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Surface hardening by diffusion in copper single crystals
SURFACE
HARDENING L.
BY DIFFUSION
C. DE
JONGHEt
and
IN COPPER I. G.
SINGLE
CRYSTALS*
GREENFIELD%
The effect of composition changes below the surface of copper single crystals on the critical-resolvedshear stress and on dislocation configuration near the surface was studied. Various gradients with a solute concentration decreasing from the surface were developed by diffusing platinum from an electroplated layer into copper crystals. Concomitant with the resulting concentration gradients are gradients of elastic constants and lattice parameters. For all surface treatments used in these experiments the critical-resolved-shear stress was increased; the highest value was found to be 360 g/ mm2, which is about four times that measured for pure untreated crystals. The steeper the composition gradient near the surface the greater was the measured criticalresolved-shear stress. For most treatments the structural changes that accompanied the strengthening were identified as networks of accommodation dislocations in the subsurface region. The mesh size of these networks increased when the composition gradient was decreased. In evaluating the surface strengthening mechanism the effects of shear modulus, orientation of the crystal, and ordering were considered. From these experiments the prominent strengthening mechanism appears to be due to the impedance of glide dislocation movement by the accommodation-dislocation network in the subsurface layer. DURCISSEMENT
EN
SURFACE
PAR DIFFUSION DE CUIVRE
DANS
LES
MONOCRISTAUX
Les auteurs ont Btudie l’influence, sur la cisaion critique et sur la configuration des dislocations au voiainage de la surface, des variations de composition sous la surface de monocristaux de cuivre. Differents gradients (la concentration du solute diminuant it partir de la surface) ont et& obtenus en diffusant du platine vers des cristaux de cuivre, Q partir d’un support recouvert electrolytiquement d’une couche de platine. En meme temps que les gradients de concentration, il apparait des gradients pour les constantes Blastiques et les parametres du reseau. Apres tous les traitements de surface utilises dans ces experiences, la cission critique s’est trouvee augment&e; la valeur la plus elevee qui ait Bte obtenue est de 360 g/mma, c.a.d. environ quatre fois la valeur mesuree pour les cristaux purs non trait&. Plus le gradient de concentration est Bleve au voisinage de la surface, plus la cission critique mesuree est grande. Pour la plupart des traitements, les variations de structure accompagnant la consolidation ont et& indent&% comme &ant des reseaux de dislocations d’accomodation dans la region sit&e immediatement sous la surface. La taille de la maille de ces reseaux augmente quand le gradient de composition diminue. En calculant le mecanisme de durcissement en surface, les auteurs ont tenu compte de l’influence du module de cisaillement, de l’orientation du cristal et de la mise en ordre. Apres ces experiences il semble que le mecanisme predominant dans le durcissement est une consequence de l’impedance du mouvement des dislocations de glissement resultant du reseau de dislocations d’accomodation dans la couche sit&e sous la surface. OBERFLACHENVERFESTIGUNG
DURCH
DIFFUSION
IN
KUPFEREINKRISTALLEN
Der Einflulj von Anderungen der Zusammensetzung an der Oberfliiche von Kupfereinkristallen auf die kritische Schubspannung und Versetzungsanordnung nahe der Oberfliiche wurden untersucht. Verschiedene von der Oberflache aus abnehmende Fremdstoffkonzentrationen wurden durch Eindiffundieren aufelektrolysierten Platins in den Kupferkristall erzeugt. Zusammen mit den Konzentrationsgradienten treten Gradienten der elastischen Konstanten und Gitterparameter auf. Bei allen in unseren Experimenten angewandten Oberflachenbehandlungen nahm die kritische Schubspannung zu; der hiichste Wert, 360 g/mm2, war etwa das Vierfache des fur nichtbehandeltes Material gemessenen Wertes. Je griil3er der Konzentrationsgradient in der N&he der Oberflache war, desto grol3er was die gemessene kristische Schubspannung. Die die Verfestigung begleitenden Strukturanderungen wurden in den meisten Fallen als ein Netzwerk von Anpassungsversetzungen in oberfliichennahen Bereichen identifiziert. Mit abnehmendem Konzentrationsgradienten nahm die ZellgroBe dieser Netzerke zu. Bei der Untersuohung des Mechanismus der Oberfliichenverfestigung wurde der EinfluB des Schubmoduls, der Kristallorientierung und der Ordnung beriicksichtigt. Aus diesen Experimenten wurde geschlossen, da13 der wichtigste Verfestigungsmechanismus die Behinderung der Gleitversetzungen durch das Netzwerk der Anpassungsversetzungen in der oberfliichennahen Schicht ist.
