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Structural changes in single crystal copper-alpha brass diffusion couples
STRUCTURAL
CHANGES
IN SINGLE CRYSTAL DIFFUSION COUPLES*t
V. Y.
DOO;
and
COPPER-ALPHA
BRASS
R. W. BALLUFFIS
Structural change8 associated with Kirkendall diffusion in single crystal copper-alpha-brass couple8 have been studied. Vapour-solid couple8 in which zinc was diffused into copper from the vapour were investigated using metallographic and X-ray techniques. The following effects were found under certain conditions in the diffusion zone: (1) dislocation formation; (2) arrangement of dislocations into subboundaries; (3) recrystallization and formation of new grains; (4) twin formation. The dislocation density and flneness of substructure were greatest at the lowest diffusion temperatures. Re-crystallization was found at low diffusion temperatures, and twin formation was always associated with recrystallization. An explanation of these phenomena is given in terms of the production and subsequent redistribution of dislocations by climb and slip mechanism8 during diffusion. MODIFICATIONS
STRUCTURALES
DANS
CRISTALLINS
LES
COUPLES
CUIVRE-LAITON
DE
DIFFUSION
MONO-
u.
Les auteurs Btudient les modifications structurales associees a la diffusion Kinkendall dans les couples monocristallins cuivre-laiton a. 118 examinent par la metallographie et les rayons X des couples vapeursolide dans lesquels le zinc diffuse de la phase vapeur dans le cuivre. 11s trouvent dans la zone de diffusion (1) Formation de dislocations (2) arrangement des et dans certaines conditions les effets suivants: dislocations en sous-joints (3) recristallisation et formation de nouveaux grains (4) formation de macles. La densite de dislocations et la finesse de la sousstructure sont les plus &levees aux temperatures de diffusion les plus basses. La recristallisation a lieu aux basses temperatures de diffusion et la formation Les auteurs donnent une explication de ces des macles est toujours assooiee 8. la recristallisation. phenomenes sur la base de la formation et de la redistribution subsequente des dislocations par les mecanismes de montee et de glissement au tours de la diffusion. STRUKTURELLE
VERANDERUNGEN
EINKRISTALLINEN
BE1
DER
DIFFUSION
IN
KUPFER-a-MESSING-PROBEN.
An einkristallinen Kupfer-a-Messingproben wurden die mit der Kirkendall-Diffusion einhergehenden strukturellen Veranderungen verfolgt. Die Proben, bei denen Zink au8 der Dampfphase in festes Kupfer eindiffundiert war, wurden mit metallographischen und Rontgen-Verfahren untersucht. In der Diffusionszone wurden unter geeigneten Bedingungen die folgenden Effekte gefunden: 1. Versetzungsentstehung, 2. Anordnung von Vesertzungen in Subkorngrenzen, 3. Rekristallisation und Kornneubildung, 4. Zwillingsbildung. Bei den niedrigsten Diffusionstemperaturen waren die Versetzungsdichte am Rekristallisation wurde bei tiefen Diffusionshiichsten und die Substruktur am feinsten ausgebildet. temperaturen gefunden, und die Zwillingsbildung trat stets gleichzeitig mit der Rekristallisation auf. Diese Erscheinungen werden auf Grund der Erzeugung und einer nachfolgenden Umordnung von Versetzungen durch Klettern und Gleitvorgange wahrend der Diffusion erklart.
1. INTRODUCTION
It is well established in Kirkendall
and X-ray
that structural
diffusion zones.(i-4)
changes occur
All
Rhines and Mehlu)
means
of these
by Balluffi
diffusion
and co-workers.(3~4~5)
systems
show
a marked
Kirkendall effect, and these effects appear to be related
found the following effects in the copper-alpha-brass
to the osmotic pressure and mass flow associated
system:
the unequal diffusion. The generation of stress in the diffusion zone has been discussed previously’6s7) and
(1) grain boundary
migration,
(2) appearance
of new grains, and (3) formation of twins. Barnesc2) reported the presence of “ghost” boundaries in the
the presence
copper-nickel
evidence
boundaries
system
and proved
by an X-ray
works in the copper-nickel,
study.
these
to be sub-
Sub-structure
silver-gold,
net-
generated
copper-alpha-
*
Received November 27, 1957. t This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18 (603) 106. Reproduction in whole or in part is permitted for any purpose by the United States Goverment. $ Dept. of Mining and Metallurgical Engineering, University of Illinois, Urbana, Illinois. METALLURGICA,
VOL.
6,
JUNE
1958
of sub-structure stresses
and that
has been takenc7)
above
the
a dislocation
428
detailed
information
about
the
yield type
occurs. The present work was undertaken
brass systems have been found by direct microscopic
ACTA
that
with
point plastic
as are
flow
to provide more
structural
changes
which occur during diffusion. The copper-alpha-brass system was chosen for study, and vapour-solid type diffusion couples, in which zinc vapour is diffused into single crystals of copper, were used. These couples have the following advantages in a study of this kind:
DO0
BALLUFFI:
AND
TABLE 1. X-ray
I
I
Diff. temp. W)
Spec.
STRUCTURAL
CHANGES
IN
Avg. sub-grain size (p)
_
Total zinc gain (%)
i
after etch _
before etch
-
Max. angular spread of X-ray reflection
X-ray meas.
I (A) Before diffusior 11
tk,P diffusion
-
880 880 880 880 880 680 680 680 680 600
-
0.57 9 ;3 169
2.3 14.1 24.4 24.3 28.0
2:: 450 450 730
;:: 12.0 12.1 5.5
(1) a strong Kirkendall investigated of initially
-
-
-
-
::
11
29
;: 63 9 13 16 15 10
58 -
effect which has been widely
exists in this system, (2) diffusion couples high crystal perfection
(3) effects can be observed surface
after
etching
technique (8) for
diffusion,
may be prepared,
directly
on the specimen
and (4) a sensitive revealing
electro-
imperfections
is
available.
Copper Bridgman
single
crystal
method
from
were
American
made
by
Smelting
Refining Co. copper at least 99.999 per cent pure. 0.114 cm thick
were placed in spectroscopically
graphite
molds
melting.
Each assembly,
vacuum
and
sealed
in Vycor
capsules
the and Slabs pure for
which was sealed under a
of 5 x 10e6 mm Hg, was traversed
zone in a horizontal
furnace,
by a hot
and single crystal
slabs
0.114 cm thick by 0.90 cm wide by 12.0 cm long were grown. prepared
Laue
Line focus
10
11’ 43’ 12’
,
:i
Poorly resolved ~360 55 75
5O 3”36’ l”32’ 2”36’ l”20 4”20’ 2’50’ 2”50’ 2’52’ 6”16’
2”: 50 12 14 14 -
is
Poorly resolved “~280 -200 -200 Poorly resolved
crystal in a graphite boat with brass chips at each end. During diffusion the temperature
variation along each
capsule was less than 3°C and the temperature controlled
to
2.2. $ficrosco&
and X-ray
examination
The surface structure and interior of each specimen
structure could be observed
on the specimen surfaces
ture treatment method’s)
of the surface.
Jacquet’s
this method
the surface is electro-polished
film is removed
by immersion
in concentrated
A, B and C, were 1.4 cm long with a
of specimens
each specimen
using
electro-polished
Before diffusion
with orthophosphoric
was
acid.
before and after diffusion
a monochromatic
method’s),
line
where the specimen
focused
focus of a bent crystal monochromator,
employed
100 cm. The beam cross-section
in Vycor
The specimens
were sealed
capsules at a pressure of 1 x 10e5 mm Hg
along with adequate zinc reservoirs of fine alpha brass
(220) or (311) reflection
HCl
of a number was obtained X-ray
is placed
Zinc was diffused into the copper single crystals from the vapour using a technique which has been previously.(4$5)
and then
electro-etched in a 0.2 per cent thiosulfate solution at 1.5 A/dms for 1 min. The resulting sulfur bearing
designated
nitric acid saw.
electro-etch In
was used to further reveal sub-structure.
and cut into specimens
slabs,
by micro-
directly after diffusion as a result of the high tempera-
for about 1 sec. An estimate of the crystal perfection
Three
was
*3”C.
scopic and X-ray methods. All sectioning was done with the acid saw. In many cases a well defined
and diffusion procedure slabs
Number of subgrains per Laue spot
before and after diffusion were investigated
2. EXPERIMENTAL
2.1. Specimen preparation
429
COUPLES
I gions near the specimen surface
aphic data for non-recrystallized and metallogr z-
Diff. time (hr)
DIFFUSION
beam
at the line
and the Cu K,
is registered at a distance
of
at the focus measured
5 x 10e3 cm by 1 cm. The total angular spread of the reflection was used as a measure of the perfection.
chips and were diffused under the conditions given in Table 1. Previous work(4t5) has shown that zinc vapour transport to the copper is rapid at diffusion tempera-
The Laue back
tures and that approximate equilibrium is maintained between the surfaces of the chips and the specimen. In the present case the chips were made from alpha
were made with a 0.051 cm dia. collimator and a 3 cm specimen to film distance. The perfection was investigated by studying the fine structure of the Laue spots, and sufficient resolution was obtained using a 0.013 cm
brass spectroscopically pure except for a faint trace of lead. Each capsule assembly contained a copper
reflection
method
with W radiation
was used for determining orientation and also for Orientation determinations studying imperfection.
dia. collimator
and a 2 cm specimen
to film distance.
