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Thermal etching of silver in various atmospheres
THERMAL
ETCHING
OF SILVER
G. E. RHEADt
IN VARIOUS
and
ATMOSPHERES*
H. MYKURAt
Investigations were made using interference microscopy of changes in the surface topography of silver specimens heated at 900°C in 0,, N,, N,/O, mixtures, a N,/H, mixture and in vacua. The development of both two and three sets of planes on an originally flat surface was studied. The observed development of {I 1 l}, { 100) and {I 10) facets when oxygen is present is ascribed to a lowering of the total surface free energy. Measurement of the angle of contact between low index surfaces (surface energy yo) and continuation-random orientation-surfaces (surface energy ye) show that Y,,/Y~ increases toward unity as the concentration of oxygen is decreased. The results indicate that about 4 per cent more oxygen is adsorbed onto {ill} and { 100) surfaces and that this anisotropy of adsorption is the main cause of the anisotropy of surface energy in oxygen bearing atmospheres. A comparison of faceting with and without net evaporation indicates that recondensation of silver atoms causes some desorption of oxygen. ATTAQCE
THERMIQUE
DE
L’ARGENT
DANS
DIVERSES
ATMOSPHERES
Les auteurs ont Btudie par microscopic d’interference les changements de la topographie superficielle cl’echantillons d’argent chauffes 8,500”C dens 0,, N,, N,/O,, N,/H, et dans le vide. Le developpement de deux ou trois groupes de plans sur une surrace initialement plane est Otudie. Le developpement en presence d’oxygene de facette {ill}, {loo} et {IlO} est attribue L un abaissement de l’energie libre totale de surface. La mesure de l’angle de contact entre surfaces it bas index (energie de surface y,,) et surfaces de continuation (orientation au hasard) (Qnergie de surface ye) montre que le rapport yo/ys augmente et tend vers l’unite lorsque la concentration de l’oxygene diminue. Les resultats indiquent qu’environ 4% en + d’oxygene est absorb6 sur les surfaces {ill} et {SOO} et que cette anisotropie d’adsorption est la raison principale de l’anistropie de l’energie de surface dans les atmospheres contenant de l’oxygene. La comparaison de formation de surfaces avec et sans evaporation nett,e indique que la recondensation d’atomes d’argent quelque d&sorption d’oxygene. THERMISCHES
ATZEN
VAN
SILBER
IN VERSCHIEDENEN
ATM~SPHBREN
Mit Hilfe der Interferenz-Mikroskopie wurde untersucht, wie sich die Oberflachen-Topographie von einer N,/H,-Mischung und in Vakuum auf Silberproben lindert, wenn sie in 0,, N,, N,/O,-Misohungen, 900°C erhitzt werden. Es wurde studiert, wie sich auf ursprtinglich ebenen Oberfliichen teils zwei, teils Ebenengruppen entwickelten. Die beobachtete Entwicklung von {ill}-, {lOO}- und {llO}-Facetten bei Anwesenheit von Sauerstoff wurde einer Erniedrigung der gesamten freien Oberfliichenenergie zugeschrieben. Messungen des Bertihrungswinkels zwischen niedrig indizierten Fliichen (Oberflachenenergie y,,) und den statistisch orientierten Zwischenfliichen (Oberflachenenergie ~0) zeigen, da6 mit abnehmendem Sauerstoffgehalt das Verhiiltnis y,,/ys zum Wert 1 hin ansteigt. Nach unseren Ergebnissen ist auf {ill}- und {lOO}-Flachen etwa 4% mehr Sauerstoff adsorbiert. Diese Anisotropie der Adsorption ist die Hauptursache der Anisotropie der Oberflachenenergie in sauerstoffhaltigen Atmospharen. Ein Vergleich der Facettenbildung mit und ohne Netto-Verdampfung zeigt, da13 Silberatome beim WiederKondensieren etwas Sauerstoff von der Oberfliiche vertreiben. INTRODUCTION
silver heated in air or oxygen
The surfaces of many metals, initially
smooth,
are
They concluded
but not in nitrogen.
that the presence of oxygen modified
found to expose low index facets and develop a hill and
the relative surface energies of crystal planes and that
valley structure when heated in certain atmospheres.
striations
Such changes
planes having
“faceting”), boundary “thermal
in surface
together and
twin
etching”.
topography
(usually
with the development boundary
grooves
Shuttleworth
called
of grain
were caused by the development lowest
free energy.
of those
Buttner
et uZ.(~)
have shown that the average surface energy of silver
are termed
measured for a range of crystal orientations
has reviewed the
by the adsorption
of oxygen.
is lowered
Kingt4) found that the
earlier work done on a number of metals and atmos-
planes developed
pheres.
has been investigated in much greater detail than any other. As there
(100) which indicates that adsorption on these planes produces a relatively greater lowering of surface
were still a number of doubtful
energy. In the simplest case of faceting
The system
behaviour
silver-oxygen
points on the faceting
of silver surfaces it was considered
worth
on silver were always either (11 l} or
the surface breaks
while to make a further study of this system to con-
up into two sets of parallel planes:
tribute
“simple”
to the understanding
of faceting
in general
and to study the effect of variation of oxygen partial pressure on the variation of surface energy with crystal
through striations.
Glasgow,
ACTA METBLLURGICA,
1962
VOL 10, SEPTEMBER
a low index or surface.
The sets
of parallel planes intersect to form ridges and valleys ; these appear as striations which usually extend right across each crystal. Fig. 1 represents a section
orientation. Chalmers et .1.(s) found that striations occurred on * Received January 24, 1962. t Department of NaturalPhilosophy,Universityof Glasgow W.2.
surface and a continuation
such a surface,
taken perpendicular
to the
The general surface 00’ has changed into a
hill and valley structure consisting of low index planes AB with surface energy y,, and continuation surfaces 843
ACTA
METALLURGICA,
Ii
VOL.
10,
1962
C
FIG. 1. Section through a striated surface (schematic). index facet. BC, continuation
BC making an angle 8 with the low index planes and with surface energy ys. By making a virtual displace-
00, original surfaoe. surface.
effects of evaporation
AR,
low
on thermal
etching
suggested that striations are produced
and have
by net evapor-
ment of the point B in the direction AB one arrives at
ation from the surface and not by a minimisation
the equation for equilibrium
total surface energy.
of the surfaces in contact
experiments
at B: y 0 = ye cos 8 -
ae
surface(‘@.
.
more
The increase in surface energy of the low index plane
AB
due to a small tilt away
position
from
the low index
is taken to be large enough to prevent
such tilt;
any
i.e. -
83
e + 87, - co9 8.
> ye sin
(2)
ae
with
concentration.
angle 13should therefore depend only on of surface energy with crystallographic (usually referred to as the “y-plot”)
be independent
of the angle u between
have
relatively
possible if
low
experiments using
the thermal etching of silver of evaporation
in pure nitrogen,
had the object of obtaining the effect of adsorption
nitrogen plus
These experiments
some quantitative
data on
on relative surface energies.
EXPERIMENTAL
surface
used.
specimens of “specpure”
The specimens,
prepared
from
silver were
about 2 cm2 x 0.2 mm, were
cold-rolled
sheet
(from
Johnson,
Matthey &Co., impurities detected spectrographically:
energies, that is if there is a large cusp in the y-plot at
Cd, Cu, Fe, Pb and Mn, each less than 1 p.p.m.).
the low index
avoid contamination
orientation.
which the angle of contact continuation
A surface between
structure
low index
surface is given by equation
for which there has been the maximum duction
of surface
energy
by simple
in and
(1) is one possible
faceting;
and
and thermal etching in mixtures of
oxygen and nitrogen,
Polycrystalline
The break up of the surface results in an increase of planes
the
and
surface and the low index plane.
index
other
We have investigated,
interference microscopy,
the original
the total surface area which is energetically
from
are reported in
of thermal etching on
hydrogen mixtures and in vacuum.
The contact
low
oxygen
here together
on the dependence
no net evaporation
the variation
the
detail
particularly
net evaporation
Further such experiments
in air and oxygen under conditions aY0
orientation
which show that striations can form even
when there is negligible
ay, sin 0
of
We have reported briefly some
rethe
To
no abtempt was made to polish
the surfaces ; interference
microscopy
showed
that
surface irregularities due to rolling were less Ohan 300 A deep. Tube
furnaces
of Mullite
were used for heating
total surface energy would be greater for a simple hill
specimens in air. For some experiments
and valley structure
were placed on a Mullite boat so that there was net
with any other value of 0.
It
follows that a surface at an angle greater than 0 from
evaporation
the low
the specimens were totally enclosed inside a silver box :
index
orientation
will not
striations which expose that plane. orientations
of striated
break
up into
Kingf4) measured
and unstriated
surfaces
of
silver heated
from the surface.
the specimens
In other experiments
the box, about 2 in. x 1 in. square, was made from “specpure”
sheet and was loosely constructed
the surrounding
atmosphere
so that
had easy access to the
in air and thus measured the contact angles for both (100) and { 11 I} planes. Later Moore(a) using an optical goniometer and also from estimates of the relative areas of low index and continuation
enclosure, the specimens hung by silver wires from a ceramic bead mounbed inside the box, in this way net evaporation of the specimens was reduced to a negli-
surfaces measured the same angles and calculated the relative surface energies ye/ye by neglecting the aye/83 term in equation (1).
gible amount. For obtaining mixtures of oxygen and nitrogen we have used a continuous flow gas system. Nitrogen,
Recently
Hondros
and Moore@) have studied
the
99.9 per cent pure, was passed from a cylinder
over
AND
RHEAD
hot
copper
turnings
to
potassium
hydroxide
controlled
flow of oxygen
stream from a voltameter electrolysed.
remove
to remove
carbon
1 in, dia.-and
and
carbon
over
dioxide.
A
to the gas
was admitted
The mixture
of gases, dried by passing
dioxide
specimen furnace.
oxygen
THERMAL
in which acidified water was
over magnesium perchlorate, at solid
MYKURA:
went through a cold trap
temperature
and into
the The
gas mixture finally flowed through a needle valve into the atmosphere
and the total flow rate was monitored
with a “Rotameter” By carefully
SILVER
845
not always satisfied;
of the additional
we therefore made use
information
given by the direction
of the striations and the directions and magnitudes surface.