1. INTRODUCTION
About thirty years ago R. Roscoe’l) surface
oxide
film caused
a marked
surface region in the deformation observed that a
The
increase
investigated
in the
* Received February 24 1969; revised April 22 1969. This work was performed by L. C. D. as a partial fulfihnent for the Degree of Masters of Applied Science at the University of Delaware. t Now at: Department of Materials Science and Engineering, University of California, Berkeley, California. 94720. $ Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, Delaware 197 11. ?
METALLURGICA,
VOL.
17, DECEMBER
1969
process of materials.
of the strengthening
in experiments
tance of environment,(2)
strength of cadmium single crystals. This work initiated other interest in the study of the role of the
ACTA
mechanisms
that involved
effects
were
the impor-
coatings,(3,4) diffusion
layer
of impurities(5s6J and removal of the surface layer.(‘) Strengthening was interpreted as being due to changes in the activation stress of the dislocation sources in in the surface,‘5ss) prevention of dislocation egress by the altered surface layer,(‘) or by a decrease in image forces that attract the dislocation to the surface.(s) Unambiguous analysis was not always possible since
1411
1412
ACTA
some aspects
of the altered
experimentally coatings,
revealed.
dislocation
METALLURGICA,
surface layers were not
In
the
networks
case
of diffusion
were found to develop
in the region of the composition gradient, even when the impurity is completely soluble in the matrix crystal. This was first observed by H. J. QueisseP) diffusion
of boron
and phosphorus
later by M. J. Marcinkowski E.
Levine,
J. Washburn
dislocation
structures
were considered of
and
and R. M. FishernO) and and G. Thornas.
developed
The
in the diffusion zone
to be accommodating
lattice spacing in the composition ical analysis
for the
in silicon,
the behavior
the misfit in
gradient. of misfit
A theoretdislocations
VOL.
Ii’,
1969
torr) at a temperature near the melting point of copper. They were then electropolished
in a 60%
acid solution,
were covered
and both
concentration lO”C/min. vacuum
each crystal
All annealing
of an
sponge
after
at a rate of
were made in a
getter.
The starting
purity of the copper was 99.999 per cent. For
the
profiles
calculations
of
after diffusion,
thickness
with
a
platinum
concentration
it is necessary
of the deposited
uring
the influence
was cooled
treatments
with titanium
the platinum deposition
investigation,
with a
gradient in the subsurface region;
this treatment
made by J. S. Vermaak In the present
phosphoric
layer of electrodeposited platinum.05) Each plated crystal was heated to develop a certain platinum
during diffusion in a binary solid solution system was and J. H. van der Merwe.n2)
faces
platinum
to know layers;
rate was determined
multiple
beam
the
hence, by meas-
interferometer
the
of plastic
thicknesses of the deposited layers after a given time. Transmission-electron-microscopical observa-
deformation of copper single crystals was studied. The subsurface region of a specimen was changed by
tions were made of the surface layers of the diffusionannealed undeformed single crystals, of annealed
from a thin electrodeposited diffusing platinum coating into a single crystal so that a platinum con-
polycrystalline
centration
prepared
altered
subsurface
layer on the initiation
gradient was developed
to 2000 A from the surface, subsurface
gradient
mentally
since
which extended up
The actual profile of the
could not be determined
present
analyzing
experi-
techniques
are
specimens.
sheet specimens and of deformed tensile
These electron microscope by electropolishing
specimens were
from
one side of the
crystal. Table
1 is a list of the thicknesses
deposited
layers of platinum,
of the electro-
the diffusion
annealing
It was found insensitive to these small changes. useful, however, to relate the diffusion treatments to
treatments and the calculated VC,,,,, for the specimens.
the maximum concentration a parameter, VC,,,, was calculated by using the method gradient. VC,,, of Stefan and Kawalkin3) for the diffusion of a thin
versal Testing Machine at a strain rate of 5.5 x 10-s
coating into an infinite matrix. experimental
diffusion
data
assumed that the diffusion
Because of a lack of
on this system, coefficient
by C. Matanod4)
( -55,700/RT)cm2
set-l].
The
[D = 0.048 exp
maximum
gradient
is expressed in this paper in units of atom fraction platinum
per micron @u-l).