ACTA
430
METALLURGICA,
VOL.
6,
1958
3. RESULTS
3.1. Structure before diffusion No structure could be detected in the single crystal slabs A, B and C by microscopic Laue spots appeared fine
structure.
focused
However,
X-ray
orientation
methods.
Also, the
quite sharp without
beam
the
detectable
monochromatic
technique
showed
line
that
the
spread of single crystal B was appreciably
larger than that of crystals A and C. These data are given
in Table
includes
broadening values.
1.
The
instrumental
angular
spread,
broadening,
was therefore
The perfection
lower
of course,
and the intrinsic than
the observed
of slab B was lower than that
of A and C, because this crystal was strained during growth (2 per cent strain). this crystal variation
The specimens made from
were used to investigate
the effect
of
of initial structure.
3.2. Structure after diffusion The structure
after
diffusion
contained
many
characteristics
typical of a metal deformed at elevated
temperature. recrystallized
grains, and twins were found in various
specimens,
Dislocations,
and their appearance
3.21. Dislocations dence
sub-grain
of a network
boundaries,
is described
and sub-boundaries. of sub-grains
below.
Direct
in the
evi-
diffusion
zone was obtained in many cases from the appearance of the
surface
after
diffusion.
The
surface
varied
FIG. 2. Specimen A3; 28 hr at 680°C; surface structure immediately after diffusion. x 1000.
according to the diffusion treatment.
At high tempera-
tures and long times a smooth shiny surface developed containing a network of grooves which clearly outlined the sub-boundary
as seen in Fig. 1. At the low tempera-
tures and shorter times the surface became rough and dull obscuring
any sub-structure
surface appeared was eliminated
(Fig. 2). This rough
to be a surface phenomenon
by smoothing
tures or long times.
which
effects at high tempera-
In several cases the sub-grain
size at the surface was measured and is given in Table 1. The measurements
were made in regions where the
average original crystal orientation
was preserved and
where
occurred.
recrystallization
certain conditions orientation
had not
new grains of completely
formed and large volumes
Under different
of the diffusion
zone were swept out by high angle grain boundaries.* The structures in these recrystallized regions were always more perfect than in the unrecrystallized material and will be described later. Further information about the sub-structure dislocation
arrangement
tained by electro-etching.
and
in the surface layers was obThis technique
appeared to
etch sub-boundaries and many comparatively isolated dislocations. The development of the sub-structure network during diffusion was clearly observed in the etched
FICA.1. Specimen Cl; 72 hr at 88O’C; surface structure immediately after diffusion. x 250.
* High angle grain boundaries are taken to be boundaries where the misorientation is of the order of 10” or higher. The mis-orientation between the sub-grains was of the order of Cl”.
DO0
AND
BALLUFFI:
STRUCTURAL
Fig. 3. Specimen C4; 730 hr at 6OO’C; electro-etched; substructure near surface produced by inward diffusion. The dislocation arrays tend to run approximately parallel to the slip plane traces (see arrows). x 250.
FIQ. 4. Specimen AS; 240 hr at 680°C; electro-etched; substructure near surface produced by inward diffusion. The sub-boundaries no longer tend to run parallel to the slip plane traces (see arrows). x 250.
CHANGES
IN
DIFFUSION
COUPLES
FIG. 5. Specimen Cl; 72 hr at 880°C; electro-etched; sub-structure near surface produced by inward diffusion. x 250
FIG. 6. Specimen C3; 168 hr at 880°C; electro-etched; sub-structure near the surface produced by inward diffusion. x 250.
432
ACTA
METALLURQICA,
structures. The sub-structure developed continuously, and in general the sub-grains became coarser and better defined the higher the diffusion temperature or the longer the diffusion time. The sub-structure at the lowest temperature (600”) is shown in Fig. 3. The dislocation walls tend to run approximately parallel to the multiple (111) slip planes, and the sub-grains between them are in most cases small and rather poorly defined. This structure appears to be strongly inherited from a distribution of dislocations which were produced on the slip planes by slip, and it contains a high dislocation density which persisted for several hundreds of hours. Typical sub-structures developed at higher temperatures are shown in Figs. 4-6. The increase in sub-grain size and the tendency towards an equi-axed shape with increased temperature and time are evident. Distributions of dislocations on (111) slip planes were found in all specimens (Fig. 9 for example). It is not certain whether all such dislocation arrangements were present at diffusion temperatures. It is possible that a slight plastic flow may have occurred during cooling to room temperature in the specimens containing concentration gradients because of the variation of the thermal contraction with composition. The possible strain generated by differences in thermal contraction is quite small and would be of the order of 0.3% for a composition difference of 30% zinc. However, slip plane dislocation arrays were observed in specimen C3 in which the concentration gradients after diffusion were extremely small. It should be emphasized that these dislocations were not introduced after cooling from the diffusion temperature, since the specimens were carefully handled and were simply electro-polished and etched. The results obtained from X-ray investigation of these structures near the surface are in close agreement with the metallographic results. Typical Laue spots showing fine structure due to the sub-structure are shown in Fig. 7. The maximum angular spread and the number of sub-grains registered per spot are given in Table 1. An approximate measurement of the sub-grain size was obtained by dividing the known irradiated area of the specimen by the number of sub-spots per Laue spot. The agreement between the sub-grain size measured metallographically and from the X-ray data is quite good. The degree of imperfection is roughly measured by the angular spread of the Laue spots and the size of the sub-grains and was greatly increased in all cases by diffusion. The structures at low temperatures appear most imperfect in agreement with the metallographic results. In these cases the Laue spots show maximum breadth,
VOL.
6,
1958
and the fine structure due to the sub-grains is poorly resolved. The angular spread of the Laue spots decreased and the sub-grain size increased with increased diffusion time at both 680” and 880°C. All of the above structures were observed near the surface where the zinc content was close to 30 per cent. A study of the variation of sub-structure with distance into the specimen was made by examining sections parallel to the diffusion. Jacquet’s etch was not effective on copper containing small amounts of zinc and, therefore, the X-ray method had to suffice for this part of the work. Detectable structural changes were only found in regions in the vicinity of the diffusion zone. The distribution of zinc was estimated from previous diffusion data.(4ps) The results for specimen A2 are given in Table 2. The angular spread of the Laue spots decreased and the size of sub-grains increased with distance into the specimen, and in the regions barely penetrated by zinc the structure approached that of the original copper. Similar results were obtained for specimen Cl which was diffused more completely (Table 2). In this case appreciable zinc reached the specimen center and the total variation of structure was smaller. However, the angular spread of the X-ray reflections still decreased and the sub-grain size increased with distance from the surface. In other specimens which were diffused
FIG. 7. Law back reflection X-ray spots (0.0127 cm dia. pinhole, 2 cm specimen-film distanoe). All the X-rayed regions are in their original orientation except (b), which is recrystallized. x 6. (a) Original copper single crystal slab C; (012) reflection. (b) Specimen C4 (730hr at 600°C); (012) reflection. (c) Specimen C4 (730 hr at 600°C); (012) reflection. (d) Original copper single crystal slab A; (111)reflection. (e) Specimen A7 (72 hr at 880°C); (111) reflection. (f) Specimen A2 (9hr at 880°C); (111) reflection. (g) Specimen Al (0.57 hr at 880°C); (111) reflection.
DO0
AND BALLUFFI: TABLE
__
-
I
of sub-grains ! Number per Laue spot
o-220 150-370 300-520 450-670 O-220 15@370 300-520 450-670
Cl
IN
DIFFUSION
433
COUPLES
L-------------_-
_____~ A2
CHANGES
2. X-ray data describing structural changes across the diffusion zone
Distance from surface (p)
Spec.
STRUCTURAL
L
I
-280 95 40 13
12 20 32 56
;; 50 24
;: 28 41
Estimated zinc content (%) (4,5)
Nax. angular spread of Laue spot
Avg. sub-grain / size f/J)
/
28.5-20.0 24.5-3.8 1 l.GO.2 0.4-O 28.526.5 27.424.3 25.4-21.2 22.8-18.5
3” 6’ 2”38’ l”37 38 l”28’ l”20’ 1” 8’ 42’
-______
to a lesser degree the pure copper interior was unaffected by the effusion. 3.22. ~ecr~~t~~~~ze~ grains and twins. In a number of cases new grains of completely different orientation formed in the matrix and occupied an appreciable volume of the diffusion zone. All of the specimens in which new grains formed are listed in Table 3 along with X-ray and metallo~aphic data. An estimate of the fractional volume of the specimen which recrystallized is given in each case. The new grains varied in size between 0.2 and 5 mm depending on diffusion temperature and time. The formation of new grains appeared to be favoured by long diffusion times at low temperatures (A5, A6, AS and C4) or by initial crystal imperfection (Bl, B2 and C2). Specimens Bl and B2 were strained (<2 per cent) during their original growth and C2 was bent to a radius of 2.5 cm and then straightened before diffusion. The new grains in specimensA5, A6, A8, C4 and B2 were platelike and formed parallel to the surface in the region penetrated by zinc. In these specimens diffusion barely reached the center, and the new grains, therefore, only formed on the diffusion zone. Specimens Bl and C2 were diffused completely through, and in these cases the new grains extended t~oughout the entire thickness, and recrystallization was complete.