Errors from *lo
to &2’
are estimated
To obtain a measure of the net evaporation at the beginning specimens
out how the evaporation
at regular intervals
rate changed as the striations
the proportion
of
THERMAL
ETCHING
IN
OXYGEN
AND
in f7
The surfaces break up into linear striations
per cent for several days.
To test the nitrogen
were made with no oxygen added
at flow rates of less than 100 cm3/min
the reaction with the hot copper was sufficiently Specimens
centrations
were
of oxygen,
flow rate of 75 f
heated
from
periods of 10 days at 900 f
10%.
for concentrations nominal cylinder.
con-
upwards,
for
For all runs a total
1 cm3/min was used.
of 10 p.p.m.
slow evolution
in various
10 p.p.m.
this method of gas preparation concentration
fast
heated in the gas did not become
We consider
satisfactory
of oxygen
down to a
but unreliable
much less than this because of the
of oxygen
purity
of
the
and the variation nitrogen
In the same furnace
from
of the
cylinder
to
and gas flow system
AIR
The general features of surfaces etched in oxygen with and without net evaporation
striated.
Some to find
the pressure (atmospheric
t,he current through the voltameter,
so that specimens
during
and at the end of each run.
were weighed
oxygen in the mixture could be kept constant to with-
t,o the gas flow;
tions which depend
are shown in Fig. 2. in direc-
on the surface orientation.
The
striations are much more widely spaced on the specimen
where
net evaporation
ference microscopy
up of strips of smooth curved
surfaces
orientations
was inhibited.
Inter-
shows that the striations are made (Fig.
flat facets joined 3).
by slightly
It has been found
from
of the grains that the striations are always
parallel to the direction of the zone axes of low index planes (ill}, the
(100) or (110).
inclinations
For (111) or (100) planes
of the facets
from
interferograms
verify that the facets are low index planes. On most of the (111) and (100) facets we have not been able to detect any departure from planarity;
specimens were heated in pure nitrogen and (without
may therefore be put at about 40 lattice spacings.
polarity
in pure oxygen.
of the voltameter
All
the
a measure
of nitrogen
and
surface (p in Fig. 1) we have taken the fringe spacing
the experiments
de-
scribed here were at 900 & 10°C. Using
a Baker
interference
made int,erferograms magnification ferogram
microscope
we have
surfaces
Fig. 3 shows a typical
of a surface heated in oxygen
the angle across a ridge-the
at a inter-
for 10 days,
contact angle-is
readily
measured to within 2” from the fringe spacings, and in favourable cases with an accuracy of f 1”. It was found necessary scope-fringe
to make a calibration
of the micro-
spacing against angle of tilt.
done with the aid of an optically
This was
ilat silvered glass
splinter mounted on a goniometer head from an X-ray diffraction camera. Several hundred grains were formed on each specimen, the crystallographic
orientations
were found from measurements
of the angle of tilt of the continuation
near the top of the ridge where the curvature surface is negligible.
of the specimen
of 800.
As
By reversing
mixtures
were obtained.
an
upper limit to step heights on these low index surfaces
the hot copper) hydrogen
for
the orientations.
+ 21 cm Hg) and the outlet flow of the gas as well as
purity experiments
of
the angles between low index facets and the general
developed.
flowmeter.
controlling
condition
OF
heating each specimen was weighed to within f 10 pug
Both the specimen furnace tube-
the furnace boat were of Mullite.
ETCHING
of some crystals
of the angles between
twin traces as described by Barrett@). This method requires at least three twin traces for each crystal, a
The measurements
fore limited to those striations The (110) facets occurred there
was
net
measurements
only
evaporation.
of the
were there-
most well developed. on specimens No
where
interferometric
could be made as the facets were too
small, they may well have been slightly curved. The contact angle was estimated from the range of orientations
on which (110) striations formed.
On the
specimen heated in air the (1 IO} facets developed rather erratically, some crystals near (110) not faceting and on others (110) facets appearing
up to 8’ from (110).
Table 1 summarizes the results of measuring the contact angles for specimens heated in air and oxygen and for conditions of both net evaporation and no net evaporation. The values obtained are compared with those of previous investigations. Certain anomalies were found with (100) striations; whereas (111) striations usually form sharp straight
ACTA
846
FIG.
METALLURGICB,
2. Thermally
VOL.
etched surfaces after (a) with evaporation
(b) evaporation
10,
1962
10 days
inhibited.
in oxygen.
RHEAD
Frc. 3. Intcrferogram TT’
facets
often
MYKURA:
AND
THERMAL
twin boundary
develop
L low index planes
(100)
with
irregularly
shaped
edges and the angles of contact,
especially
during the early stages of etching, concentrations found.
OF
SILVER
of striations on a twinned crystal after 10 days in oxygen inhibited). Fringe spacing = 0.29 ,u.
ridges
low as 15°-180.
ETCHING
are sometimes
C continuation
be interpreted variations evidence
as
of
of changes
(evaporation
surfaces
by means contact
847
of equation
angle
with
(1) and any
atmosphere
of the y-plot
For each angle an upper limit for ~J&J~is given by cos 0,
In the later work at lolver oxygen
the lower limit depends on the value assumed for ay,/%.
similar low angle (100) striations were
Since these angles are not stable they have not
For specimens tinuation
been included in the average values quoted here. In terms of surface energies the contact angles may
heated
in air and oxygen
surfaces have orientations
1. _ Contact
Kinat
Air (specimen evaporating) Air
(specimen evaporating)
angles 0
{1 10) striations (111) striations { IOO} striations (No. of crystals measured in bracket,s) _______ _______ 2.5” 36.5”
33.3” +
1.8” (88)
33.8” +
1.0” (21)
4” & 4”
30.5’
1.0” (24)
-
Air (specimen evaporating)
25.4” + 1.1” (Ii)
This work
Air
19.4”
This work
Oxygen
(specimen evaporating)
26.1” rt 1.3” (12)
34.2” & 1.0” (27)
This work
Oxygen
(no net, evaporation)
21.9” & 0.8”
31.6” +
(no net evaporation*)
-.
26.2” & 2.2” (56)
This work
&
1.0”
* Hondros and Moore’GJ and Moore ,‘7b) claim that faceting but some of the photographs show distinct faceting.
(8)
(7)
+
1.6” (26)
the con-
considerably
moved from (111) and (100) orient’ations.
TABLE
_luthor
are
with atmosphere.
14” + 2’ (6) -
does not occur when there is no net evaporation,
re-
Since the
ACTA
848
METALLURGICA,
VOL.
10,
1962
FIG. 4. Interferogram of (100) facets (A) with mainly 1111) steps after 10 days in oxygen with evaporation. The narrow twin shows (111) facets (B) with (100) steps.
greatest change in the y-plot is expected within about
respectively,
10” of the low index orientations
arcs are drawn at angles from the low index
30” is probably
equal to the mean values for the angles of contact.
aye/%’ at 8 = 20” to less than a tenth (7s - r,,)/e so that
found for specimens
heated in air;
cos e should give a value for ye/ye which is perhaps 1 or
Only surfaces with orientations
2 per cent too high.
come striated, grains with orientations
of inverted
This is confirmed by observations
twin boundaries,
on twins both oriented
near the limit of faceting, which give a direct measure of $@f3 or (111)
orientation
it was sometimes
found
that
striations did not form but instead the surface changed into large areas of low index planes bounded straight steps.
within these arcs beoutside the arcs
are found to remain smooth and unstriated. Secondary faceting may be explained by noting that if a continuation
(Mykura@)).
When the surface of a grain was very near to a (100)
the poles
surface joining
has an orientation
segments
of (100) facet
along AZ it can break up into (111) III
by sharp
The steps are usually shallow strips of
low index facet, in Fig. 4 the surface is mainly (100) planes and the steps (11 l} planes. This type of etching was frequently found only where there was net evaporation ; if low index surfaces have relatively low evaporation
rates it would
be expected
that evap-
oration would expose these surfaces. After
the formation
of linear striations
faceting) the continuation
(primary
surface itself may break up
into a hill and valley structure with low index facets (secondary faceting). Moore(s) has shown how secondary faceting occurs if the orientation
of the continua-
tion surface lies in the region ACZ of the unit stereographic triangle shown in Fig. 5. The arcs AB, CD and EF are the loci of orientations of the continuation
surfaces for (loo),
(111) and (110) striations
FIG. 5. Stereographic triangle illustrating secondary and simultaneous primary faceting. Points in ACZ: general surface orientations of crystals showing simultaneous primary faceting. Points in BDZ: orientation of corresponding “gadle ends”.
RHEAD
AND NYKURA:
facets and a surface with an orientation thus the final orientation equilibrium
THERMAL
ETCHING
OF
SILVER
a49
along CZ,
of a continuation
III
surface in
with both (100) and (111) facets should be Grains with surface orientations with-
at the point Z.
in the region ACZ facets (simultaneous tinuation
surface
can develop
in equilibrium
should have an orientation Examples
have
development
both (100) and (111)
primary faceting),
been
/
again the con-
with
both
facets
at Z. found
this is presumably
because
facets develop much faster than (110) facets. of secondary
and simultaneous the observed
predict
Measure-
tinuation surfaces. an example
primary faceting does
orientations
of the
con-
The int’erferogram of Fig. 6 shows
of simultaneous
The surface has developed
primary
faceting
in air.
into three sets of facets:
(100) planes, (111) planes and surfaces at various inclinations and in contact with both sets of low index surfaces ; we will refer t’o these surfaces as “gable Orientations were determined from fringe ends”.