For as-deposited
of
coatings
for long diffusion times, VC,,, V%l,X is infinite; approaches zero. For short diffusion anneals at low temperatures, steep concentration gradients are produced. Since a finite thickness of platinum was electrodeposited
on the surface, a diffusion
decrease in the surface concentration
per sec.
anneal leads to a of the platinum
with an Instron
Special grips, reported on elsewhere,
developed to allow uniaxial deformation specimens.
it was
is independent
of concentration and that it can be extrapolated to the temperatures of the present treatments by using the values determined
Tensile tests were performed
Uniwere
of the tensile
3. RESULTS
3.1 Xtructures The as-plated observed
electrodeposited
in the electron
the copper-crystal typical pattern
structure from
platinum
microscope
substrate
layer was
after removing
by electropolishing.
A
is shown in Fig. 1. The diffraction
this area indicates
that
the electro-
deposited layer is single crystal. The small regions of varying contrast in Fig. 1 are a result of subgrains formed during the growth of the electrodeposited layer.
Accommodation
in transmission between
dislocations
specimens
the as-deposited
are not observed
that contain
the interface
surface layer and the bulk
Copper single crystals in the form of tensile specimens 1 mm thick, with a reduced test section 30 mm
copper, although other investigators obtained evidence of dislocation arrays at the interface between two different materials.‘17-1s) If the lattice parameters for platinum and copper are considered, the misfit dislocation spacing’20’ is expected to be about
long and 3 mm wide were grown in random orientations by using a Bridgeman technique. The crystals were annealed for about 40 hr in a high vacuum ( 1O-6
30 A. Tt is possible that in the present experiments, critical diffraction conditions necessary to observe these closely spaced dislocations’21) were not satisfied.
in addition
to the decrease of VC,,,,,.
2. EXPERIMENTAL
PROCEDURE
DE JONGHE
AND GREENFIELD: TABLE
Spec.
Deposited thickness (4
903 108 903d
675 595
9Old 114 102 119
113 112 104 901 902a 120 96
BY
DIFFUSION
IN Cu
1413
5: :: 14 15 108 15 15 52 55 51 -
-
Observations Dislocation Moire network spacing spacing (A) (iu)
Profile 8 urface vGn,x cone W’) -0.96; -0.93
0
559
600 615 704 672 645 705 705 675 675 695
HARDENING
1. Summary of treatments and results
Diffusion anneal Time Temp. (min) (“C)
200 200 250 200 200 460 140 460 450 150 120 200 200 200
902
SURFACE
No.85* 0.33 0.29 0.31 0.15 0.28 0.31 0.10 0.07 0.13 0.07 1.0 0
-
70 55 100 -
>500 > 500 -55
*
0.04 0.035 0.04 0.10 0.22 not determined 0.17 0.20 0.27 0.28 0.32 -
::: 3.3 33:: 2.9 1.8 1.1 1.0 0.01 co 0
* Interpolated.
lb) Cu,Pt and CuPt.(221 As a consequence tion pattern seen.
in Fig. 2 superlattice
Moreover,
moire fringe contrast at two orienta-
tions are noted in this electron imposed Fra. 1. (a) Electrodeposited platinum layer. The copper substrate has been removed. The foil contains many defects: some of the contrast is due to slight misorientation of the subgrains. The diffraction pattern (b) indicates that the film is single crystalline. After veloped
diffusion
annealing,
in the subsurface
various layers
st’ructures
de-
of the specimens.
The typical patterns that were revealed by transmission electron microscopy are listed in Table 1 and will be discussed in the following section. For short annealing treatments, as with specimens 902 and 903, the surface concentration of platinum is high and the profile of platinum in copper contains compositions which include the ordered structures
in the diffrac-
spots are clearly
111 and 332 diffraction
that the orientation
micrograph.
Super-
patterns
indicate
of the surface normal is between
[ill] and [332]. The moire fringe contrast in area A corresponds to the operating vector [113] ; whereas in area B it corresponds
to the operating vector [OB].
The average moire fringe spacing was measured to be 70 A (0. = 2&.* The appearance of the subsurface layer of a specimen heated for 2 min at 595°C (Fig. 3) is basically the same as the previous figure, but with a smaller moire fringe spacing of 55 A (u = 24. The moire fringes were always irregular, a geometry which indicates the presence of lattice imperfections. It was * Standard deviation.
ACTA
METALLURGICA,
VOL.