The new grains are seen to be considerably more perfect than the co-existing matrix material. The angular spread of the X-ray reflections was smaller and the sub-grain size in the new grains was larger. Metallographic examination also revealed the greater perfection of the new grains, and examples of structural differences across the high angle boundaries separating new grains from the matrix material are shown in Figs. 8 and 9. The perfection of the new grains however, remained appreciably lower than that of the single crystals before diffusion. Several typical structures in new grains are shown in Figs. 10 and 11 where isolated dislocations and low angle boundaries in various stages of development are evident. These structures indicate that a repetition of the process which produced the sub-structure in the original matrix material took place in the new grains to some extent. The o~entations of a number of the new grains in specimens A6, A8, Bl and B2 were determined, and the single rotations necessary to bring their orientation into coincidence with the original material are given in Table 4. The rotation axis was any one of the following major crystallographic axes within an accuracy of 4’: [loo], [IlO], [ill], or [112]. All specimens in which new grains formed also contained many twins. Twins were found impinging
TABLE 3. X-ray and metallographio data for recrystallized regions in the diffusion zone near the specimen surfaoe ___~.___ ..___i_-.._ V /
Spec.
Diff. temp. (“C)
Diff. time (hr)
_
Avg. sub-grain size (p) -. Before etch ._
680 680 680 600 880 880 880
After etch
X-ray meas.
!
!
j
I&3x. angular spread of Laue spot
/
Number of subgrains per Laue spot
-.-_ 37 39
-
40 52
-
iif &it
ii
I
27
Poorly resolved 25 15
1” 4’ 40’
--
j
-
-r
--
Estimated fraction of material recrystallized (%) (5 (25 (25 <25 <50 100 100
434
ACTA
METALLURGICA,
VOL.
6,
1958
A6; FnG. 8. specimen 450 hr at 680°C; electro-etched; shem-s difference in structure near surface between the rex 250. ergmtallized (bottom) and unrecrystallized (top) grains.
FIG. 10. Specimen Bl; 72 hr at 880°C; electro-etched; structure in recrystallized region near surface. Arrows indicate (111) traces. x 250.
C4; 730 hr at 600°C; electro-etched; FI GI. 9.1 Specimen shlows difference in sub-structure near surface between the (right) and unrecrystallized (left) grains. The retxystallized disdocation arrays tend to run approximately parallel to the Slkp traces (see arrows). The orientation between ^._^ difference ___^^_ ^_^ these gratis corresponds to a rotation of 10” around LIUUJ X 15U
FIG. 11. Specimen A6; 450 hr at 680%; eleotro-etched; structure in recrystallized region near surface. x 250.
DO0
BALLUFFI:
AND
STRUCTURAL
CHANGES
IN
DIFFUSION
was found to be <0.7
435
COUPLES
per cent indicating
tially all of the dimensional
changes
t,hat essen-
were restricted
to the diffusion direction. 4. DIFFUSION
The observed
MODEL
structural
changes
associated with dislocations
are undoubtedly
in the diffusion zone, and
we next discuss the basic diffusion processes producing the
dislocations.
During
diffusion
inward
flow
of
zinc occurs more rapidly than outward flow of copper and the diffusion zone tends to expand. and
sinks
currents occurs
which
are most by
support likely
a vacancy
the
The sources
unequal
dislocations.
mechanism,
diffusion
If diffusion
the
dislocations
climb and generate a net number of vacancies are pumped
out by the net incoming
The vacancy
concentration
due to the pumping and the deviation driving
which
atomic
flux.
will not be in equilibrium
action of the chemical gradient, from equilibrium provides the
force for climb.
A number
cesses may act to produce
of distinct
dislocations,
pro-
and they are
discussed below. (a) Dislocation climb. Various climb processes may
FIG. 12. Specimen A5; 450 hr at 68O’C; electro-etched; unrecrystallized and recrystallized (top) grains. x 250.
increase the dislocation
density.
Geometrical details Extensive
of possible mechanisms are given elsewhere.
climb may occur at pinned segments of edge character at the specimen occasionally Fig.
found
(12).
distorted
surface or grain boundaries
In many and
deformation
isolated
within
and were
new
grains
cases the twin boundaries
curved
indicating
that
were
significant
occurred after their formation.
which operate nite number a strong
mills creating an indefi-
10ops.(~~~~~) Dislocations
screw component
prismatic climb.
as dislocation of new
may
also produce
dislocations. (i3) Entire networks
with spiral
may also
In this case, the increase in dislocation
density
will be less than in the above mechanisms. 3.3. Dimensional
changes
Previous work(4p10) has shown that any dimensional changes during diffusion
are completely
restricted
to
the diffusion direction whenever the specimen thickness is sufficiently
large.
This effect was measured in the
present specimens by the use of molybdenum on
specimen
molybdenum their
A7.
Short
of
markers
0.003 in. dia.
wires first sintered to the surface
separation
measured.
lengths
before
The expansion
and
after
diffusion
and was
in the plane of the surface
TABLE 4. Rotation angle around appropriate axis describing orientation relationship between matrix material and a new grain. (Each angle refers to an individual grain.) Rotation Axis
Specimen
[1111
,[1ool I Bl B2
24’
0
:% 30°,350
-
28” 18”
30’,24’ 22”
[112] -
0
XP 40”
(b) W+ caused by restraints on volume changes. The present experiments indicate that plastic flow by slip occurred
during diffusion
causing further dislocation
production.
The dislocation
distributions
and
example,
already
9, for
evidence
have
for this conclusion.*
in Figs. 3
been
Each volume
cited
as
element
penetrated by zinc tends to expand, and if the expansion is restrained by the non-diffused material osmotic stresses
are built
up which
will produce
slip. (6p7)
* Note added in proof: further evidence for the presence of extensive slip hss been obtained by careful examination of the surface of specimens immediately after diffusion. A dense fornmtion of slip bands of average spacing ~1-2~ was observed on three different slip systems under the optical microscope. The slip was only observed in specimens diffused for short times at low temperatures (2 hr at SOO’C). Apparently the surface steps were eliminated by smoothing effects at longer times or higher temperatures once the main wave of diffusion passed the surface region. The observed bands were not as sharply defined as are usual slip bands produced at room temperature indicating that some smoothing had occurred. This smoothing is evidence that the bands were produced during diffusion, since it was found that sharp slip bands produced by deforming brass at room temperature did not round off appreciably as a result of heating to 6OO”C,holding for 10 mm, and cooling back to room temperature.
ACTA
436
This
slip should
be particularly
The deformation
and complicated
is necessarily
controlling
the dislocation The velocity
inhomogeneous,
written(i4)
As Brink-
to
discuss
will,
In the present case it is
the
expansion
of
a small
volume
element in the diffusion zone in terms of two
parts:
(1) the expansion
due to the increase in the
number of atoms in the element as a result of unequal diffusion,
and (2) the considerably
smaller expansion
due to the increase in lattice parameter with increasing zinc.
When
penetrated
a volume
element
containing
by zinc to a composition
cent zinc, there is a total volume 33 per cent if D,,lD,, spacing accounts percent
(1) is purely
since it is caused pansion
expansion
expansion
l/6
by unequal
show
that
of about 5
dependent.
This relation
to unity:
allowed
holds when the quantity
the extremes
where b is
or parallel to the st.ress, o.
When b is
perpendicular
to c,
f=f, where
we consider
= [y
+Fln
($)I, V
Gb2/r is the restoring
tension
of the dislocation
force
pn($)I is the force tending to produce of the vacancy
climb in the presence
subsaturation
ratio N,/N,O.
is parallel to cr, f = f,, = fi --ab.
the volume
ratio
expansion
to
the
due to the lattice parameter The plastic direction.
diffusion
due to the line
curved to a radius r, and
normal to the diffusion direction is (0.7 percent, and a small amount of slip, therefore, must occur to restrain increase
energy, 7~is the
perpendicular
The
expansion
u
a condition satisfied in the present discussion.
For simplicity
while ex-
process.
v,,/v, should indicate
of the volume
(T cannot
greatly
principal
Gb2/r is equivalent
perpendicular
A considerably
be required
to
the
to restrain the larger volume
(1) to the direction
diffusion
greater amount of slip may expansion
to unity
to a stress, Gblr, which should not
Using these values the ratio v,,/ul is close when the vacancy
sub-saturation
is a few
cubic crystal we may expect the volume expansion due to climbing
in the
therefore
occur at a vacancy
when the volume
per cent.
We note that the above analysis of the effect
dislocations
of constraints.