I V III
(111)
ments we have made show that the above explanation not
\
/
of the simuhaneous
of (100) and (111) facets but not of (Ill)
with (110) facets,
h
FIG. 7. Schematic
To explain
representation
this apparently
/
\
IO0
Ill
d/
of Fig. 6.
anomalous
necessary to consider the equilibrium
00
effect it is
of three surfaces
which etched in this way the gable ends have a range
taken as a whole rather than the equilibrium between pairs of surfaces. The equilibrium configuration of the
of orientations
three sets of facets will be the one with the minimum
spacings and it has been found that on each crystal
predicted. surfaces
all in the region BZD
The orientations
and not at Z as
of the original
general
and gable ends for three such crystals
total surface energy.
showing
Since the low index surfaces are
at minima in the y-plot they may be considered with respect
plotted in Fig. 5.
Frc:. 6. Interferogram
are
to rotations.
simultaneous primary faceting in sir after 10 days. B, (111) facet; Q, “gable end”.
A minimization
A,
(100) facet;
fixed
of total
850
ACTA
energy gable
can therefore end ;
equilibrium
1
only occur by rotation
it is shown orientation
approximately
METALLURGICA,
in the appendix of
the
gable
of the
that
the
end is given
by
10, 1962
VOL.
shape of a continuation boundary
surface where it crosses a twin
and is in contact with two low index facets
(Fig. 3) and for the shape of the continuation on pyramids
found during enhanced
both these cases the surfaces become Ylll
-2 ( YG
set 8 1 +
in
steeper in the
region near the point of contact of the three surfaces.
‘?! Yc
= 2 set 4 -
surface
evaporation;
see 0 21
see3 f$ -
-
1
YG
+c sin 4 sec2 4
THERMAL ETCHING IN NITROGEN, HYDROGEN AND VACUUM
(3)
Striations
a+
where 8i, 8, and + are the angles of inclination
t,o the
oxygen-free
did not form
on specimens
heated
in
atmospheres.
The
heated
in
general surface of the( 11 l), (100) facets and gable end
“pure”
respectively
nitrogen plus 0.1 per cent hydrogen were very similar.
and where yin, yle,, and yc are the surface
If the ay/ae and 6’y/&j terms are neglected and the approximate
values ylil/yc
cos 25” are substituted with typical
= cos 34” and yi,,Jyo =
in the above equation together
values 8, = 324” and 0, = 24”, then 4 is
found to be about
loo-the
orientation
end should therefore be in the region the point Z. explained
The orientations
therefore
of the gable
BZD
and not at
of the gable ends can be
if it is assumed
surfaces are in equilibrium
that the three
simultaneously
as a unit.
It was found that on a given crystal the smaller gable ends are tilted most from the general surface, this is presumably facet.
(less than lo-’
Grain boundaries
energies.
surfaces
nitrogen
surfaces
because
occurs
equilibrium
most
rapidly
The same explanation
Fla.
between
across
the three
small areas of
would account
for the
were delineated
and both twin boundary were observed-evidence surface
energy
parts oxygen)
after a few hours
grooves and inverted grooves of a definite
with crystalline
shows a surface
heated
variation
orientation.
in nitrogen
grooves
the
is slow
were only about 0.3 ,u deep
and rolling marks had not completely diffusion
was probably
presence of impurities Evaporation
by
off. the
which are removed by oxygen.
to evaporate
Evaporation
facet (Fig. 9).
smoothed
suppressed
roughening was observed on specimens
heated and allowed mm Hg).
8
with etching in air, even after 5 days the
grain boundary Surface
of
Fig.
for 5 days,
kinetics of etching in these inert atmospheres compared
and in
exposed
But on specimens
in vacuum
(
large areas of plane heated in vacuum
8. Surface after 5 days heating in nitrogen. Shallow grain boundaries and inverted twin boundaries (T). The horizontal markings are rolling marks.
RHEAD
9. Evaporation
FIG.
and completely evaporation
enclosed
MYKURA:
AND
roughening
in a silver box
no evaporation
roughening
THERMAL
with
ETCHING
the development (Interferogram.)
to inhibit
occurred and
OF
of facets
after
SILVER
30 min
851
in v~cuurn.
degrees higher than those for 10 p.p.m. contact
angles for all concentrations
The mean
are shown
in
the surfaces were similar to those heated in nitrogen
Table 2 and the variation
and the nitrogen plus hydrogen
angle with the logarithm of oxygen partial pressure is
mixture.
plotted THERMAL WITH
Specimens atmospheres
ETCHING IN LOW OXYGEN
were heated with
parts by weight:
for periods
nominal
oxygen
of 10 days in concentrations,
10P5, 3 x 10V5, 10P4, 3 x 10-4, 10-3,
In 10 p.p.m. striated,
of oxygen
only about half the grains
considerably
striated than on the air-etched also some evaporation occurred
12.
The table
on specimens
summarizes
which
in vacuum.
more grains were unspecimens.
roughening
There was
but not as much as
The increase in the experimental
the contact
angles at low oxygen
concentrations
in the measurements
at these concentrations.
dition crystals
of the specimens; furthest
it was found
upstream
much more than those downstream, a higher concentration
the
concentrations
fringe
spacings.
The results are plotted
of the
in a unit
that
those
it is possible that
of silver vapour
unstriated, were oriented and from interferograms
surfaces for both (100)
This
in the gas flow striated
would clean off some of the adsorbed
of the continuation
and
of the surface con-
and
and (111) st,riations we found by measurement
to
error in
especially at 10 p.p.m. is due to a much wider scatter
Some 46 grains, striated
orientations
all the
were allowed
evaporate.
scatter is the result of variations
and 10-2. became
in Fig.
measurements
ATMOSPHERES CONTENT
of the cosine of the contact
downstream
oxygen.
the etched topography
At low
is complicated
by the surface roughness
caused by evaporation,
areas of smooth
were found
grains
facets
surface
formed
few
and on many
on the sides of
hillocks
and
stereographic t’riangle in Fig. 10(a) and a t’ypical area of the specimen is shown in Fig. 11. The mean contact
t,roughs where the surface was tilted by several degrees
angles were : {lOO}> 17.6’ + 2.0“;
were found on the underneath surfaces of specimens heated in low2 and 10e3 parts of oxygen, this is
these angles are appreciably air-etched specimens.
{ill},
24.9” & 2.0”;
lower than the angles for
Comparable results for an oxygen concentration of about 100 p.p.m. are shown in Fig. 10(b). At this concentration however the contact angles were several
from the general orientation.
Occasional
(1 lo} facets
possibly due to contact with Mullite. A few small areas of plane facet with orientations near the (110) pole developed on the specimens heated in 10-J parts of oxygen.
_4CTA
(a) oxygen concentration
METALLURGICA,
10e5
VOL.
10,
1962
(b) oxygen concentration
lo-’
FIG. 10. Stereographic projections showing orientations of: 0 grains which formed striations with (100) facets. n grains which formed striations with (111) facets. 0 continuation surfaces in equilibrium with (100) facets. l continuation surfaces in equilibrium with (100) facets. x unstriated grains.
FIG. 11. Typical
area of surface heated for 10 days in 1O-5 parts oxygen
It appears t,hat reducing the oxygen concentration produces a marked decrease in the contact angles. The orientations of unstriated grains were always found in the region of the stereographic triangle outside the arcs drawn at the orientations of the continuation surfaces. For concentrations where the arcs do not intersect no examples of simultaneous primary etching were found.
EVAPORATION
AND
The net loss of material
THERMAL
ETCHING
by evaporation
from the
specimens heated in air was limited by the rate of diffusion of vapour through the air in the sealed furnace tube. To find how thermal etching was affected by a faster evaporation rate specimens were heated in a steady flow of air, and as a result, a quite
RHEAD
MYKURA:
AND
THERMAL
ETCHING
OF
853
SILVER
TABLE 2. Contact angles at different oxygen concentrations
-
Nominal concentration
1.00 2.04 0.92 1.23 2.46 0.90 3.70 1.23
Oxygen Air 10-Z IO-3 3 x 10-a 10-d 3 x 10-s 10--s
x + & * * * k
10-l 0.05 0.06 0.14 0.05 0.22 0.06
x x x x x x
Contact angles 0 {Ill} striations { 100) striations (no. of crystals measured in brackets) __34.2” + 1.0” (27) 26.0” * 1.3” (12) 33.8” l 1.0” (21) 25.4’ & 1.1” (17) 27.2” + 1.6” (22) 32.0’ + 1.4” (18) 23.5” i 1.5” (17) 28.6” * 1.2” (27) 21.9” 4 1.8” (16) 29.8’ + 1.0’ (25) 20.0” * 1.7” (17) 29.4” * 1.7” (17) 21.6” k 2.0” (26) 29.2” * 1.4” (41) 17.6” * 2.0” (13) 24.9” f 2.0” (19)
Partial pressure 0, mm Hg.
Relative concentration parts 0, by weight
970 155 9.05 1.21 2.41 0.88 3.63 1.21
10-Z 10-s 1O-4 10-d 10-S IOW
x x x x
10-r IO-’ lOme 1OW
evaporation
of the general surface and that evapor-
ation from low index than the average formation
surfaces
rate.
lower
Additional
in-
on this point comes from the variation
evaporation
rate
with
time
etching as the proportion index
is appreciably
evaporation
facets
specimen
which
occurs
of surface made up of low
progressively
increases.
A
typical
was heated in air in a sealed furnace
and the weight of the specimen tervals up to 300 hr.
found
tube
at 20 hr in-
The tube had previously
used for several thousand
of
during
been
hours for heating silver so
that it may be assumed that the silver vapour near the specimen was in dynamic pressure
constant
fraction
during
equilibrium
and the vapour
the experiment.
As the
of the surface made up of visible low index
facet changed from zero at the beginning to not more
.808 -2
than 40 per cent after 300 hr the weight loss changed -I
0
I
2
from about 20 ,ug/cm2 per hr to 12 pg/cm2 per hr. Part of the change in evaporation rate may be due to an
3
increase in surface impurity concentration
FIG. 12. Variation of the cosine of the contact angles “Least with logarithm of partial pressure of oxygen. squares” straight lines.
from the interior of the specimen, mainly
to a lower evaporation
rate from low index
different form of etching was found on many crystals.
surfaces
After a few hours dots appeared on the surface, these
times more slowly
were apparently
clusions can be drawn from observations
small hillocks and had a density of about 2 x lo6 cm-2; they may be the sites of screw dislocations.