17,
1969
FIG. 2. Surface layer of specimen 902. In region A the fringes are Ferpendicular to [113] and in B they are perpendicular to [022]. The diffraction pattern shows diffraction spots due to ordering and double diffraction. The fringes have a 70 A spacing.
estimated
that VC,,,
was greater
than 500 ,~-l for
the above specimens. At lower VC,,, in addition
values of 55 ,~-l, as in specimen 108,
to moire fringes, a dislocation
seen, see Fig. 4.
These dislocation
more clearly demonstrated network
is
graphs.
The diffraction
networks
in subsequent
will be
photomicro-
pattern of this area contains
superlattice spots as well as spots resulting from double diffraction. Network
dislocations
in the affected
zone of the
subsurface are separated by larger distances for the more extensive diffusion treatments which produce lower
VC,,,
Specimen
values.
An
electron
903d with the calculated
is shown in Fig. 5. The dislocations imperfect
network.
Tilting
microscope
demonstrated
distributed
throughout
micrograph VC,,,,
of
of 7.3 ,L-I
are arranged in an
of foils in the electron
that the dislocation
nets are
the diffused region at various
distances from the surface.
There is also a tendency
for some of the dislocations
to be spatially arranged parallel to each other in ribbons. An example of these ribbons can be seen in Fig. 5 at R. The mesh size, which is determined by counting the average number of mesh boundaries intersecting a unit length of lines drawn at random on the micrograph was found for FIG. 3. Specimen 903. has produced
The diffusion annealing treatment moire fringes with a spacing of 55 A.
this specimen
to be 0.035 ,u. Some ordering
Cu,Pt type was also observed
of the
in these specimens.
DE
JONGHE
&ND GREE~FI~L~:
SURFACE
HARDENING
BY
(a)
DIFFUSION
IN
Cu
(b)
Fro. 4. For VC,,,,, of about 55 p-i (specimen 108) both moire fringes (A) and a dislocation net (B) are observed. The diffraction pattern of this area contains many super-lattice reflections.
The general aspect of the subsurface of specimens of 1.0 ,u-l is shown in Fig. 6. Since with VC,,, multiple-beam diffracting conditions existed in this area all the dislocations are expected to be in contrast. The observed dislocation network (mesh size 0.28 ,u) with ribbon-lil~e arrays in this figure is quite uniform; the Burgers vector of the dislocations in the ribbons were found to be the same (42 (110)). For VC,,, of 0.01 p-l, the dislocation density is much lower in the diffusion zone. This change in density is apparent in
Fig. 7. The appearance of Kikuohi lines in the diffraction pattern indicates that the foil was rather thick so that the apparent low dislocation density cannot be interpreted as a foil thickness effect.
The treated single crystal specimens were deformed at room temperature up to 2 ‘A in tension. The orientations of tensile axis and the resolved-stress-strain curves are shown in Fig. 8. A resolved-stress-strain curve of an untreated, pure copper crystal is also included in Fig. 8 so that comparisons of the mechanical behavior can be made. In general the slope of the easy-glide region is not significantly affected by the surface treatment. Crystals 119 and 102, on the other hand, are near a symmetrical orientation where double slip occurs; consequently, easy glide is not seen. The critical-resolved-shear stress in these experiments is defined as the stress at which the linearelastic portion of the resolved-stress-strain curve terminated. Table 2 is a list of these experimental values. The strain resolution in these experiments was about 1 x 10-5. The critical-resolved-shear stress ranges from less than 100 g/mm2 for the untreated t_
TABLE
2
---
Specimen
FIQ. 5. Subsurface region for a specimen whom V&,, is 7.3 ,a-i. A distinct network aspect appears, while in certain directions dislocations tend to cluster in ribbons R.
1% 104 108 112 113 114 119 120
Critical-resolvedshear stress (g/mmz) 97 255 115 360 215 176 204 227 180
ACTA
1416
FIG. 6. VC,,,
~ETALLURGICA,
VOL.