For a face-centered
exceed
and the term
per cent (for instance, v,,/vl = 8 when N,/Nt m 0.97). An almost maximum amount of plastic flow will
absence
of diffusion.
exceed o.
b
the degree of anisotropy
expansion.
the critical shear stress (~10~ dyne/cm2)
directions
When
An estimate of the
strains due to this effect will be ~1 percent in the two direction.
some
kT
--
Bnfe
merits
climb may be
fb2/kT, where b is the Burgers vector, is small compared
phenomenon,
diffusion;
the
effect).
and
number of jogs per unit length, and B is temperature
of about
of the total
a Kirkendall
(2) will occur in any diffusion
measurements
copper is
climb
of dislocation
where f is the force, U is an activation
of 28 weight per-
= 5.4. The increase in lattice
for a volume
(or approximately
Expansion
v =
most of the slip must terminate
remain trapped.
convenient
1958
discussion.
within the crystal and many of the dislocations therefore,
6,
in intro-
multiple slip is required.
man has emphasized,
VOL.
into the diffusion
effective
ducing large numbers of dislocations zinc.
METALLURGICA,
to be closely isotropic However,
expansion is restrained a two dimensional stress is established direction
which
perpendicular
hinders
having Burgers vectors the stress direction.(6S7)
the
compressive
to the diffusion
climb
of
which produce
dislocations
expansions
in
Two cases may occur which
define the limiting amounts of plastic flow which could result from this process: (1) the stress may reach a value which is sufficient to essentially stop the climbing
of
dislocations
vector component
with
appreciable
parallel to the stress;
Burgers
(2) the stress
may have only a minor effect in restraining dislocation climb, and the expansion continue to be isotropic.
due to source action would In this case a plastic flow
process by slip is required to simultaneously squeeze the expanding material into the direction of diffusion. Case (1) corresponds to no plastic flow, and case (2) corresponds to maximum plastic flow. The actual state
of affairs
will be determined
by the factors
of stress on dislocation
sub-saturation
climb
of a few
differs from
the one
carried out by Brinkman.(6) The large amount of slip observed indicates been
that the vacancy
large
enough
near the surface
sub-saturation
to produce
must have
considerable
plastic
flow due to the divergence of the vacancy current and the stresses generated by climbing dislocations in these regions. The situation is less clear deeper within the specimen. We may expect the sub-saturation to fall off with distance from the surface, and eventually
the
slip due to the vacancy divergence will be substantially reduced. However, the amount of slip associated with a given change in lattice parameter should remain constant everywhere. The relative importance of these factors in producing slip at considerable distances within the specimens cannot be deduced from the present results. In a previous paper(‘) it was suggested that the stress levels generated by the restraints on
DO0
AND
BALLUFFI:
STRUCTURAL
CHANGES
volume expansion should depend directly upon the magnitude of the vacancy supersaturation. Such a situation would only occur if lattice parameter changes were negligible. In actual systems, such as the present, the deviations from vacancy equilibrium may become sufficiently small so that the stress and associated slip are not controlled by the deviations from vacancy equilibrium but are controlled by the volume changes induced by lattice parameter changes instead. It is of interest to attempt to visualize the rate of dislocation production in the diffusion zone as a function of time and distance as diffusion sweeps into the specimen. The rate of dislocation production in any region which results from t,he climb, and slip processes associated with the unequal diffusion should vary approximately as the divergence of the vacancy current. The rate of dislocation production associated with the slip induced by lattice parameter changes should vary approxiInately as the rate of change of chemical composition. The dislocation production, therefore, may be followed crudely by focusing attention on the regions where the vacancy divergence and the rate of change of chemical composition have maximum values. Using Darken’s relations(i5’ the vacancy divergence is given by -D
aN cu )-??! a~
;
(&[(4,
- D,,t
aN
-$
1)
= 0.
(3)
Making the change of variable A = x/l/t, and using the well known result that Nzn = f(2) it is found that equation (3) is satisfied by J. = a. Putting 2 = A into equation (2), (div J,),,, = B/t = C/a9 where A, B, and t! are constants. At the region of maximum rate of composition change
Using the same procedure equation (4) is satisfied by = S/t = T/x2, where R, S, nmx
DIFFUSION
COUPLES
437
and T are constants. The maxima of the vacancy divergence and the rate of change of composition, therefore, do not necessarily coincide. In general we may conclude that the rate of dislocation production acts as a wave with maxima which move into the specimen parabolically with time and fall off in magnitude at least as rapidly as x-a. 5. DISCUSSION
The proportion of dislocations contributed by climb and glide cannot be deduced from the present results. The structures at the lower diffusion temperatures where many of the dislocations appeared associated with the slip planes is good evidence for the presence of slip dislocations. The formation of dislocations by climb would be a more random process which could not be detected by present methods. The sub-boundary formation must be due to the grouping of these dislocations into arrays causing a decrease in potential energy. The kinetics of the subboundary formation should be similar to sub-boundary formation during high temperature deformation. In this case it is known that the simultaneous presence of stress and deformation accelerate the formation of sub- boundaries. The development of the sub- boundary network occurred continuously, and the structure became coarse and equi-axed at the higher temperatures of diffusion, Such behavior would be expected after the main wave of diffusion passed since fewer dislocations were then added and the diffusion process became almost equivalent t.o annea~ng at elevated temperatures. The continuous decrease in angular spread of the Laue spots and increase in the sub-grain size indicate a decrease in the average dislocation density caused by mutual annihilation of dislocations of opposite sign. At the lower temperatures these annealing effects were extremely slow and a high dislocation density persisted for long periods. The formation of new grains was favored by low temperatures and long diffusion periods and by low initial crystal perfection. At low temperatures a structure containing a relatively high density of dislocations was produced and maintained for long periods and eventually recrystallization occurred. The details of the nucleation process are not known, but eventually a small region of the dislocated structure must have reached a configuration with an ability to grow. Growth then occurred under the driving force of the difference in d~~loeation density (Pigs. 8 and 9). The nucleation rate in the matrix was apparently quite low since few new grains formed in each recrystallized specimen. These few nuclei which did form then grew to a comparatively large
1 (54
where Q = atomic volume, the Di are the intrinsic diffusivities, and -Nzn is the atomic fraction of zinc. The approximations involved in using Darken’s equations for a vacancy diffusion process are discussed elsewhere.“@ At the region of maximum divergence
IN
438
ACTA
METALLURGICA,
size. In the partially diffused specimens growth of the new grainscould only occur in the narrow heavily dislocated diffusion zone, and the new grains in such cases were thin and plate-like and occupied only the width of the diffusion zone. The increased tendency of the initially deformed specimens to recrystallize during diffusion can be attributed to an increased dislocation content. For instance, the initial dislocation density of crystal B which was deformed during growth was crudely estimatedo’) to be about five times that of crystals A and C using the monochromatic line focused X-ray data (Table 1). Twins were always found in the recrystallized specimens and their formation was most likely similar to the formation of the usual annealing twins in cold-worked and annealed structures. The mechanism of annealing twin formation has been discussed extensively (ls). Preferred conditions for twin formation are predicted under certain conditions at grain boundaries where twin formation can cause a decrease in interfacial energy. The present results seem in agreement with such a mechanism. Examples of twin formation at an advancing grain boundary are seen in Fig. 12.
VOL.
6, 1958 ACKNOWLEDGMENT
The writers would like to thank Prof. T. A. Read for his enthusiastic support of this research. REFERENCES
Trans.Amer. Inst. Min. 1. F. RHINES and R. F. MEHL (Metall.) Engrs. 128,185 (1938). 2. R. S. BARNES Proc. Phys. Sot. 65, 512 (1952). R. W. BALLUFFI J. Appl. Phys. 23, 1407 (1952). 5: R. W. BALLUFFI and L. L. SEI~LE J. Appl. Phys.25, 607 (1954).
5. R. RESNICK and R. W. BALLUFFI Trans.Amer. Inst. Min. (Met&Z.) Engrs.203,1004 (1955). ActaMet. 3, 140(1955). 6. J. A. BRINKMAN 7. R. W. BALLUFFI and L. L. SEICLE Acta Met. 5, 449 11%X7\. x----r
8. P. A.JACQUET ActaMet. 2, 752 (1954). 9. H. LAMBOT. L. VASSAMILLETand J. DEJACE 10. 11. 12. 13. 14. 15.
Acfa Met.
3, 150 (1955). L. C. C. DA SILVAand R. F. MEHL Tmns. Amer. Inst. Min. (Metall.) Engre. 191, 155 (1951). R. S. BARNES Acta Met. 2, 380 (1954). J. BARDEEN and C. HERRING A.S.M. Seminar on Atom Movements Cleveland. Ohio P.L.87 (19511. S.AMILINCEX,W. BONTINC~, W. DEKEYSE;, an&F. SEITZ PhiZ.Mag. 2, (Ser. 8) 355 (1957). N. F. MOTT Proc. Phys. Sot. B 34,729 (1951). L. S. DARKEN Trans. Amer. Inst. Min. (MetaZZ.)Enws. ” 175,184(1948).
16. H. FARA and R. W. BALLUFFI To be published. 17. T. S. NOGQLE and J. S. KOEHLER Acta Met. 3, 260 (1965) 18. J. E. BURKE and D. TURNBULL, Progress in Metal Physics Vol. 3. p. 282. Pergamon Press, London (1952).