The dots became the nucleation
the formation extending
of facets which grew into striations
by
sideways (Fig. 13). Under these conditions
of fast evaporation consisted
sites for
mainly
the final structure of large pyramids
after 20 days
with exact
low
then these surfaces
frequently
spontaneous
is not howfor
changes of a flat surface under equilib-
rium conditions. The interferograms show that close to the base of the pyramids a shallow groove forms and the correct contact angles are preserved. The heights of the pyramids-sometimes greater than 10 ,u-when compared with the net weight loss from the surface, 14 mg/cm2, indicate that they are formed mainly by
con-
on specimens
higher than the surrounding
grains
by several microns. The specimens heated in a silver enclosure showed surface
which accounts
at least ten Similar
found grain surfaces, made almost entirely
Fig. 4, standing
the general surface at angles greater than the equilibwith the theory
than the average.
of smooth low index facets, similar to those shown in
negligible
ever in conflict
evaporate
heated in atmospheres of low oxygen content ; we have
index sides (Fig. 14) ; the sides were often inclined to rium contact angles given in Table l-this
by diffusion
but if it is ascribed
weight
location
losses.
The
effective
due to evaporation
changes
1O-2 ,u, while the striations were very pronounced the low index facets projected
in
were less than and
several microns above
the general surface. This is clear evidence that net evaporation is not essential for the development of striations. However the striations are more widely spaced
where net evaporation
is inhibited
and the
much higher density of striations on evaporating specimens shows that nucleation is considerably enhanced by net evaporation.
ACTA
FIG. 13. The formation
METALLURGICA,
VOL.
of facets during enhanced
10,
1962
evaporation.
After 2 days in air.
FIG. 14. Interferogram of pyramids formed by enhanced evaporation. After 20 days in air. The height of the pyramids is greater than t,he dept,h of focus of the microscopr.
RHEAD
MYKURA:
AND
THERMAL
TABLE 3. Net evaporat,ion rates of silver in various atmos-
pheres at 900°C
oxymm
changes in the partial pressure of oxygen
The variation of contact angle with oxygen pressure may be accounted
NO.18 Air Aj, Evaporation mhibited &4irFast stream
10-20
cause a relatively surface
2.53.5
et d.(3) found for the variation
1’ = 228 -
3-5
between 0.2 and 1O-4 atm.
~10,600
equation
mhibited
the coefficient
different atmospheres.
rates
are given
for
For similar specimens heated
atmosphere
there
losses of as much
quoted are typical ones.
were differences
as threefold,
in
the values
DISCUSSION
growth
of linear facets
various
mass transport
experiment of dynamic
during
account
thermal
mechanisms.
of the
etching
Comparison
for of
net evaporation.
investigations
we
surfaces
vary with oxygen
yL and continuation
average surface energy we may write: YL(P) = Y&(O) -
K,
log,0 P
(5)
Ye(P) = ye(o) -
K, log,, P*
(6)
Putting yL(o) = y,(o) y-plot
are caused
i.e. assuming that cusps in the
mostly
by differential
cos 8 = 1 -
K, - Ko l%(P)
tion and surface diffusion
justified by the experimental
ment of striations on silver. Striations do not always occur when there are finite cusps in the y-plot,
as shown for example
verted twin boundaries
by the in-
on silver heated in nitrogen.
be taken as a constant. following
This evidence is not however in conflict with the view that thermal etching is driven by a lowering of total
Kill -
surface energy. For values of yo/yO near unity the contact angles will be necessarily small and aye/at3
0.007
real value
of O-this
point
has been discussed
by
Blakely and Mykura”“. evaporation in air are comparable with the angles for conditions of net evaporation in 1O-4 parts of oxygen. This effect may be ascribed to the desorption of
calculation accuracy)
(all that is
K, -
-.-
R,
can
Ye(P)
From the slopes of the lines
values are found : K,,, -
K, = 8.3 & 1.6 K, = 6.4 h 1.4 ergs cm-2 i.e. K, K loo - K”= 0.044 -+ 0.009 ; ___= 0.034 -+
cm-2; R
K,, ---
K
Since K, m I’? and K is proportional
to r we may
conclude that about 4 per cent more oxygen atoms per unit area are adsorbed
The contact angles found for conditions of negligible
log,, P,
drawn in Fig. 12 and putting ye = 600 ergs cm-2 the ergs
ma,y be too large for equation (1) to be satisfied for any
adsorption
and neglecting the ay,Jae term in equation (1) we find :
For an order of magnitude
to the develop-
surfaces ye
pressure in the same way as the
have made indicate that both evaporation-condensacontribute
density for the par-
If it is assumed that t’he surface energies of both tJhe low index
i.e. where there is negligible
Some preliminary
is proportional
oxygen atoms, I‘, and has
lOI cm-2 (Herring(12)).
with theory should be made for conditions equilibrium
(4)
From the Gibbs adsorption
been taken to imply a constant
were as much as a quarter those in air.
a theoretical
ergs cm-2.
ticular pressure range and temperature : r = 0.95 x
The weight losses in nitrogen
Mullins’l’J) has given
P
of log,, p, x,
to the density of adsorbed
* The figure for evaporation in vacuum is for a period of 30 min and for vacuum with evaporation inhibited, 10 hr. All the other rates are mean values over 5-10 days.
weight
188 log,,
where p is the oxygen partial pressure in atmospheres
4-10
3 net evaporat’ion
Buttner
of the average surface
energy of silver at 900°C
Evaporation
in the same
greater decrease in the low index
energies as the pressure increased.
j-7
In Table
for by a relatively higher density of
adsorption sites on the low index surfaces which would
S-16
*Vacuum
affect the
changing the den-
sity of the adsorbed layer.
-18
Sitrozen I + 10-3 parts Nitrogen hydrogen *Vacuum
855
OF SILVER
surface energy without appreciably
Evaporation rata in pg/cm2 per hr
Atmosphere
ETCHING
onto low index surfaces than
onto surfaces with other orientations. If it is assumed that y&(o) = ye(o) w 1200 ergs cm-2 at a partial pressure of about 10e6 atm the 4 per cent difference between K, and K (low index) predicts for the ratio
oxygen following adsorption of silver vapour-only a small fraction of the adsorbed oxygen would need to
of surface energies at 10-l atm: yL/ys e 0.85 which is in accord with t,he observed values of the contact
be
angles.
removed-Buttner
et CZ~.(~)showed
that
large
ACTA
856
METALLURGICA,
APPENDIX
The
A surface structure similar to that shown in Fig. 6 is drawn schematically of surfaces, (ill),
on average
is a pyramid,
configuration consider energy
of
an
will be reached
for example
of the pyramid bringing
about
areas, but the inclinations
be
shown
from
-
aa, -
sin xl
(10)
XJ sin x1 + sin xz
aa,
aaloo
sin xs
01)
sin x1 + sin xs
VW-%-
pyramid.
is a minimum. changes
The
surface
of the low index facets may
in t’he y-plot.
(12)
total
of the three
in relative
be considered fixed crystallographically at sharp minima
can
when the total surface
surface energy can change by rotations surfaces
relationships
are
To find the equilibrium elementary
1962
aall1 --
of the three sets of surfaces we need only
equilibrium
Equilibrium
following
The basic
the bases of the pyramids
parallel to the general surface.
10,
geometry :
in Fig. 7. There are three sets
(100) and “gable ends”.
unit of surface topography ABCD,
VOL.
since they are
Therefore
only the
where xl = < DAC
and xs =
the projected
angles in the plane ABC of Fig. 7. On substitution these relationships condition
in equation
of
(9) the equilibrium
becomes :
“gable end” may rotate, which it may do (i) by movement of B toward
A, and C away from A (or vice
versa) ; this changes the relative areas of (111) : (100) of D along AD,
low index surfaces ; (ii) by movement
Yloo sinxz
Ylll sin Xl yG cos B,(sin x1 + sin xs)
+
yo cos e&sin xl + sin xz)
this varies t,he ratio of low index surface to gable end = 2 set 4 -
surface. The total surface energy E of the pyramid w&ten
may be
:
which * = YllPlll + Y100%00 + cos 81
YG% (8)
cos 4
cos e2
alOOand aG are the fractional areas of the projected onto ABC and 0,, (I2 and $ the
wherea,,,, facets
corresponding equilibrium
angles of inclination orientation
to ABC.
of the gable
For the
end we need
consider rotations of type (ii) ; to obtain the minimum energy
condition
we differentiate
aE
respect to I$ and put q
cos 0,
+
?100~
(8) with
= 0
aaloo
aall Ylllv
equation
aa,
+ YGF+
cos 0,
cos $
sin
aGG = 0.
+ YG+ 4 + __ cos I$ cos2 c$
sec3 I$ -
(9)
can be approximated
identical
to equation
1 aYa sin d - _ __ yc a+ toss d
to equation
(13)
(3) and is
(3) for the symmetrical
case
where x1 = xs. REFERENCES 1. R. SHCTTLEWORTH, Metallurgia 38, 125 (1948). 2. B.CHALMERS,R.KING andR. SHUTTLEWORTH, P~oc.Roy. Sot. A193. 465 (1948). 3. F. H.BuTTNER;E.R.FuN~ andH. UDIN,J. Phys.Chem. 58, 657 (1952). 4. R. KING, Thesis, London University (1955). 5. A. J. W. MOORE, Acta Met. 6, 293 (1958). 6. E. D. HOXDROS and A. J. W. MOORE, Acta Met. 8, 751 (1960). 7a. G. E. RHEAD and H. MYKURA, Acta Met. 10, 578 (1962). (b) A. J. W. MOORE, Ibid. 10,579 (1962) 8. C. S. BARRETT, Structure qf Metals (2nd Ed.) p. 41. McGraw-Hill, New York (1952). 9. H. MYKURA, Acta Met. 9, 570 (1961). 10. W. W. MULLINS, Phil. Mag. 6, 1313 (1961). 11. J. M. BLAEELY and H. MYKURA, Acta Met. 9, 595 (1961). 12. C. HERRING, Structure and Properties of Solid Su$zces (Edited by R. GOMER and C. SMITH)p. 46. Univ. of Chicago Press (1953).