17,
1969
is 1.0 cc-’ in this specimen (104). The dislocation ribbons are quite clear in this uniform network.
crystal to about 360 g/mm2 for specimen 108 with a gradient of about 55 ,L-l. All surface treatments produce increases in the critical-resolved-shear stress. The strengthening effect for steeper gradients than 55 p-r were not investigated at this time. IIowever, in the as-plated condition (no diffusion annealing treatment) where the gradient may be considered as being infinite, the critical-resolved-sheer stress was only 180 g/mm =. This value is considerably lower than that measured for the specimen with a gradient of 55 p-r. It is interesting to note that Ruddle and Wilsdorf(2s) observed a decrease in critical-resolved-shear stress for copper crystals with as-plated nickel or gold. Electron microscope examinations of diffusion annealed specimens deformed up to 2% have not indicated any significant change in the accommodation dislocation network structure near the surface.
concentration gradient will be produced over the range of the composition for which ordering occurs. Hence, for this condition the shape of the concentration gradient can be predicted from the phase diagram. For example, after a diffusion anneal at a given temperature T (Fig. 9a) the concentration gradient from the surface (Fig. 9b) will be relatively shallow to cr ; the slope will be steep in the ordered region to ea. Above this composition the slope will be relatively shallow again. Moire contrast can result from this type of discontinuity in a transmission-electron-microscope specimen because of the difference in the lattice parameters on each side of the thin ordered layer. For a given temperature these lattice parameters can be determined by considering the concentrations c1 and c, and by converting these values into a, and aa by using data of A. Sehneider and U. Esch.(25) The calculated and measured moire fringe spacing for two treatments agree well and are listed in Table 3.
4. DISCUSSION
4.1 lMoirdfriqe
TABLE 3. Moir6 fringe spacing (f)).
colztrm7t
S. D. Gertariken and I. Ya DekhtyaP) reported that the self-diffusion coefficients decrease diacontinuously when disordered f.c.c. alloys are ordered. Thus as a result of the diffusion annealing treatments, in the present experiments, it is expected that a steep
Temperature Platinum concentration (“C) 675 595
0% 0.34
0% 0.80
Lattice parameter (A) 3.%4 3.730
3.27 3.856
D talc (A)
D ohs (A)
69 57
70 (0 = 2) 55(cr = 2)
DE
JONGHE
AND
GREENFIELD:
SURFACE
HARDENING
BY
DIFFUSION
IN
Cu
1417
VC maxis high, the dislocation spacing was calculated to be about 30 ,!I; this spacing was too small for dislooation imaging. For longer diffusion treatments, the average dislocation separation increases and at a VC,,, of about 65 ,u-l dislocations are observed in networks (Fig. 4). Hence, 8s VC,,, increases the average mesh size decreases 8s shown in Pig. 10. Apparently between VC,, of 7 ,t-’ to 55 y-1 little change in mesh size of the network occurred. The distribution of the accommodation dislocations in a ~oneentration gradient was investigated theoretically by J. S. Vermaak and J. H. van der Merwe.(28) They proposed that for a given change in lattice parameter a given number of dislocations results and the dislocations are redistributed by the diffusioninduced stresses into several parallel subinterfaces located throughout the diffusion zone. Since in the present case, the as-deposited platinum layer is of the order of 200 8, some accommodation dislocations are likely to reach the free surface by climb@O) during the I
I
119 700 FIG. 7. For VC,,,,, = 0.01 p-l, the network size has increased, while the apparent dislocation density has decreased. Kikuchi lines in the diffraction pattern indicate that the foil is rather thick.
The moir6 fringes observed are not parallel over the entire areas in Fig. 3; moreover, examination of the patterns rcvea,la many terminating fringes. Deviations of small groups of fringes can come from slight rotational misfit of the two layers as a result of subgrain structure probably introduced upon deposition of the platinum layer on the surface; terminating fringes are indicative of the presence of dislocations, (see S. Amelinckx@@). Moire fringe contrast is not observed in specimens with concentration profiles that contained only the Cu,Pt type ordering. It is expected that, at the diffusion annealing temperatures used in these experiments, the decrease in diffusion coefficient for Cu,Pt type ordering is much smaller than the decrease for CuPt type ordering,(27,2s) and hence the eomposition profile does not contain a large discontinuity. This conclusion is also supported by the fact that moir6 fringe contrast is absent when only Cu,Pt type ordering is found in the subsurface layer, 4.2 Dislocations in the diffmion
zone
Electron microscope observations of transmission specimens revealed that the sizes of the dislocation networks in the diffusion zone were related to the calFor short diffusion treatments, where culated VC,,,.
600i
0 .02
.Oi
0 Shear
strain
Fro. 8. Resolved-shear stress as a function of shear strain. The treatments are described in Table 1. The curve for Specimen 90 is typical for pure copper. Spocimen 120 is an as-plated specimen.
ACTA
METALLURGICA,
VOL.