CHANGES
IN SINGLE CRYSTAL DIFFUSION COUPLES*t
V. Y.
DOO;
and
COPPER-ALPHA
BRASS
R. W. BALLUFFIS
Structural change8 associated with Kirkendall diffusion in single crystal copper-alpha-brass couple8 have been studied. Vapour-solid couple8 in which zinc was diffused into copper from the vapour were investigated using metallographic and X-ray techniques. The following effects were found under certain conditions in the diffusion zone: (1) dislocation formation; (2) arrangement of dislocations into subboundaries; (3) recrystallization and formation of new grains; (4) twin formation. The dislocation density and flneness of substructure were greatest at the lowest diffusion temperatures. Re-crystallization was found at low diffusion temperatures, and twin formation was always associated with recrystallization. An explanation of these phenomena is given in terms of the production and subsequent redistribution of dislocations by climb and slip mechanism8 during diffusion. MODIFICATIONS
STRUCTURALES
DANS
CRISTALLINS
LES
COUPLES
CUIVRE-LAITON
DE
DIFFUSION
MONO-
u.
Les auteurs Btudient les modifications structurales associees a la diffusion Kinkendall dans les couples monocristallins cuivre-laiton a. 118 examinent par la metallographie et les rayons X des couples vapeursolide dans lesquels le zinc diffuse de la phase vapeur dans le cuivre. 11s trouvent dans la zone de diffusion (1) Formation de dislocations (2) arrangement des et dans certaines conditions les effets suivants: dislocations en sous-joints (3) recristallisation et formation de nouveaux grains (4) formation de macles. La densite de dislocations et la finesse de la sousstructure sont les plus &levees aux temperatures de diffusion les plus basses. La recristallisation a lieu aux basses temperatures de diffusion et la formation Les auteurs donnent une explication de ces des macles est toujours assooiee 8. la recristallisation. phenomenes sur la base de la formation et de la redistribution subsequente des dislocations par les mecanismes de montee et de glissement au tours de la diffusion. STRUKTURELLE
VERANDERUNGEN
EINKRISTALLINEN
BE1
DER
DIFFUSION
IN
KUPFER-a-MESSING-PROBEN.
An einkristallinen Kupfer-a-Messingproben wurden die mit der Kirkendall-Diffusion einhergehenden strukturellen Veranderungen verfolgt. Die Proben, bei denen Zink au8 der Dampfphase in festes Kupfer eindiffundiert war, wurden mit metallographischen und Rontgen-Verfahren untersucht. In der Diffusionszone wurden unter geeigneten Bedingungen die folgenden Effekte gefunden: 1. Versetzungsentstehung, 2. Anordnung von Vesertzungen in Subkorngrenzen, 3. Rekristallisation und Kornneubildung, 4. Zwillingsbildung. Bei den niedrigsten Diffusionstemperaturen waren die Versetzungsdichte am Rekristallisation wurde bei tiefen Diffusionshiichsten und die Substruktur am feinsten ausgebildet. temperaturen gefunden, und die Zwillingsbildung trat stets gleichzeitig mit der Rekristallisation auf. Diese Erscheinungen werden auf Grund der Erzeugung und einer nachfolgenden Umordnung von Versetzungen durch Klettern und Gleitvorgange wahrend der Diffusion erklart.
1. INTRODUCTION
It is well established in Kirkendall
and X-ray
that structural
diffusion zones.(i-4)
changes occur
All
Rhines and Mehlu)
means
of these
by Balluffi
diffusion
and co-workers.(3~4~5)
systems
show
a marked
Kirkendall effect, and these effects appear to be related
found the following effects in the copper-alpha-brass
to the osmotic pressure and mass flow associated
system:
the unequal diffusion. The generation of stress in the diffusion zone has been discussed previously’6s7) and
(1) grain boundary
migration,
(2) appearance
of new grains, and (3) formation of twins. Barnesc2) reported the presence of “ghost” boundaries in the
the presence
copper-nickel
evidence
boundaries
system
and proved
by an X-ray
works in the copper-nickel,
study.
these
to be sub-
Sub-structure
silver-gold,
net-
generated
copper-alpha-
*
Received November 27, 1957. t This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18 (603) 106. Reproduction in whole or in part is permitted for any purpose by the United States Goverment. $ Dept. of Mining and Metallurgical Engineering, University of Illinois, Urbana, Illinois. METALLURGICA,
VOL.
6,
JUNE
1958
of sub-structure stresses
and that
has been takenc7)
above
the
a dislocation
428
detailed
information
about
the
yield type
occurs. The present work was undertaken
brass systems have been found by direct microscopic
ACTA
that
with
point plastic
as are
flow
to provide more
structural
changes
which occur during diffusion. The copper-alpha-brass system was chosen for study, and vapour-solid type diffusion couples, in which zinc vapour is diffused into single crystals of copper, were used. These couples have the following advantages in a study of this kind:
DO0
BALLUFFI:
AND
TABLE 1. X-ray
I
I
Diff. temp. W)
Spec.
STRUCTURAL
CHANGES
IN
Avg. sub-grain size (p)
_
Total zinc gain (%)
i
after etch _
before etch
-
Max. angular spread of X-ray reflection
X-ray meas.
I (A) Before diffusior 11
tk,P diffusion
-
880 880 880 880 880 680 680 680 680 600
-
0.57 9 ;3 169
2.3 14.1 24.4 24.3 28.0
2:: 450 450 730
;:: 12.0 12.1 5.5
(1) a strong Kirkendall investigated of initially
-
-
-
-
::
11
29
;: 63 9 13 16 15 10
58 -
effect which has been widely
exists in this system, (2) diffusion couples high crystal perfection
(3) effects can be observed surface
after
etching
technique (8) for
diffusion,
may be prepared,
directly
on the specimen
and (4) a sensitive revealing
electro-
imperfections
is
available.
Copper Bridgman
single
crystal
method
from
were
American
made
by
Smelting
Refining Co. copper at least 99.999 per cent pure. 0.114 cm thick
were placed in spectroscopically
graphite
molds
melting.
Each assembly,
vacuum
and
sealed
in Vycor
capsules
the and Slabs pure for
which was sealed under a
of 5 x 10e6 mm Hg, was traversed
zone in a horizontal
furnace,
by a hot
and single crystal
slabs
0.114 cm thick by 0.90 cm wide by 12.0 cm long were grown. prepared
Laue
Line focus
10
11’ 43’ 12’
,
:i
Poorly resolved ~360 55 75
5O 3”36’ l”32’ 2”36’ l”20 4”20’ 2’50’ 2”50’ 2’52’ 6”16’
2”: 50 12 14 14 -
is
Poorly resolved “~280 -200 -200 Poorly resolved
crystal in a graphite boat with brass chips at each end. During diffusion the temperature
variation along each
capsule was less than 3°C and the temperature controlled
to
2.2. $ficrosco&
and X-ray
examination
The surface structure and interior of each specimen
structure could be observed
on the specimen surfaces
ture treatment method’s)
of the surface.
Jacquet’s
this method
the surface is electro-polished
film is removed
by immersion
in concentrated
A, B and C, were 1.4 cm long with a
of specimens
each specimen
using
electro-polished
Before diffusion
with orthophosphoric
was
acid.
before and after diffusion
a monochromatic
method’s),
line
where the specimen
focused
focus of a bent crystal monochromator,
employed
100 cm. The beam cross-section
in Vycor
The specimens
were sealed
capsules at a pressure of 1 x 10e5 mm Hg
along with adequate zinc reservoirs of fine alpha brass
(220) or (311) reflection
HCl
of a number was obtained X-ray
is placed
Zinc was diffused into the copper single crystals from the vapour using a technique which has been previously.(4$5)
and then
electro-etched in a 0.2 per cent thiosulfate solution at 1.5 A/dms for 1 min. The resulting sulfur bearing
designated
nitric acid saw.
electro-etch In
was used to further reveal sub-structure.
and cut into specimens
slabs,
by micro-
directly after diffusion as a result of the high tempera-
for about 1 sec. An estimate of the crystal perfection
Three
was
*3”C.
scopic and X-ray methods. All sectioning was done with the acid saw. In many cases a well defined
and diffusion procedure slabs
Number of subgrains per Laue spot
before and after diffusion were investigated
2. EXPERIMENTAL
2.1. Specimen preparation
429
COUPLES
I gions near the specimen surface
aphic data for non-recrystallized and metallogr z-
Diff. time (hr)
DIFFUSION
beam
at the line
and the Cu K,
is registered at a distance
of
at the focus measured
5 x 10e3 cm by 1 cm. The total angular spread of the reflection was used as a measure of the perfection.
chips and were diffused under the conditions given in Table 1. Previous work(4t5) has shown that zinc vapour transport to the copper is rapid at diffusion tempera-
The Laue back
tures and that approximate equilibrium is maintained between the surfaces of the chips and the specimen. In the present case the chips were made from alpha
were made with a 0.051 cm dia. collimator and a 3 cm specimen to film distance. The perfection was investigated by studying the fine structure of the Laue spots, and sufficient resolution was obtained using a 0.013 cm
brass spectroscopically pure except for a faint trace of lead. Each capsule assembly contained a copper
reflection
method
with W radiation
was used for determining orientation and also for Orientation determinations studying imperfection.
dia. collimator
and a 2 cm specimen
to film distance.