ETCHING
OF SILVER
G. E. RHEADt
IN VARIOUS
and
ATMOSPHERES*
H. MYKURAt
Investigations were made using interference microscopy of changes in the surface topography of silver specimens heated at 900°C in 0,, N,, N,/O, mixtures, a N,/H, mixture and in vacua. The development of both two and three sets of planes on an originally flat surface was studied. The observed development of {I 1 l}, { 100) and {I 10) facets when oxygen is present is ascribed to a lowering of the total surface free energy. Measurement of the angle of contact between low index surfaces (surface energy yo) and continuation-random orientation-surfaces (surface energy ye) show that Y,,/Y~ increases toward unity as the concentration of oxygen is decreased. The results indicate that about 4 per cent more oxygen is adsorbed onto {ill} and { 100) surfaces and that this anisotropy of adsorption is the main cause of the anisotropy of surface energy in oxygen bearing atmospheres. A comparison of faceting with and without net evaporation indicates that recondensation of silver atoms causes some desorption of oxygen. ATTAQCE
THERMIQUE
DE
L’ARGENT
DANS
DIVERSES
ATMOSPHERES
Les auteurs ont Btudie par microscopic d’interference les changements de la topographie superficielle cl’echantillons d’argent chauffes 8,500”C dens 0,, N,, N,/O,, N,/H, et dans le vide. Le developpement de deux ou trois groupes de plans sur une surrace initialement plane est Otudie. Le developpement en presence d’oxygene de facette {ill}, {loo} et {IlO} est attribue L un abaissement de l’energie libre totale de surface. La mesure de l’angle de contact entre surfaces it bas index (energie de surface y,,) et surfaces de continuation (orientation au hasard) (Qnergie de surface ye) montre que le rapport yo/ys augmente et tend vers l’unite lorsque la concentration de l’oxygene diminue. Les resultats indiquent qu’environ 4% en + d’oxygene est absorb6 sur les surfaces {ill} et {SOO} et que cette anisotropie d’adsorption est la raison principale de l’anistropie de l’energie de surface dans les atmospheres contenant de l’oxygene. La comparaison de formation de surfaces avec et sans evaporation nett,e indique que la recondensation d’atomes d’argent quelque d&sorption d’oxygene. THERMISCHES
ATZEN
VAN
SILBER
IN VERSCHIEDENEN
ATM~SPHBREN
Mit Hilfe der Interferenz-Mikroskopie wurde untersucht, wie sich die Oberflachen-Topographie von einer N,/H,-Mischung und in Vakuum auf Silberproben lindert, wenn sie in 0,, N,, N,/O,-Misohungen, 900°C erhitzt werden. Es wurde studiert, wie sich auf ursprtinglich ebenen Oberfliichen teils zwei, teils Ebenengruppen entwickelten. Die beobachtete Entwicklung von {ill}-, {lOO}- und {llO}-Facetten bei Anwesenheit von Sauerstoff wurde einer Erniedrigung der gesamten freien Oberfliichenenergie zugeschrieben. Messungen des Bertihrungswinkels zwischen niedrig indizierten Fliichen (Oberflachenenergie y,,) und den statistisch orientierten Zwischenfliichen (Oberflachenenergie ~0) zeigen, da6 mit abnehmendem Sauerstoffgehalt das Verhiiltnis y,,/ys zum Wert 1 hin ansteigt. Nach unseren Ergebnissen ist auf {ill}- und {lOO}-Flachen etwa 4% mehr Sauerstoff adsorbiert. Diese Anisotropie der Adsorption ist die Hauptursache der Anisotropie der Oberflachenenergie in sauerstoffhaltigen Atmospharen. Ein Vergleich der Facettenbildung mit und ohne Netto-Verdampfung zeigt, da13 Silberatome beim WiederKondensieren etwas Sauerstoff von der Oberfliiche vertreiben. INTRODUCTION
silver heated in air or oxygen
The surfaces of many metals, initially
smooth,
are
They concluded
but not in nitrogen.
that the presence of oxygen modified
found to expose low index facets and develop a hill and
the relative surface energies of crystal planes and that
valley structure when heated in certain atmospheres.
striations
Such changes
planes having
“faceting”), boundary “thermal
in surface
together and
twin
etching”.
topography
(usually
with the development boundary
grooves
Shuttleworth
called
of grain
were caused by the development lowest
free energy.
of those
Buttner
et uZ.(~)
have shown that the average surface energy of silver
are termed
measured for a range of crystal orientations
has reviewed the
by the adsorption
of oxygen.
is lowered
Kingt4) found that the
earlier work done on a number of metals and atmos-
planes developed
pheres.
has been investigated in much greater detail than any other. As there
(100) which indicates that adsorption on these planes produces a relatively greater lowering of surface
were still a number of doubtful
energy. In the simplest case of faceting
The system
behaviour
silver-oxygen
points on the faceting
of silver surfaces it was considered
worth
on silver were always either (11 l} or
the surface breaks
while to make a further study of this system to con-
up into two sets of parallel planes:
tribute
“simple”
to the understanding
of faceting
in general
and to study the effect of variation of oxygen partial pressure on the variation of surface energy with crystal
through striations.
Glasgow,
ACTA METBLLURGICA,
1962
VOL 10, SEPTEMBER
a low index or surface.
The sets
of parallel planes intersect to form ridges and valleys ; these appear as striations which usually extend right across each crystal. Fig. 1 represents a section
orientation. Chalmers et .1.(s) found that striations occurred on * Received January 24, 1962. t Department of NaturalPhilosophy,Universityof Glasgow W.2.
surface and a continuation
such a surface,
taken perpendicular
to the
The general surface 00’ has changed into a
hill and valley structure consisting of low index planes AB with surface energy y,, and continuation surfaces 843
ACTA
METALLURGICA,
Ii
VOL.
10,
1962
C
FIG. 1. Section through a striated surface (schematic). index facet. BC, continuation
BC making an angle 8 with the low index planes and with surface energy ys. By making a virtual displace-
00, original surfaoe. surface.
effects of evaporation
AR,
low
on thermal
etching
suggested that striations are produced
and have
by net evapor-
ment of the point B in the direction AB one arrives at
ation from the surface and not by a minimisation
the equation for equilibrium
total surface energy.
of the surfaces in contact
experiments
at B: y 0 = ye cos 8 -
ae
surface(‘@.
.
more
The increase in surface energy of the low index plane
AB
due to a small tilt away
position
from
the low index
is taken to be large enough to prevent
such tilt;
any
i.e. -
83
e + 87, - co9 8.
> ye sin
(2)
ae
with
concentration.
angle 13should therefore depend only on of surface energy with crystallographic (usually referred to as the “y-plot”)
be independent
of the angle u between
have
relatively
possible if
low
experiments using
the thermal etching of silver of evaporation
in pure nitrogen,
had the object of obtaining the effect of adsorption
nitrogen plus
These experiments
some quantitative
data on
on relative surface energies.
EXPERIMENTAL
surface
used.
specimens of “specpure”
The specimens,
prepared
from
silver were
about 2 cm2 x 0.2 mm, were
cold-rolled
sheet
(from
Johnson,
Matthey &Co., impurities detected spectrographically:
energies, that is if there is a large cusp in the y-plot at
Cd, Cu, Fe, Pb and Mn, each less than 1 p.p.m.).
the low index
avoid contamination
orientation.
which the angle of contact continuation
A surface between
structure
low index
surface is given by equation
for which there has been the maximum duction
of surface
energy
by simple
in and
(1) is one possible
faceting;
and
and thermal etching in mixtures of
oxygen and nitrogen,
Polycrystalline
The break up of the surface results in an increase of planes
the
and
surface and the low index plane.
index
other
We have investigated,
interference microscopy,
the original
the total surface area which is energetically
from
are reported in
of thermal etching on
hydrogen mixtures and in vacuum.
The contact
low
oxygen
here together
on the dependence
no net evaporation
the variation
the
detail
particularly
net evaporation
Further such experiments
in air and oxygen under conditions aY0
orientation
which show that striations can form even
when there is negligible
ay, sin 0
of
We have reported briefly some
rethe
To
no abtempt was made to polish
the surfaces ; interference
microscopy
showed
that
surface irregularities due to rolling were less Ohan 300 A deep. Tube
furnaces
of Mullite
were used for heating
total surface energy would be greater for a simple hill
specimens in air. For some experiments
and valley structure
were placed on a Mullite boat so that there was net
with any other value of 0.
It
follows that a surface at an angle greater than 0 from
evaporation
the low
the specimens were totally enclosed inside a silver box :
index
orientation
will not
striations which expose that plane. orientations
of striated
break
up into
Kingf4) measured
and unstriated
surfaces
of
silver heated
from the surface.
the specimens
In other experiments
the box, about 2 in. x 1 in. square, was made from “specpure”
sheet and was loosely constructed
the surrounding
atmosphere
so that
had easy access to the
in air and thus measured the contact angles for both (100) and { 11 I} planes. Later Moore(a) using an optical goniometer and also from estimates of the relative areas of low index and continuation
enclosure, the specimens hung by silver wires from a ceramic bead mounbed inside the box, in this way net evaporation of the specimens was reduced to a negli-
surfaces measured the same angles and calculated the relative surface energies ye/ye by neglecting the aye/83 term in equation (1).
gible amount. For obtaining mixtures of oxygen and nitrogen we have used a continuous flow gas system. Nitrogen,
Recently
Hondros
and Moore@) have studied
the
99.9 per cent pure, was passed from a cylinder
over
AND
RHEAD
hot
copper
turnings
to
potassium
hydroxide
controlled
flow of oxygen
stream from a voltameter electrolysed.
remove
to remove
carbon
1 in, dia.-and
and
carbon
over
dioxide.
A
to the gas
was admitted
The mixture
of gases, dried by passing
dioxide
specimen furnace.
oxygen
THERMAL
in which acidified water was
over magnesium perchlorate, at solid
MYKURA:
went through a cold trap
temperature
and into
the The
gas mixture finally flowed through a needle valve into the atmosphere
and the total flow rate was monitored
with a “Rotameter” By carefully
SILVER
845
not always satisfied;
of the additional
we therefore made use
information
given by the direction
of the striations and the directions and magnitudes surface.