17,
1969
the antiphase-domain size could not be determined while an increase in critical-resolved-shear stress was observed for all gradients whether ordering was or was not detected by diffraction. Thus, it is concluded that a thin layer oforder phase in the subsurface region is not an important source of strengthening. 4.4 The effect of surface orientation
C2
cI At %
When a dislocation leaves a crystal a ledge of new surface on the crystal surface is created. The energy associated with formation of the new surface area for a unit length of dislocation is ~/sbsin 8, where ys is the surface energy and 0 is angle that the Burgers vector makes with the trace of the primary slip plane on the surface. If the egress of the dislocation were dependent upon the area of the new surface energy, the critical resolved shear stress should increase with sin 8 ; this effect has been discussed by F. R. N. Nabarro.(3b) In the present experiments there was no correlation between the initial-resolve-shear stress and sin 8.
Platinum (4
disordered --II---
4.5 Effect of elastic m~odulus and lattice parameter
ordered
on ~mechanicalproperties
Distance
from surface, (b)
x.
FIG. 9. (a) Platinum concentration profile near surface region. Annealing treatment carried out at temperature T. (b) Orderingregions in CuPt phase d&ram.
annealing treatment. The egress of dislocations are assisted, moreover, by the image forces attracting the dislocations to the surface. This reduction of the total number of dislocations in the diffusion zone is seen in the sequence of photomicro~aphs since the entire diffusion gradient with the misfit dislocations was contained in the foils viewed for VC,,,,, larger than 0.5 p-1. A tendency for dislocations to form ribbon-like networks parallel to the surface is shown in Figs. 5,6 and 7. Since the Burgers vectors of the parallel dislocations in ribbons were observed to be the same, the arrangement of dislocations is similar to that observed in subgrain formation (see J. Friedel(31)).
Cslculationst32) and experimental evidence(3s*s*) indicate that the maximum strengthening as a result of ordering should occur in a narrow range of a domain size in the vicinity of 30 A. In the present experiments
Associated with a platinum concentration profile near the surface are gradients in shear modulus and lattice parameter. A change in lattice parameter results in a change in the magnitude of the Burgers vector of a dislocation. The shear modulus and the lattice parameter for platinum-copper alloys are larger than those for pure copper. Thus, the self energy of a dislocation located in the alloy is increased when the platinum concentration is increased. On the other hand, the self energy decreases as the dislocation approaches the surface.c3i) Based on these energy considerations a calculation of the force acting on a
FIG. 10. Mesh size, L, as a function of concentration gradient Vb,,,.
DE
JONGHE
AND
GREENFIELD:
SURFACE
dislocation in the gradients with VC,,, greater than 20 p-r indicated that the hardening due to the change in shear modulus and lattice parameter was not significant. If gold is used instead of platinum as the solute, the image force should attract the dislocations more strongly to the surface since the modulus for gold is less than that for platinum. However, experiments with gold still show a hardening effect ;(36) and consequently with diffused layers the modulus and lattice parameter effects appear to have a secondary influence to surface strengthening. 4.6 The effect of the accommodatio~~~slo~utio?z. network on the glide dislocations Accommodation dislocations were observed in a limited three dimensional network near the surface. The glide dislocations initiated either in the surface layer or in the bulk of the crystal will be influenced by the presence of this dislocation network. Nabarro and Basinskit3Q in a recent, review have considered modes of strengthening ; they noted that several strengthening mechanisms can be described by the relation LYr= ,41-” where AT is the increase in critical-resolved-shear stress, A and n are parameters which depend on the model, and 1 is a characteristic distance between the obstacles to the glide dislocations. When it is assumed that the sources of the glide dislocations are in the surface layer, then I is about equal to L, the observed mesh size. Also, for this model n = -I, and A = J&/O>, where o is a constant related t,o the geometry and the nature of the pinning points. In the present case, comparison with the experiments shown that cr)is in order of 50 to 100, a value which is more than an order of magnitude above the theoretical value. Friedel(3x) considered the interaction between a pile-up of glide dislocations and a dislocation network, For this model n in the above relationship is equal to -3. The observed data is in better agreement with the Friedel model if there are three to six dislocations in the pile-up. More experiments are necessary to determine the details of the surface hardening mechanism, but on the basis of the present results a pile-up model is more appropriate. Because of solution hardening at the surface and because of the accommodation- dislocation network near the surface, surface sources are impeded. Thus, glide dislocations originating in the bulk can reach the surface only after cutting through the accommodation-dislocation network.