ACTA
430
METALLURGICA,
VOL.
6,
1958
3. RESULTS
3.1. Structure before diffusion No structure could be detected in the single crystal slabs A, B and C by microscopic Laue spots appeared fine
structure.
focused
However,
X-ray
orientation
methods.
Also, the
quite sharp without
beam
the
detectable
monochromatic
technique
showed
line
that
the
spread of single crystal B was appreciably
larger than that of crystals A and C. These data are given
in Table
includes
broadening values.
1.
The
instrumental
angular
spread,
broadening,
was therefore
The perfection
lower
of course,
and the intrinsic than
the observed
of slab B was lower than that
of A and C, because this crystal was strained during growth (2 per cent strain). this crystal variation
The specimens made from
were used to investigate
the effect
of
of initial structure.
3.2. Structure after diffusion The structure
after
diffusion
contained
many
characteristics
typical of a metal deformed at elevated
temperature. recrystallized
grains, and twins were found in various
specimens,
Dislocations,
and their appearance
3.21. Dislocations dence
sub-grain
of a network
boundaries,
is described
and sub-boundaries. of sub-grains
below.
Direct
in the
evi-
diffusion
zone was obtained in many cases from the appearance of the
surface
after
diffusion.
The
surface
varied
FIG. 2. Specimen A3; 28 hr at 680°C; surface structure immediately after diffusion. x 1000.
according to the diffusion treatment.
At high tempera-
tures and long times a smooth shiny surface developed containing a network of grooves which clearly outlined the sub-boundary
as seen in Fig. 1. At the low tempera-
tures and shorter times the surface became rough and dull obscuring
any sub-structure
surface appeared was eliminated
(Fig. 2). This rough
to be a surface phenomenon
by smoothing
tures or long times.
which
effects at high tempera-
In several cases the sub-grain
size at the surface was measured and is given in Table 1. The measurements
were made in regions where the
average original crystal orientation
was preserved and
where
occurred.
recrystallization
certain conditions orientation
had not
new grains of completely
formed and large volumes
Under different
of the diffusion
zone were swept out by high angle grain boundaries.* The structures in these recrystallized regions were always more perfect than in the unrecrystallized material and will be described later. Further information about the sub-structure dislocation
arrangement
tained by electro-etching.
and
in the surface layers was obThis technique
appeared to
etch sub-boundaries and many comparatively isolated dislocations. The development of the sub-structure network during diffusion was clearly observed in the etched
FICA.1. Specimen Cl; 72 hr at 88O’C; surface structure immediately after diffusion. x 250.
* High angle grain boundaries are taken to be boundaries where the misorientation is of the order of 10” or higher. The mis-orientation between the sub-grains was of the order of Cl”.
DO0
AND
BALLUFFI:
STRUCTURAL
Fig. 3. Specimen C4; 730 hr at 6OO’C; electro-etched; substructure near surface produced by inward diffusion. The dislocation arrays tend to run approximately parallel to the slip plane traces (see arrows). x 250.
FIQ. 4. Specimen AS; 240 hr at 680°C; electro-etched; substructure near surface produced by inward diffusion. The sub-boundaries no longer tend to run parallel to the slip plane traces (see arrows). x 250.
CHANGES
IN
DIFFUSION
COUPLES
FIG. 5. Specimen Cl; 72 hr at 880°C; electro-etched; sub-structure near surface produced by inward diffusion. x 250
FIG. 6. Specimen C3; 168 hr at 880°C; electro-etched; sub-structure near the surface produced by inward diffusion. x 250.
432
ACTA
METALLURQICA,
structures. The sub-structure developed continuously, and in general the sub-grains became coarser and better defined the higher the diffusion temperature or the longer the diffusion time. The sub-structure at the lowest temperature (600”) is shown in Fig. 3. The dislocation walls tend to run approximately parallel to the multiple (111) slip planes, and the sub-grains between them are in most cases small and rather poorly defined. This structure appears to be strongly inherited from a distribution of dislocations which were produced on the slip planes by slip, and it contains a high dislocation density which persisted for several hundreds of hours. Typical sub-structures developed at higher temperatures are shown in Figs. 4-6. The increase in sub-grain size and the tendency towards an equi-axed shape with increased temperature and time are evident. Distributions of dislocations on (111) slip planes were found in all specimens (Fig. 9 for example). It is not certain whether all such dislocation arrangements were present at diffusion temperatures. It is possible that a slight plastic flow may have occurred during cooling to room temperature in the specimens containing concentration gradients because of the variation of the thermal contraction with composition. The possible strain generated by differences in thermal contraction is quite small and would be of the order of 0.3% for a composition difference of 30% zinc. However, slip plane dislocation arrays were observed in specimen C3 in which the concentration gradients after diffusion were extremely small. It should be emphasized that these dislocations were not introduced after cooling from the diffusion temperature, since the specimens were carefully handled and were simply electro-polished and etched. The results obtained from X-ray investigation of these structures near the surface are in close agreement with the metallographic results. Typical Laue spots showing fine structure due to the sub-structure are shown in Fig. 7. The maximum angular spread and the number of sub-grains registered per spot are given in Table 1. An approximate measurement of the sub-grain size was obtained by dividing the known irradiated area of the specimen by the number of sub-spots per Laue spot. The agreement between the sub-grain size measured metallographically and from the X-ray data is quite good. The degree of imperfection is roughly measured by the angular spread of the Laue spots and the size of the sub-grains and was greatly increased in all cases by diffusion. The structures at low temperatures appear most imperfect in agreement with the metallographic results. In these cases the Laue spots show maximum breadth,
VOL.
6,
1958
and the fine structure due to the sub-grains is poorly resolved. The angular spread of the Laue spots decreased and the sub-grain size increased with increased diffusion time at both 680” and 880°C. All of the above structures were observed near the surface where the zinc content was close to 30 per cent. A study of the variation of sub-structure with distance into the specimen was made by examining sections parallel to the diffusion. Jacquet’s etch was not effective on copper containing small amounts of zinc and, therefore, the X-ray method had to suffice for this part of the work. Detectable structural changes were only found in regions in the vicinity of the diffusion zone. The distribution of zinc was estimated from previous diffusion data.(4ps) The results for specimen A2 are given in Table 2. The angular spread of the Laue spots decreased and the size of sub-grains increased with distance into the specimen, and in the regions barely penetrated by zinc the structure approached that of the original copper. Similar results were obtained for specimen Cl which was diffused more completely (Table 2). In this case appreciable zinc reached the specimen center and the total variation of structure was smaller. However, the angular spread of the X-ray reflections still decreased and the sub-grain size increased with distance from the surface. In other specimens which were diffused
FIG. 7. Law back reflection X-ray spots (0.0127 cm dia. pinhole, 2 cm specimen-film distanoe). All the X-rayed regions are in their original orientation except (b), which is recrystallized. x 6. (a) Original copper single crystal slab C; (012) reflection. (b) Specimen C4 (730hr at 600°C); (012) reflection. (c) Specimen C4 (730 hr at 600°C); (012) reflection. (d) Original copper single crystal slab A; (111)reflection. (e) Specimen A7 (72 hr at 880°C); (111) reflection. (f) Specimen A2 (9hr at 880°C); (111) reflection. (g) Specimen Al (0.57 hr at 880°C); (111) reflection.
DO0
AND BALLUFFI: TABLE
__
-
I
of sub-grains ! Number per Laue spot
o-220 150-370 300-520 450-670 O-220 15@370 300-520 450-670
Cl
IN
DIFFUSION
433
COUPLES
L-------------_-
_____~ A2
CHANGES
2. X-ray data describing structural changes across the diffusion zone
Distance from surface (p)
Spec.
STRUCTURAL
L
I
-280 95 40 13
12 20 32 56
;; 50 24
;: 28 41
Estimated zinc content (%) (4,5)
Nax. angular spread of Laue spot
Avg. sub-grain / size f/J)
/
28.5-20.0 24.5-3.8 1 l.GO.2 0.4-O 28.526.5 27.424.3 25.4-21.2 22.8-18.5
3” 6’ 2”38’ l”37 38 l”28’ l”20’ 1” 8’ 42’
-______
to a lesser degree the pure copper interior was unaffected by the effusion. 3.22. ~ecr~~t~~~~ze~ grains and twins. In a number of cases new grains of completely different orientation formed in the matrix and occupied an appreciable volume of the diffusion zone. All of the specimens in which new grains formed are listed in Table 3 along with X-ray and metallo~aphic data. An estimate of the fractional volume of the specimen which recrystallized is given in each case. The new grains varied in size between 0.2 and 5 mm depending on diffusion temperature and time. The formation of new grains appeared to be favoured by long diffusion times at low temperatures (A5, A6, AS and C4) or by initial crystal imperfection (Bl, B2 and C2). Specimens Bl and B2 were strained (<2 per cent) during their original growth and C2 was bent to a radius of 2.5 cm and then straightened before diffusion. The new grains in specimensA5, A6, A8, C4 and B2 were platelike and formed parallel to the surface in the region penetrated by zinc. In these specimens diffusion barely reached the center, and the new grains, therefore, only formed on the diffusion zone. Specimens Bl and C2 were diffused completely through, and in these cases the new grains extended t~oughout the entire thickness, and recrystallization was complete.