Errors from *lo
to &2’
are estimated
To obtain a measure of the net evaporation at the beginning specimens
out how the evaporation
at regular intervals
rate changed as the striations
the proportion
of
THERMAL
ETCHING
IN
OXYGEN
AND
in f7
The surfaces break up into linear striations
per cent for several days.
To test the nitrogen
were made with no oxygen added
at flow rates of less than 100 cm3/min
the reaction with the hot copper was sufficiently Specimens
centrations
were
of oxygen,
flow rate of 75 f
heated
from
periods of 10 days at 900 f
10%.
for concentrations nominal cylinder.
con-
upwards,
for
For all runs a total
1 cm3/min was used.
of 10 p.p.m.
slow evolution
in various
10 p.p.m.
this method of gas preparation concentration
fast
heated in the gas did not become
We consider
satisfactory
of oxygen
down to a
but unreliable
much less than this because of the
of oxygen
purity
of
the
and the variation nitrogen
In the same furnace
from
of the
cylinder
to
and gas flow system
AIR
The general features of surfaces etched in oxygen with and without net evaporation
striated.
Some to find
the pressure (atmospheric
t,he current through the voltameter,
so that specimens
during
and at the end of each run.
were weighed
oxygen in the mixture could be kept constant to with-
t,o the gas flow;
tions which depend
are shown in Fig. 2. in direc-
on the surface orientation.
The
striations are much more widely spaced on the specimen
where
net evaporation
ference microscopy
up of strips of smooth curved
surfaces
orientations
was inhibited.
Inter-
shows that the striations are made (Fig.
flat facets joined 3).
by slightly
It has been found
from
of the grains that the striations are always
parallel to the direction of the zone axes of low index planes (ill}, the
(100) or (110).
inclinations
For (111) or (100) planes
of the facets
from
interferograms
verify that the facets are low index planes. On most of the (111) and (100) facets we have not been able to detect any departure from planarity;
specimens were heated in pure nitrogen and (without
may therefore be put at about 40 lattice spacings.
polarity
in pure oxygen.
of the voltameter
All
the
a measure
of nitrogen
and
surface (p in Fig. 1) we have taken the fringe spacing
the experiments
de-
scribed here were at 900 & 10°C. Using
a Baker
interference
made int,erferograms magnification ferogram
microscope
we have
surfaces
Fig. 3 shows a typical
of a surface heated in oxygen
the angle across a ridge-the
at a inter-
for 10 days,
contact angle-is
readily
measured to within 2” from the fringe spacings, and in favourable cases with an accuracy of f 1”. It was found necessary scope-fringe
to make a calibration
of the micro-
spacing against angle of tilt.
done with the aid of an optically
This was
ilat silvered glass
splinter mounted on a goniometer head from an X-ray diffraction camera. Several hundred grains were formed on each specimen, the crystallographic
orientations
were found from measurements
of the angle of tilt of the continuation
near the top of the ridge where the curvature surface is negligible.
of the specimen
of 800.
As
By reversing
mixtures
were obtained.
an
upper limit to step heights on these low index surfaces
the hot copper) hydrogen
for
the orientations.
+ 21 cm Hg) and the outlet flow of the gas as well as
purity experiments
of
the angles between low index facets and the general
developed.
flowmeter.
controlling
condition
OF
heating each specimen was weighed to within f 10 pug
Both the specimen furnace tube-
the furnace boat were of Mullite.
ETCHING
of some crystals
of the angles between
twin traces as described by Barrett@). This method requires at least three twin traces for each crystal, a
The measurements
fore limited to those striations The (110) facets occurred there
was
net
measurements
only
evaporation.
of the
were there-
most well developed. on specimens No
where
interferometric
could be made as the facets were too
small, they may well have been slightly curved. The contact angle was estimated from the range of orientations
on which (110) striations formed.
On the
specimen heated in air the (1 IO} facets developed rather erratically, some crystals near (110) not faceting and on others (110) facets appearing
up to 8’ from (110).
Table 1 summarizes the results of measuring the contact angles for specimens heated in air and oxygen and for conditions of both net evaporation and no net evaporation. The values obtained are compared with those of previous investigations. Certain anomalies were found with (100) striations; whereas (111) striations usually form sharp straight
ACTA
846
FIG.
METALLURGICB,
2. Thermally
VOL.
etched surfaces after (a) with evaporation
(b) evaporation
10,
1962
10 days
inhibited.
in oxygen.
RHEAD
Frc. 3. Intcrferogram TT’
facets
often
MYKURA:
AND
THERMAL
twin boundary
develop
L low index planes
(100)
with
irregularly
shaped
edges and the angles of contact,
especially
during the early stages of etching, concentrations found.
OF
SILVER
of striations on a twinned crystal after 10 days in oxygen inhibited). Fringe spacing = 0.29 ,u.
ridges
low as 15°-180.
ETCHING
are sometimes
C continuation
be interpreted variations evidence
as
of
of changes
(evaporation
surfaces
by means contact
847
of equation
angle
with
(1) and any
atmosphere
of the y-plot
For each angle an upper limit for ~J&J~is given by cos 0,
In the later work at lolver oxygen
the lower limit depends on the value assumed for ay,/%.
similar low angle (100) striations were
Since these angles are not stable they have not
For specimens tinuation
been included in the average values quoted here. In terms of surface energies the contact angles may
heated
in air and oxygen
surfaces have orientations
1. _ Contact
Kinat
Air (specimen evaporating) Air
(specimen evaporating)
angles 0
{1 10) striations (111) striations { IOO} striations (No. of crystals measured in bracket,s) _______ _______ 2.5” 36.5”
33.3” +
1.8” (88)
33.8” +
1.0” (21)
4” & 4”
30.5’
1.0” (24)
-
Air (specimen evaporating)
25.4” + 1.1” (Ii)
This work
Air
19.4”
This work
Oxygen
(specimen evaporating)
26.1” rt 1.3” (12)
34.2” & 1.0” (27)
This work
Oxygen
(no net, evaporation)
21.9” & 0.8”
31.6” +
(no net evaporation*)
-.
26.2” & 2.2” (56)
This work
&
1.0”
* Hondros and Moore’GJ and Moore ,‘7b) claim that faceting but some of the photographs show distinct faceting.
(8)
(7)
+
1.6” (26)
the con-
considerably
moved from (111) and (100) orient’ations.
TABLE
_luthor
are
with atmosphere.
14” + 2’ (6) -
does not occur when there is no net evaporation,
re-
Since the
ACTA
848
METALLURGICA,
VOL.
10,
1962
FIG. 4. Interferogram of (100) facets (A) with mainly 1111) steps after 10 days in oxygen with evaporation. The narrow twin shows (111) facets (B) with (100) steps.
greatest change in the y-plot is expected within about
respectively,
10” of the low index orientations
arcs are drawn at angles from the low index
30” is probably
equal to the mean values for the angles of contact.
aye/%’ at 8 = 20” to less than a tenth (7s - r,,)/e so that
found for specimens
heated in air;
cos e should give a value for ye/ye which is perhaps 1 or
Only surfaces with orientations
2 per cent too high.
come striated, grains with orientations
of inverted
This is confirmed by observations
twin boundaries,
on twins both oriented
near the limit of faceting, which give a direct measure of $@f3 or (111)
orientation
it was sometimes
found
that
striations did not form but instead the surface changed into large areas of low index planes bounded straight steps.
within these arcs beoutside the arcs
are found to remain smooth and unstriated. Secondary faceting may be explained by noting that if a continuation
(Mykura@)).
When the surface of a grain was very near to a (100)
the poles
surface joining
has an orientation
segments
of (100) facet
along AZ it can break up into (111) III
by sharp
The steps are usually shallow strips of
low index facet, in Fig. 4 the surface is mainly (100) planes and the steps (11 l} planes. This type of etching was frequently found only where there was net evaporation ; if low index surfaces have relatively low evaporation
rates it would
be expected
that evap-
oration would expose these surfaces. After
the formation
of linear striations
faceting) the continuation
(primary
surface itself may break up
into a hill and valley structure with low index facets (secondary faceting). Moore(s) has shown how secondary faceting occurs if the orientation
of the continua-
tion surface lies in the region ACZ of the unit stereographic triangle shown in Fig. 5. The arcs AB, CD and EF are the loci of orientations of the continuation
surfaces for (loo),
(111) and (110) striations
FIG. 5. Stereographic triangle illustrating secondary and simultaneous primary faceting. Points in ACZ: general surface orientations of crystals showing simultaneous primary faceting. Points in BDZ: orientation of corresponding “gadle ends”.
RHEAD
AND NYKURA:
facets and a surface with an orientation thus the final orientation equilibrium
THERMAL
ETCHING
OF
SILVER
a49
along CZ,
of a continuation
III
surface in
with both (100) and (111) facets should be Grains with surface orientations with-
at the point Z.
in the region ACZ facets (simultaneous tinuation
surface
can develop
in equilibrium
should have an orientation Examples
have
development
both (100) and (111)
primary faceting),
been
/
again the con-
with
both
facets
at Z. found
this is presumably
because
facets develop much faster than (110) facets. of secondary
and simultaneous the observed
predict
Measure-
tinuation surfaces. an example
primary faceting does
orientations
of the
con-
The int’erferogram of Fig. 6 shows
of simultaneous
The surface has developed
primary
faceting
in air.
into three sets of facets:
(100) planes, (111) planes and surfaces at various inclinations and in contact with both sets of low index surfaces ; we will refer t’o these surfaces as “gable Orientations were determined from fringe ends”.
I V III
(111)
ments we have made show that the above explanation not
\
/
of the simuhaneous
of (100) and (111) facets but not of (Ill)
with (110) facets,
h
FIG. 7. Schematic
To explain
representation
this apparently
/
\
IO0
Ill
d/
of Fig. 6.
anomalous
necessary to consider the equilibrium
00
effect it is
of three surfaces
which etched in this way the gable ends have a range
taken as a whole rather than the equilibrium between pairs of surfaces. The equilibrium configuration of the
of orientations
three sets of facets will be the one with the minimum
spacings and it has been found that on each crystal
predicted. surfaces
all in the region BZD
The orientations
and not at Z as
of the original
general
and gable ends for three such crystals
total surface energy.
showing
Since the low index surfaces are
at minima in the y-plot they may be considered with respect
plotted in Fig. 5.
