMISPHERE APPROXIMATING
OF
HEMISPHERE
FINAL
(h k 1)
RADIUS R, IRRADIATED
PLANE
OBSERVED
CYLINDER OF (h k l, PLANES OBSERVED DURING EVAPORATION
OF
TIP
1349
TUNGSTEN
LAST (h k 1, OBSERVED
PLANE
SURFACE+ /
9. The model of the specimen used to calculate the depleted zone geometry and its relationship to the SIA’s in the lattice around it. The initial and final surfaces of the specimen were approximated by hemispheres of radii R, and R,, respectively. The quantity 0 is the angle between the [Ol I] and the normal to the (Ml) plane. The cylinder of (Ml) planes observed during field evaporat,ion was determined by the locations of (Ml) planes on the two hemispheres.
‘Fm.
case
was 48fi
which
differed
from
the
calculated
(112), (121), (141) and (i41)
value by less than 5 per cent. In addition, the measured
standard
and calculated
this Appendix
by less than considered
values of the direction 1”.
Hence,
the model
of S differed employed
was
011 stereogram
is to describe the (hkl)
determining
planes as shown on the
in Fig. 10.
The purpose
the methods
directions
along
of
used for
which
SIAs
to be a realistic one.
It should be noted that the bottom
end of the de-
pleted zone moved away from the central axis of the specimen process
during the course of the field evaporation (see
Fig. 5).
for the depleted which
This
displacement
zone detected
was less than
(111) plane studied.
one-half
was 14 L%
in the (111) the diameter
plane, of the
Hence, it was assumed for the
analysis of the SIA positions
presented
B that the (111) planes lay inside a cylinder whose axis was a [Ol l] direction. The same assumption was made for all the other
{hkl}
planes
examined
for
It should be noted that if R were a constant the field evaporation cylinders
containing
[Oil .I direction
process the {hkl)
then
SIh
OBSERVED
i
@
SIAs.
i !
during
the axis of the
planes
would
DEPLETED ZONE DETECTED PLANE
Relation of the position of the SIAs the depleted zone
lY 111
,N
(IllI
I’ ,’ /
_\
B
relative to
The 25 SlAs located outside of the depleted zone detected in the (111) plane were found in the (ill),
!
@
@
be a
exactly. APPENDIX
i
HERE
in Appendix
’
’ _.__ , m-4a--
/
,.
U
FIG. 10. A standard 011 stereogram showing the location of the (111) plane where the depleted zone was detected, and the planes in which SIAs were observed outside of the depleted zone.
1350
ACTA
METALLURGICA,
may have propagated away from the depleted zone. The directions considered were always low index directions along which focused replacement sequences could occur. The easiest SIAs to analyze were those found in the (111) plane unde~eath the depleted zone (SIAs Nos. 2-6 in Fig. 5) at distances between 45 and 80 A (Table 1). Since these SIAs lay within the cylinder of (111) planes whose axis was the [Oil] direction, it was clear that they could have only been driven away from the depleted zone along the [Oii] direction. Next we consider the analysis of the SIAs found in the (141) plane (SIA Nos. 16-22 in Fig. 5). Since the model chosen for the tip is a hemisphere we took the normal vectors to the (111) and (141) planes to be r1 = 5[111] and r, = 2[141], which only differ in magnitude by < 2 per cent. Therefore, ri and r2 are radii of a hemisphere, and have their origin at the center of the hemisphere. The vector r, from the center (or pole) of the (111) plane to the pole of the (141) plane, both of which are in the initial surface, -is r, (ra = r2 - I$ which is the [ill] vector. Since the cylinders containing these planes are parallel to the [Oil] direction the vector r, and [Oil] define the vertical (2li) plane which passes through the midpoints of all the (111) and (141) planes observed during the field evaporation process. Hence, any SIAs driven out of the depleted zone which were found in the (141) planes must have traveled along (h%Z)directions in the (21i) plane or (!&I) directions which were almost coplanar to the (2li) plane, The
VOL.
19,
1971 TABLE 2
Vertical Plane SIA on r3 (111) Defined plane to (~~2) by rs plfma and [Ol l] (W ;;;;j
None (217)
(121)
[232]
I%;
(741)
[735]
(671)
_.-
Low index directions in vertical plane
roi 1.1 [iiij
None None
None
Nearly Coplanar low index directions and offiet from
_ [iOf] 35-40 [iii]
7
[loll
20
[iii] _-
7
[iii] direction satisfies this condition, and any STA in the (141) plane at a depth which was within the length of the depleted zone along the [Oil] direction was most likely driven out along the [ill] direction (see SIA Nos. 18-22 in Fig. 5). The [lOi] is nearly coplanar with the (2li) plane, and the distance which the end of the vector parallel to the [iOi] would be away from the (21i) plane depends on the total distance traversed along this direction from its origin in the (111) plane. For SIA Nos. 16 and 17 the offset away from the vertical (2li) plane at the (141) plane is 40 and 35 A, respectively. Since the (141) planes were POA in width it is possible that these 2 SIAs were propagated along the [TOT] direction from the outside edge of the depleted zone to the inside edge of the (141) plane. The SIAs on the other planes were analyzed in a similar manner. The results of these analyses are shown in Table 2 where the parameters discussed above are listed.