HARDENING
BP
DIFFUSION
IN
Cu
1419
5. CONCLUSION
1. Platinum deposits epitaxially on copper single crystals in the electropolishing process. 2. A very steep platinum concentration gradient exists during diffusion over the range of composition for which CuPt type ordering occurs. 3. For longer diffusion annealing treatments the gradient in lattice parameter induces an accommodation dislocation network arranged throughout the diffusion zone in the surface layer of the crystal. There is also a tendency for groups of dislocations to form parallel arrangements similar to low angle boundaries. 4. Correlation between the size of the network and the maximum steepness of the platinum concentration gradient was found. 5. Correlation between the critical-resolved-shear stress and the size of the network was found. The strengthening increases as the net size decreases. 6. In these experiments it was found that a gradient in elastic modulus, in solute concentration and in lattice parameter are not important cont~butors to the surface hardening effect. 7. Surface sources are impeded by the surface treatment. 8. Initiation of deformation occurs by dislocations being pushed through the network by dislocation pile-ups. ACKNOWLEDGEMENT
We are grateful to the National Science Foundation for support of this program. REFERENCES I. 2. 3. 4.
R. RO~COE, N&u?e 199,912 (1934). I. R. KRAXER and J. DEMER, Acta Me& 1, 2 (1953). C. 5. BARRETT, Acti &let. 1, 2 (1953). F. R. LIPSE~ and R. KING, P&e. Sot. PTOC. B70,608
11957f. t----r-
5. F. D. Rosr, Acta Met. 5, 348 (1957). 6. M. R. PICKUS and E. R. PARKER,J. Metals 191,792 (1951). 7. C. FENS and I. R. KRAMER, Trans. metall. Sot. A.I.M.E. 283, 1467 (1965). 8. A. K. HEAD, Phil. Msg. 44, 92 (1953). 9. H. J. QUEISSER,J. app1. Phys. 32, 1776 (1961). 10. M. J. MARCINKOWSKIand R. M. FISHER, Sixth Int. Cont. for Electron. Microscopy, Kyoto. 299 (1966). 11. E. LEVINE, J. WASHBURN and G. THOMAS,J. appl. Phy~. 38. 81 (1967). 12. J. S. V~RX&AK and J. H. V.+N DER MERWE, Phil. .&fag. 10,786(1964). 13. A. STEFAN, W&%eP Akad. W&wensch. II, 79, 161 (1879). W. KAWALXI, W&d. Ann. 52, 166 (1894) as cited, by W. JOST, ~~~~8~on in,Solid~+,L~~~s and t&am. Academic Press f 1952). 14. C. M.&No,‘Japan J. Phys. $41 (1934). 15. L. C. DE JONGEE and I. G. GREENFIELD, University of Delaware, Report No. 99. February (1969). 16. T. LYNA.N (editor) Metals Handbook, p. 1108. American Society for Metals (1948). 17. J. H. VAN DER MERWE, Proc. phys. Sot. A@, 616 (1960). 18. J. W. MATTEEWS, Phil. Mag. 8, 711 (1963). 19. U. GRADMANN, Ann. Phya. 7, 213 (1964). 20. H. BROOKS,Metal Interfaces, p. 20. American Society for Metals (1952).
1420
ACTA
METALLURGICA,
21. P. B. HIRSCH, R. B. HOWIE, R. B. NICHOLSON and D. W. PASIILEY, Electron Microscopy of Thin Cry&ala. Butterworths (1965). 22. M. HANSEN, Co~t~~~~ of B&my A&ye. ~cGpaw-Hill 119Eit3I. x----r 23. G. E. RUDDLE and H. G. F. WILSDORF, J. Metals 20, A44, No. 1 (1968). 97th AIME Annuel Meet&z. _I New York, New Ybrk. 24. S. D. GERTSRIKEN and I. YA. DEKHTYAR, Solid State Diffu8ion in Metals. AEC-tr 6313 (1960). 25. A. SCHNEIDERand U. ESCR, 2. Elektrochem. 50,290 (1944). 26. S. AZ+XIELINCKX, The Direct ob8e~t~~ of D-i&cations. Academic Press ( 1964). 27. Y. ADDA and J. PHILIBERT, La Di&.ssdon darts EesSoEides. Presses Universitaires de France (1966).
VOL.