Frc:. 6. Interferogram
are
to rotations.
simultaneous primary faceting in sir after 10 days. B, (111) facet; Q, “gable end”.
A minimization
A,
(100) facet;
fixed
of total
850
ACTA
energy gable
can therefore end ;
equilibrium
1
only occur by rotation
it is shown orientation
approximately
METALLURGICA,
in the appendix of
the
gable
of the
that
the
end is given
by
10, 1962
VOL.
shape of a continuation boundary
surface where it crosses a twin
and is in contact with two low index facets
(Fig. 3) and for the shape of the continuation on pyramids
found during enhanced
both these cases the surfaces become Ylll
-2 ( YG
set 8 1 +
in
steeper in the
region near the point of contact of the three surfaces.
‘?! Yc
= 2 set 4 -
surface
evaporation;
see 0 21
see3 f$ -
-
1
YG
+c sin 4 sec2 4
THERMAL ETCHING IN NITROGEN, HYDROGEN AND VACUUM
(3)
Striations
a+
where 8i, 8, and + are the angles of inclination
t,o the
oxygen-free
did not form
on specimens
heated
in
atmospheres.
The
heated
in
general surface of the( 11 l), (100) facets and gable end
“pure”
respectively
nitrogen plus 0.1 per cent hydrogen were very similar.
and where yin, yle,, and yc are the surface
If the ay/ae and 6’y/&j terms are neglected and the approximate
values ylil/yc
cos 25” are substituted with typical
= cos 34” and yi,,Jyo =
in the above equation together
values 8, = 324” and 0, = 24”, then 4 is
found to be about
loo-the
orientation
end should therefore be in the region the point Z. explained
The orientations
therefore
of the gable
BZD
and not at
of the gable ends can be
if it is assumed
surfaces are in equilibrium
that the three
simultaneously
as a unit.
It was found that on a given crystal the smaller gable ends are tilted most from the general surface, this is presumably facet.
(less than lo-’
Grain boundaries
energies.
surfaces
nitrogen
surfaces
because
occurs
equilibrium
most
rapidly
The same explanation
Fla.
between
across
the three
small areas of
would account
for the
were delineated
and both twin boundary were observed-evidence surface
energy
parts oxygen)
after a few hours
grooves and inverted grooves of a definite
with crystalline
shows a surface
heated
variation
orientation.
in nitrogen
grooves
the
is slow
were only about 0.3 ,u deep
and rolling marks had not completely diffusion
was probably
presence of impurities Evaporation
by
off. the
which are removed by oxygen.
to evaporate
Evaporation
facet (Fig. 9).
smoothed
suppressed
roughening was observed on specimens
heated and allowed mm Hg).
8
with etching in air, even after 5 days the
grain boundary Surface
of
Fig.
for 5 days,
kinetics of etching in these inert atmospheres compared
and in
exposed
But on specimens
in vacuum
(
large areas of plane heated in vacuum
8. Surface after 5 days heating in nitrogen. Shallow grain boundaries and inverted twin boundaries (T). The horizontal markings are rolling marks.
RHEAD
9. Evaporation
FIG.
and completely evaporation
enclosed
MYKURA:
AND
roughening
in a silver box
no evaporation
roughening
THERMAL
with
ETCHING
the development (Interferogram.)
to inhibit
occurred and
OF
of facets
after
SILVER
30 min
851
in v~cuurn.
degrees higher than those for 10 p.p.m. contact
angles for all concentrations
The mean
are shown
in
the surfaces were similar to those heated in nitrogen
Table 2 and the variation
and the nitrogen plus hydrogen
angle with the logarithm of oxygen partial pressure is
mixture.
plotted THERMAL WITH
Specimens atmospheres
ETCHING IN LOW OXYGEN
were heated with
parts by weight:
for periods
nominal
oxygen
of 10 days in concentrations,
10P5, 3 x 10V5, 10P4, 3 x 10-4, 10-3,
In 10 p.p.m. striated,
of oxygen
only about half the grains
considerably
striated than on the air-etched also some evaporation occurred
12.
The table
on specimens
summarizes
which
in vacuum.
more grains were unspecimens.
roughening
There was
but not as much as
The increase in the experimental
the contact
angles at low oxygen
concentrations
in the measurements
at these concentrations.
dition crystals
of the specimens; furthest
it was found
upstream
much more than those downstream, a higher concentration
the
concentrations
fringe
spacings.
The results are plotted
of the
in a unit
that
those
it is possible that
of silver vapour
unstriated, were oriented and from interferograms
surfaces for both (100)
This
in the gas flow striated
would clean off some of the adsorbed
of the continuation
and
of the surface con-
and
and (111) st,riations we found by measurement
to
error in
especially at 10 p.p.m. is due to a much wider scatter
Some 46 grains, striated
orientations
all the
were allowed
evaporate.
scatter is the result of variations
and 10-2. became
in Fig.
measurements
ATMOSPHERES CONTENT
of the cosine of the contact
downstream
oxygen.
the etched topography
At low
is complicated
by the surface roughness
caused by evaporation,
areas of smooth
were found
grains
facets
surface
formed
few
and on many
on the sides of
hillocks
and
stereographic t’riangle in Fig. 10(a) and a t’ypical area of the specimen is shown in Fig. 11. The mean contact
t,roughs where the surface was tilted by several degrees
angles were : {lOO}> 17.6’ + 2.0“;
were found on the underneath surfaces of specimens heated in low2 and 10e3 parts of oxygen, this is
these angles are appreciably air-etched specimens.
{ill},
24.9” & 2.0”;
lower than the angles for
Comparable results for an oxygen concentration of about 100 p.p.m. are shown in Fig. 10(b). At this concentration however the contact angles were several
from the general orientation.
Occasional
(1 lo} facets
possibly due to contact with Mullite. A few small areas of plane facet with orientations near the (110) pole developed on the specimens heated in 10-J parts of oxygen.
_4CTA
(a) oxygen concentration
METALLURGICA,
10e5
VOL.
10,
1962
(b) oxygen concentration
lo-’
FIG. 10. Stereographic projections showing orientations of: 0 grains which formed striations with (100) facets. n grains which formed striations with (111) facets. 0 continuation surfaces in equilibrium with (100) facets. l continuation surfaces in equilibrium with (100) facets. x unstriated grains.
FIG. 11. Typical
area of surface heated for 10 days in 1O-5 parts oxygen
It appears t,hat reducing the oxygen concentration produces a marked decrease in the contact angles. The orientations of unstriated grains were always found in the region of the stereographic triangle outside the arcs drawn at the orientations of the continuation surfaces. For concentrations where the arcs do not intersect no examples of simultaneous primary etching were found.
EVAPORATION
AND
The net loss of material
THERMAL
ETCHING
by evaporation
from the
specimens heated in air was limited by the rate of diffusion of vapour through the air in the sealed furnace tube. To find how thermal etching was affected by a faster evaporation rate specimens were heated in a steady flow of air, and as a result, a quite
RHEAD
MYKURA:
AND
THERMAL
ETCHING
OF
853
SILVER
TABLE 2. Contact angles at different oxygen concentrations
-
Nominal concentration
1.00 2.04 0.92 1.23 2.46 0.90 3.70 1.23
Oxygen Air 10-Z IO-3 3 x 10-a 10-d 3 x 10-s 10--s
x + & * * * k
10-l 0.05 0.06 0.14 0.05 0.22 0.06
x x x x x x
Contact angles 0 {Ill} striations { 100) striations (no. of crystals measured in brackets) __34.2” + 1.0” (27) 26.0” * 1.3” (12) 33.8” l 1.0” (21) 25.4’ & 1.1” (17) 27.2” + 1.6” (22) 32.0’ + 1.4” (18) 23.5” i 1.5” (17) 28.6” * 1.2” (27) 21.9” 4 1.8” (16) 29.8’ + 1.0’ (25) 20.0” * 1.7” (17) 29.4” * 1.7” (17) 21.6” k 2.0” (26) 29.2” * 1.4” (41) 17.6” * 2.0” (13) 24.9” f 2.0” (19)
Partial pressure 0, mm Hg.
Relative concentration parts 0, by weight
970 155 9.05 1.21 2.41 0.88 3.63 1.21
10-Z 10-s 1O-4 10-d 10-S IOW
x x x x
10-r IO-’ lOme 1OW
evaporation
of the general surface and that evapor-
ation from low index than the average formation
surfaces
rate.
lower
Additional
in-
on this point comes from the variation
evaporation
rate
with
time
etching as the proportion index
is appreciably
evaporation
facets
specimen
which
occurs
of surface made up of low
progressively
increases.
A
typical
was heated in air in a sealed furnace
and the weight of the specimen tervals up to 300 hr.
found
tube
at 20 hr in-
The tube had previously
used for several thousand
of
during
been
hours for heating silver so
that it may be assumed that the silver vapour near the specimen was in dynamic pressure
constant
fraction
during
equilibrium
and the vapour
the experiment.
As the
of the surface made up of visible low index
facet changed from zero at the beginning to not more
.808 -2
than 40 per cent after 300 hr the weight loss changed -I
0
I
2
from about 20 ,ug/cm2 per hr to 12 pg/cm2 per hr. Part of the change in evaporation rate may be due to an
3
increase in surface impurity concentration
FIG. 12. Variation of the cosine of the contact angles “Least with logarithm of partial pressure of oxygen. squares” straight lines.
from the interior of the specimen, mainly
to a lower evaporation
rate from low index
different form of etching was found on many crystals.
surfaces
After a few hours dots appeared on the surface, these
times more slowly
were apparently
clusions can be drawn from observations
small hillocks and had a density of about 2 x lo6 cm-2; they may be the sites of screw dislocations.