The new grains are seen to be considerably more perfect than the co-existing matrix material. The angular spread of the X-ray reflections was smaller and the sub-grain size in the new grains was larger. Metallographic examination also revealed the greater perfection of the new grains, and examples of structural differences across the high angle boundaries separating new grains from the matrix material are shown in Figs. 8 and 9. The perfection of the new grains however, remained appreciably lower than that of the single crystals before diffusion. Several typical structures in new grains are shown in Figs. 10 and 11 where isolated dislocations and low angle boundaries in various stages of development are evident. These structures indicate that a repetition of the process which produced the sub-structure in the original matrix material took place in the new grains to some extent. The o~entations of a number of the new grains in specimens A6, A8, Bl and B2 were determined, and the single rotations necessary to bring their orientation into coincidence with the original material are given in Table 4. The rotation axis was any one of the following major crystallographic axes within an accuracy of 4’: [loo], [IlO], [ill], or [112]. All specimens in which new grains formed also contained many twins. Twins were found impinging
TABLE 3. X-ray and metallographio data for recrystallized regions in the diffusion zone near the specimen surfaoe ___~.___ ..___i_-.._ V /
Spec.
Diff. temp. (“C)
Diff. time (hr)
_
Avg. sub-grain size (p) -. Before etch ._
680 680 680 600 880 880 880
After etch
X-ray meas.
!
!
j
I&3x. angular spread of Laue spot
/
Number of subgrains per Laue spot
-.-_ 37 39
-
40 52
-
iif &it
ii
I
27
Poorly resolved 25 15
1” 4’ 40’
--
j
-
-r
--
Estimated fraction of material recrystallized (%) (5 (25 (25 <25 <50 100 100
434
ACTA
METALLURGICA,
VOL.
6,
1958
A6; FnG. 8. specimen 450 hr at 680°C; electro-etched; shem-s difference in structure near surface between the rex 250. ergmtallized (bottom) and unrecrystallized (top) grains.
FIG. 10. Specimen Bl; 72 hr at 880°C; electro-etched; structure in recrystallized region near surface. Arrows indicate (111) traces. x 250.
C4; 730 hr at 600°C; electro-etched; FI GI. 9.1 Specimen shlows difference in sub-structure near surface between the (right) and unrecrystallized (left) grains. The retxystallized disdocation arrays tend to run approximately parallel to the Slkp traces (see arrows). The orientation between ^._^ difference ___^^_ ^_^ these gratis corresponds to a rotation of 10” around LIUUJ X 15U
FIG. 11. Specimen A6; 450 hr at 680%; eleotro-etched; structure in recrystallized region near surface. x 250.
DO0
BALLUFFI:
AND
STRUCTURAL
CHANGES
IN
DIFFUSION
was found to be <0.7
435
COUPLES
per cent indicating
tially all of the dimensional
changes
t,hat essen-
were restricted
to the diffusion direction. 4. DIFFUSION
The observed
MODEL
structural
changes
associated with dislocations
are undoubtedly
in the diffusion zone, and
we next discuss the basic diffusion processes producing the
dislocations.
During
diffusion
inward
flow
of
zinc occurs more rapidly than outward flow of copper and the diffusion zone tends to expand. and
sinks
currents occurs
which
are most by
support likely
a vacancy
the
The sources
unequal
dislocations.
mechanism,
diffusion
If diffusion
the
dislocations
climb and generate a net number of vacancies are pumped
out by the net incoming
The vacancy
concentration
due to the pumping and the deviation driving
which
atomic
flux.
will not be in equilibrium
action of the chemical gradient, from equilibrium provides the
force for climb.
A number
cesses may act to produce
of distinct
dislocations,
pro-
and they are
discussed below. (a) Dislocation climb. Various climb processes may
FIG. 12. Specimen A5; 450 hr at 68O’C; electro-etched; unrecrystallized and recrystallized (top) grains. x 250.
increase the dislocation
density.
Geometrical details Extensive
of possible mechanisms are given elsewhere.
climb may occur at pinned segments of edge character at the specimen occasionally Fig.
found
(12).
distorted
surface or grain boundaries
In many and
deformation
isolated
within
and were
new
grains
cases the twin boundaries
curved
indicating
that
were
significant
occurred after their formation.
which operate nite number a strong
mills creating an indefi-
10ops.(~~~~~) Dislocations
screw component
prismatic climb.
as dislocation of new
may
also produce
dislocations. (i3) Entire networks
with spiral
may also
In this case, the increase in dislocation
density
will be less than in the above mechanisms. 3.3. Dimensional
changes
Previous work(4p10) has shown that any dimensional changes during diffusion
are completely
restricted
to
the diffusion direction whenever the specimen thickness is sufficiently
large.
This effect was measured in the
present specimens by the use of molybdenum on
specimen
molybdenum their
A7.
Short
of
markers
0.003 in. dia.
wires first sintered to the surface
separation
measured.
lengths
before
The expansion
and
after
diffusion
and was
in the plane of the surface
TABLE 4. Rotation angle around appropriate axis describing orientation relationship between matrix material and a new grain. (Each angle refers to an individual grain.) Rotation Axis
Specimen
[1111
,[1ool I Bl B2
24’
0
:% 30°,350
-
28” 18”
30’,24’ 22”
[112] -
0
XP 40”
(b) W+ caused by restraints on volume changes. The present experiments indicate that plastic flow by slip occurred
during diffusion
causing further dislocation
production.
The dislocation
distributions
and
example,
already
9, for
evidence
have
for this conclusion.*
in Figs. 3
been
Each volume
cited
as
element
penetrated by zinc tends to expand, and if the expansion is restrained by the non-diffused material osmotic stresses
are built
up which
will produce
slip. (6p7)
* Note added in proof: further evidence for the presence of extensive slip hss been obtained by careful examination of the surface of specimens immediately after diffusion. A dense fornmtion of slip bands of average spacing ~1-2~ was observed on three different slip systems under the optical microscope. The slip was only observed in specimens diffused for short times at low temperatures (2 hr at SOO’C). Apparently the surface steps were eliminated by smoothing effects at longer times or higher temperatures once the main wave of diffusion passed the surface region. The observed bands were not as sharply defined as are usual slip bands produced at room temperature indicating that some smoothing had occurred. This smoothing is evidence that the bands were produced during diffusion, since it was found that sharp slip bands produced by deforming brass at room temperature did not round off appreciably as a result of heating to 6OO”C,holding for 10 mm, and cooling back to room temperature.
ACTA
436
This
slip should
be particularly
The deformation
and complicated
is necessarily
controlling
the dislocation The velocity
inhomogeneous,
written(i4)
As Brink-
to
discuss
will,
In the present case it is
the
expansion
of
a small
volume
element in the diffusion zone in terms of two
parts:
(1) the expansion
due to the increase in the
number of atoms in the element as a result of unequal diffusion,
and (2) the considerably
smaller expansion
due to the increase in lattice parameter with increasing zinc.
When
penetrated
a volume
element
containing
by zinc to a composition
cent zinc, there is a total volume 33 per cent if D,,lD,, spacing accounts percent
(1) is purely
since it is caused pansion
expansion
expansion
l/6
by unequal
show
that
of about 5
dependent.
This relation
to unity:
allowed
holds when the quantity
the extremes
where b is
or parallel to the st.ress, o.
When b is
perpendicular
to c,
f=f, where
we consider
= [y
+Fln
($)I, V
Gb2/r is the restoring
tension
of the dislocation
force
pn($)I is the force tending to produce of the vacancy
climb in the presence
subsaturation
ratio N,/N,O.
is parallel to cr, f = f,, = fi --ab.
the volume
ratio
expansion
to
the
due to the lattice parameter The plastic direction.
diffusion
due to the line
curved to a radius r, and
normal to the diffusion direction is (0.7 percent, and a small amount of slip, therefore, must occur to restrain increase
energy, 7~is the
perpendicular
The
expansion
u
a condition satisfied in the present discussion.
For simplicity
while ex-
process.
v,,/v, should indicate
of the volume
(T cannot
greatly
principal
Gb2/r is equivalent
perpendicular
A considerably
be required
to
the
to restrain the larger volume
(1) to the direction
diffusion
greater amount of slip may expansion
to unity
to a stress, Gblr, which should not
Using these values the ratio v,,/ul is close when the vacancy
sub-saturation
is a few
cubic crystal we may expect the volume expansion due to climbing
in the
therefore
occur at a vacancy
when the volume
per cent.
We note that the above analysis of the effect
dislocations
of constraints.