The dots became the nucleation
the formation extending
of facets which grew into striations
by
sideways (Fig. 13). Under these conditions
of fast evaporation consisted
sites for
mainly
the final structure of large pyramids
after 20 days
with exact
low
then these surfaces
frequently
spontaneous
is not howfor
changes of a flat surface under equilib-
rium conditions. The interferograms show that close to the base of the pyramids a shallow groove forms and the correct contact angles are preserved. The heights of the pyramids-sometimes greater than 10 ,u-when compared with the net weight loss from the surface, 14 mg/cm2, indicate that they are formed mainly by
con-
on specimens
higher than the surrounding
grains
by several microns. The specimens heated in a silver enclosure showed surface
which accounts
at least ten Similar
found grain surfaces, made almost entirely
Fig. 4, standing
the general surface at angles greater than the equilibwith the theory
than the average.
of smooth low index facets, similar to those shown in
negligible
ever in conflict
evaporate
heated in atmospheres of low oxygen content ; we have
index sides (Fig. 14) ; the sides were often inclined to rium contact angles given in Table l-this
by diffusion
but if it is ascribed
weight
location
losses.
The
effective
due to evaporation
changes
1O-2 ,u, while the striations were very pronounced the low index facets projected
in
were less than and
several microns above
the general surface. This is clear evidence that net evaporation is not essential for the development of striations. However the striations are more widely spaced
where net evaporation
is inhibited
and the
much higher density of striations on evaporating specimens shows that nucleation is considerably enhanced by net evaporation.
ACTA
FIG. 13. The formation
METALLURGICA,
VOL.
of facets during enhanced
10,
1962
evaporation.
After 2 days in air.
FIG. 14. Interferogram of pyramids formed by enhanced evaporation. After 20 days in air. The height of the pyramids is greater than t,he dept,h of focus of the microscopr.
RHEAD
MYKURA:
AND
THERMAL
TABLE 3. Net evaporat,ion rates of silver in various atmos-
pheres at 900°C
oxymm
changes in the partial pressure of oxygen
The variation of contact angle with oxygen pressure may be accounted
NO.18 Air Aj, Evaporation mhibited &4irFast stream
10-20
cause a relatively surface
2.53.5
et d.(3) found for the variation
1’ = 228 -
3-5
between 0.2 and 1O-4 atm.
~10,600
equation
mhibited
the coefficient
different atmospheres.
rates
are given
for
For similar specimens heated
atmosphere
there
losses of as much
quoted are typical ones.
were differences
as threefold,
in
the values
DISCUSSION
growth
of linear facets
various
mass transport
experiment of dynamic
during
account
thermal
mechanisms.
of the
etching
Comparison
for of
net evaporation.
investigations
we
surfaces
vary with oxygen
yL and continuation
average surface energy we may write: YL(P) = Y&(O) -
K,
log,0 P
(5)
Ye(P) = ye(o) -
K, log,, P*
(6)
Putting yL(o) = y,(o) y-plot
are caused
i.e. assuming that cusps in the
mostly
by differential
cos 8 = 1 -
K, - Ko l%(P)
tion and surface diffusion
justified by the experimental
ment of striations on silver. Striations do not always occur when there are finite cusps in the y-plot,
as shown for example
verted twin boundaries
by the in-
on silver heated in nitrogen.
be taken as a constant. following
This evidence is not however in conflict with the view that thermal etching is driven by a lowering of total
Kill -
surface energy. For values of yo/yO near unity the contact angles will be necessarily small and aye/at3
0.007
real value
of O-this
point
has been discussed
by
Blakely and Mykura”“. evaporation in air are comparable with the angles for conditions of net evaporation in 1O-4 parts of oxygen. This effect may be ascribed to the desorption of
calculation accuracy)
(all that is
K, -
-.-
R,
can
Ye(P)
From the slopes of the lines
values are found : K,,, -
K, = 8.3 & 1.6 K, = 6.4 h 1.4 ergs cm-2 i.e. K, K loo - K”= 0.044 -+ 0.009 ; ___= 0.034 -+
cm-2; R
K,, ---
K
Since K, m I’? and K is proportional
to r we may
conclude that about 4 per cent more oxygen atoms per unit area are adsorbed
The contact angles found for conditions of negligible
log,, P,
drawn in Fig. 12 and putting ye = 600 ergs cm-2 the ergs
ma,y be too large for equation (1) to be satisfied for any
adsorption
and neglecting the ay,Jae term in equation (1) we find :
For an order of magnitude
to the develop-
surfaces ye
pressure in the same way as the
have made indicate that both evaporation-condensacontribute
density for the par-
If it is assumed that t’he surface energies of both tJhe low index
i.e. where there is negligible
Some preliminary
is proportional
oxygen atoms, I‘, and has
lOI cm-2 (Herring(12)).
with theory should be made for conditions equilibrium
(4)
From the Gibbs adsorption
been taken to imply a constant
were as much as a quarter those in air.
a theoretical
ergs cm-2.
ticular pressure range and temperature : r = 0.95 x
The weight losses in nitrogen
Mullins’l’J) has given
P
of log,, p, x,
to the density of adsorbed
* The figure for evaporation in vacuum is for a period of 30 min and for vacuum with evaporation inhibited, 10 hr. All the other rates are mean values over 5-10 days.
weight
188 log,,
where p is the oxygen partial pressure in atmospheres
4-10
3 net evaporat’ion
Buttner
of the average surface
energy of silver at 900°C
Evaporation
in the same
greater decrease in the low index
energies as the pressure increased.
j-7
In Table
for by a relatively higher density of
adsorption sites on the low index surfaces which would
S-16
*Vacuum
affect the
changing the den-
sity of the adsorbed layer.
-18
Sitrozen I + 10-3 parts Nitrogen hydrogen *Vacuum
855
OF SILVER
surface energy without appreciably
Evaporation rata in pg/cm2 per hr
Atmosphere
ETCHING
onto low index surfaces than
onto surfaces with other orientations. If it is assumed that y&(o) = ye(o) w 1200 ergs cm-2 at a partial pressure of about 10e6 atm the 4 per cent difference between K, and K (low index) predicts for the ratio
oxygen following adsorption of silver vapour-only a small fraction of the adsorbed oxygen would need to
of surface energies at 10-l atm: yL/ys e 0.85 which is in accord with t,he observed values of the contact
be
angles.
removed-Buttner
et CZ~.(~)showed
that
large
ACTA
856
METALLURGICA,
APPENDIX
The
A surface structure similar to that shown in Fig. 6 is drawn schematically of surfaces, (ill),
on average
is a pyramid,
configuration consider energy
of
an
will be reached
for example
of the pyramid bringing
about
areas, but the inclinations
be
shown
from
-
aa, -
sin xl
(10)
XJ sin x1 + sin xz
aa,
aaloo
sin xs
01)
sin x1 + sin xs
VW-%-
pyramid.
is a minimum. changes
The
surface
of the low index facets may
in t’he y-plot.
(12)
total
of the three
in relative
be considered fixed crystallographically at sharp minima
can
when the total surface
surface energy can change by rotations surfaces
relationships
are
To find the equilibrium elementary
1962
aall1 --
of the three sets of surfaces we need only
equilibrium
Equilibrium
following
The basic
the bases of the pyramids
parallel to the general surface.
10,
geometry :
in Fig. 7. There are three sets
(100) and “gable ends”.
unit of surface topography ABCD,
VOL.
since they are
Therefore
only the
where xl = < DAC
and xs =
the projected
angles in the plane ABC of Fig. 7. On substitution these relationships condition
in equation
of
(9) the equilibrium
becomes :
“gable end” may rotate, which it may do (i) by movement of B toward
A, and C away from A (or vice
versa) ; this changes the relative areas of (111) : (100) of D along AD,
low index surfaces ; (ii) by movement
Yloo sinxz
Ylll sin Xl yG cos B,(sin x1 + sin xs)
+
yo cos e&sin xl + sin xz)
this varies t,he ratio of low index surface to gable end = 2 set 4 -
surface. The total surface energy E of the pyramid w&ten
may be
:
which * = YllPlll + Y100%00 + cos 81
YG% (8)
cos 4
cos e2
alOOand aG are the fractional areas of the projected onto ABC and 0,, (I2 and $ the
wherea,,,, facets
corresponding equilibrium
angles of inclination orientation
to ABC.
of the gable
For the
end we need
consider rotations of type (ii) ; to obtain the minimum energy
condition
we differentiate
aE
respect to I$ and put q
cos 0,
+
?100~
(8) with
= 0
aaloo
aall Ylllv
equation
aa,
+ YGF+
cos 0,
cos $
sin
aGG = 0.
+ YG+ 4 + __ cos I$ cos2 c$
sec3 I$ -
(9)
can be approximated
identical
to equation
1 aYa sin d - _ __ yc a+ toss d
to equation
(13)
(3) and is
(3) for the symmetrical
case
where x1 = xs. REFERENCES 1. R. SHCTTLEWORTH, Metallurgia 38, 125 (1948). 2. B.CHALMERS,R.KING andR. SHUTTLEWORTH, P~oc.Roy. Sot. A193. 465 (1948). 3. F. H.BuTTNER;E.R.FuN~ andH. UDIN,J. Phys.Chem. 58, 657 (1952). 4. R. KING, Thesis, London University (1955). 5. A. J. W. MOORE, Acta Met. 6, 293 (1958). 6. E. D. HOXDROS and A. J. W. MOORE, Acta Met. 8, 751 (1960). 7a. G. E. RHEAD and H. MYKURA, Acta Met. 10, 578 (1962). (b) A. J. W. MOORE, Ibid. 10,579 (1962) 8. C. S. BARRETT, Structure qf Metals (2nd Ed.) p. 41. McGraw-Hill, New York (1952). 9. H. MYKURA, Acta Met. 9, 570 (1961). 10. W. W. MULLINS, Phil. Mag. 6, 1313 (1961). 11. J. M. BLAEELY and H. MYKURA, Acta Met. 9, 595 (1961). 12. C. HERRING, Structure and Properties of Solid Su$zces (Edited by R. GOMER and C. SMITH)p. 46. Univ. of Chicago Press (1953).