For a face-centered
exceed
and the term
per cent (for instance, v,,/vl = 8 when N,/Nt m 0.97). An almost maximum amount of plastic flow will
absence
of diffusion.
exceed o.
b
the degree of anisotropy
expansion.
the critical shear stress (~10~ dyne/cm2)
directions
When
An estimate of the
strains due to this effect will be ~1 percent in the two direction.
some
kT
--
Bnfe
merits
climb may be
fb2/kT, where b is the Burgers vector, is small compared
phenomenon,
diffusion;
the
effect).
and
number of jogs per unit length, and B is temperature
of about
of the total
a Kirkendall
(2) will occur in any diffusion
measurements
copper is
climb
of dislocation
where f is the force, U is an activation
of 28 weight per-
= 5.4. The increase in lattice
for a volume
(or approximately
Expansion
v =
most of the slip must terminate
remain trapped.
convenient
1958
discussion.
within the crystal and many of the dislocations therefore,
6,
in intro-
multiple slip is required.
man has emphasized,
VOL.
into the diffusion
effective
ducing large numbers of dislocations zinc.
METALLURGICA,
to be closely isotropic However,
expansion is restrained a two dimensional stress is established direction
which
perpendicular
hinders
having Burgers vectors the stress direction.(6S7)
the
compressive
to the diffusion
climb
of
which produce
dislocations
expansions
in
Two cases may occur which
define the limiting amounts of plastic flow which could result from this process: (1) the stress may reach a value which is sufficient to essentially stop the climbing
of
dislocations
vector component
with
appreciable
parallel to the stress;
Burgers
(2) the stress
may have only a minor effect in restraining dislocation climb, and the expansion continue to be isotropic.
due to source action would In this case a plastic flow
process by slip is required to simultaneously squeeze the expanding material into the direction of diffusion. Case (1) corresponds to no plastic flow, and case (2) corresponds to maximum plastic flow. The actual state
of affairs
will be determined
by the factors
of stress on dislocation
sub-saturation
climb
of a few
differs from
the one
carried out by Brinkman.(6) The large amount of slip observed indicates been
that the vacancy
large
enough
near the surface
sub-saturation
to produce
must have
considerable
plastic
flow due to the divergence of the vacancy current and the stresses generated by climbing dislocations in these regions. The situation is less clear deeper within the specimen. We may expect the sub-saturation to fall off with distance from the surface, and eventually
the
slip due to the vacancy divergence will be substantially reduced. However, the amount of slip associated with a given change in lattice parameter should remain constant everywhere. The relative importance of these factors in producing slip at considerable distances within the specimens cannot be deduced from the present results. In a previous paper(‘) it was suggested that the stress levels generated by the restraints on
DO0
AND
BALLUFFI:
STRUCTURAL
CHANGES
volume expansion should depend directly upon the magnitude of the vacancy supersaturation. Such a situation would only occur if lattice parameter changes were negligible. In actual systems, such as the present, the deviations from vacancy equilibrium may become sufficiently small so that the stress and associated slip are not controlled by the deviations from vacancy equilibrium but are controlled by the volume changes induced by lattice parameter changes instead. It is of interest to attempt to visualize the rate of dislocation production in the diffusion zone as a function of time and distance as diffusion sweeps into the specimen. The rate of dislocation production in any region which results from t,he climb, and slip processes associated with the unequal diffusion should vary approximately as the divergence of the vacancy current. The rate of dislocation production associated with the slip induced by lattice parameter changes should vary approxiInately as the rate of change of chemical composition. The dislocation production, therefore, may be followed crudely by focusing attention on the regions where the vacancy divergence and the rate of change of chemical composition have maximum values. Using Darken’s relations(i5’ the vacancy divergence is given by -D
aN cu )-??! a~
;
(&[(4,
- D,,t
aN
-$
1)
= 0.
(3)
Making the change of variable A = x/l/t, and using the well known result that Nzn = f(2) it is found that equation (3) is satisfied by J. = a. Putting 2 = A into equation (2), (div J,),,, = B/t = C/a9 where A, B, and t! are constants. At the region of maximum rate of composition change
Using the same procedure equation (4) is satisfied by = S/t = T/x2, where R, S, nmx
DIFFUSION
COUPLES
437
and T are constants. The maxima of the vacancy divergence and the rate of change of composition, therefore, do not necessarily coincide. In general we may conclude that the rate of dislocation production acts as a wave with maxima which move into the specimen parabolically with time and fall off in magnitude at least as rapidly as x-a. 5. DISCUSSION
The proportion of dislocations contributed by climb and glide cannot be deduced from the present results. The structures at the lower diffusion temperatures where many of the dislocations appeared associated with the slip planes is good evidence for the presence of slip dislocations. The formation of dislocations by climb would be a more random process which could not be detected by present methods. The sub-boundary formation must be due to the grouping of these dislocations into arrays causing a decrease in potential energy. The kinetics of the subboundary formation should be similar to sub-boundary formation during high temperature deformation. In this case it is known that the simultaneous presence of stress and deformation accelerate the formation of sub- boundaries. The development of the sub- boundary network occurred continuously, and the structure became coarse and equi-axed at the higher temperatures of diffusion, Such behavior would be expected after the main wave of diffusion passed since fewer dislocations were then added and the diffusion process became almost equivalent t.o annea~ng at elevated temperatures. The continuous decrease in angular spread of the Laue spots and increase in the sub-grain size indicate a decrease in the average dislocation density caused by mutual annihilation of dislocations of opposite sign. At the lower temperatures these annealing effects were extremely slow and a high dislocation density persisted for long periods. The formation of new grains was favored by low temperatures and long diffusion periods and by low initial crystal perfection. At low temperatures a structure containing a relatively high density of dislocations was produced and maintained for long periods and eventually recrystallization occurred. The details of the nucleation process are not known, but eventually a small region of the dislocated structure must have reached a configuration with an ability to grow. Growth then occurred under the driving force of the difference in d~~loeation density (Pigs. 8 and 9). The nucleation rate in the matrix was apparently quite low since few new grains formed in each recrystallized specimen. These few nuclei which did form then grew to a comparatively large
1 (54
where Q = atomic volume, the Di are the intrinsic diffusivities, and -Nzn is the atomic fraction of zinc. The approximations involved in using Darken’s equations for a vacancy diffusion process are discussed elsewhere.“@ At the region of maximum divergence
IN
438
ACTA
METALLURGICA,
size. In the partially diffused specimens growth of the new grainscould only occur in the narrow heavily dislocated diffusion zone, and the new grains in such cases were thin and plate-like and occupied only the width of the diffusion zone. The increased tendency of the initially deformed specimens to recrystallize during diffusion can be attributed to an increased dislocation content. For instance, the initial dislocation density of crystal B which was deformed during growth was crudely estimatedo’) to be about five times that of crystals A and C using the monochromatic line focused X-ray data (Table 1). Twins were always found in the recrystallized specimens and their formation was most likely similar to the formation of the usual annealing twins in cold-worked and annealed structures. The mechanism of annealing twin formation has been discussed extensively (ls). Preferred conditions for twin formation are predicted under certain conditions at grain boundaries where twin formation can cause a decrease in interfacial energy. The present results seem in agreement with such a mechanism. Examples of twin formation at an advancing grain boundary are seen in Fig. 12.
VOL.
6, 1958 ACKNOWLEDGMENT
The writers would like to thank Prof. T. A. Read for his enthusiastic support of this research. REFERENCES
Trans.Amer. Inst. Min. 1. F. RHINES and R. F. MEHL (Metall.) Engrs. 128,185 (1938). 2. R. S. BARNES Proc. Phys. Sot. 65, 512 (1952). R. W. BALLUFFI J. Appl. Phys. 23, 1407 (1952). 5: R. W. BALLUFFI and L. L. SEI~LE J. Appl. Phys.25, 607 (1954).
5. R. RESNICK and R. W. BALLUFFI Trans.Amer. Inst. Min. (Met&Z.) Engrs.203,1004 (1955). ActaMet. 3, 140(1955). 6. J. A. BRINKMAN 7. R. W. BALLUFFI and L. L. SEICLE Acta Met. 5, 449 11%X7\. x----r
8. P. A.JACQUET ActaMet. 2, 752 (1954). 9. H. LAMBOT. L. VASSAMILLETand J. DEJACE 10. 11. 12. 13. 14. 15.
Acfa Met.
3, 150 (1955). L. C. C. DA SILVAand R. F. MEHL Tmns. Amer. Inst. Min. (Metall.) Engre. 191, 155 (1951). R. S. BARNES Acta Met. 2, 380 (1954). J. BARDEEN and C. HERRING A.S.M. Seminar on Atom Movements Cleveland. Ohio P.L.87 (19511. S.AMILINCEX,W. BONTINC~, W. DEKEYSE;, an&F. SEITZ PhiZ.Mag. 2, (Ser. 8) 355 (1957). N. F. MOTT Proc. Phys. Sot. B 34,729 (1951). L. S. DARKEN Trans. Amer. Inst. Min. (MetaZZ.)Enws. ” 175,184(1948).
16. H. FARA and R. W. BALLUFFI To be published. 17. T. S. NOGQLE and J. S. KOEHLER Acta Met. 3, 260 (1965) 18. J. E. BURKE and D. TURNBULL, Progress in Metal Physics Vol. 3. p. 282. Pergamon Press, London (1952).