17, 1969
28. W. L. BRA~Q and E. J. WILLIAMS, Proc. R. Sot. Al&, 699 (1934); AlSl, 540 (1935). 29. J. S. VER~XAAKand J. H. VAN DIR MERWE, Phil. M~Q. 12,453 (1965). 30. J. P. HIRTH, Sing& Crystal Films. Pergsmon Press (1964). 31. J. FIUEDEL, D&ocations. Pergamon Press (1964). 32. A. H. COTTRELL, Seminar on Relation of Properties to Microstwcture, p. 151. American Society for Metals (1955). 33. N. S. STOLOFF and R. G. DAVIES, Prog. mater. Sci. 18, 84 (1960). 34. G. W. ARDLEY, Acta Met. 3, 525 (1955). 35. F. R. N. NABARRO, A&. P&8. 1, 269 (1952). 36. F. R. N. NABARRO, 2. S. BASINSEX and D. HOLT, A&. Phys. 18, 193 (1964).
HARDENING L.
BY DIFFUSION
C. DE
JONGHEt
and
IN COPPER I. G.
SINGLE
CRYSTALS*
GREENFIELD%
The effect of composition changes below the surface of copper single crystals on the critical-resolvedshear stress and on dislocation configuration near the surface was studied. Various gradients with a solute concentration decreasing from the surface were developed by diffusing platinum from an electroplated layer into copper crystals. Concomitant with the resulting concentration gradients are gradients of elastic constants and lattice parameters. For all surface treatments used in these experiments the critical-resolved-shear stress was increased; the highest value was found to be 360 g/ mm2, which is about four times that measured for pure untreated crystals. The steeper the composition gradient near the surface the greater was the measured criticalresolved-shear stress. For most treatments the structural changes that accompanied the strengthening were identified as networks of accommodation dislocations in the subsurface region. The mesh size of these networks increased when the composition gradient was decreased. In evaluating the surface strengthening mechanism the effects of shear modulus, orientation of the crystal, and ordering were considered. From these experiments the prominent strengthening mechanism appears to be due to the impedance of glide dislocation movement by the accommodation-dislocation network in the subsurface layer. DURCISSEMENT
EN
SURFACE
PAR DIFFUSION DE CUIVRE
DANS
LES
MONOCRISTAUX
Les auteurs ont Btudie l’influence, sur la cisaion critique et sur la configuration des dislocations au voiainage de la surface, des variations de composition sous la surface de monocristaux de cuivre. Differents gradients (la concentration du solute diminuant it partir de la surface) ont et& obtenus en diffusant du platine vers des cristaux de cuivre, Q partir d’un support recouvert electrolytiquement d’une couche de platine. En meme temps que les gradients de concentration, il apparait des gradients pour les constantes Blastiques et les parametres du reseau. Apres tous les traitements de surface utilises dans ces experiences, la cission critique s’est trouvee augment&e; la valeur la plus elevee qui ait Bte obtenue est de 360 g/mma, c.a.d. environ quatre fois la valeur mesuree pour les cristaux purs non trait&. Plus le gradient de concentration est Bleve au voisinage de la surface, plus la cission critique mesuree est grande. Pour la plupart des traitements, les variations de structure accompagnant la consolidation ont et& indent&% comme &ant des reseaux de dislocations d’accomodation dans la region sit&e immediatement sous la surface. La taille de la maille de ces reseaux augmente quand le gradient de composition diminue. En calculant le mecanisme de durcissement en surface, les auteurs ont tenu compte de l’influence du module de cisaillement, de l’orientation du cristal et de la mise en ordre. Apres ces experiences il semble que le mecanisme predominant dans le durcissement est une consequence de l’impedance du mouvement des dislocations de glissement resultant du reseau de dislocations d’accomodation dans la couche sit&e sous la surface. OBERFLACHENVERFESTIGUNG
DURCH
DIFFUSION
IN
KUPFEREINKRISTALLEN
Der Einflulj von Anderungen der Zusammensetzung an der Oberfliiche von Kupfereinkristallen auf die kritische Schubspannung und Versetzungsanordnung nahe der Oberfliiche wurden untersucht. Verschiedene von der Oberflache aus abnehmende Fremdstoffkonzentrationen wurden durch Eindiffundieren aufelektrolysierten Platins in den Kupferkristall erzeugt. Zusammen mit den Konzentrationsgradienten treten Gradienten der elastischen Konstanten und Gitterparameter auf. Bei allen in unseren Experimenten angewandten Oberflachenbehandlungen nahm die kritische Schubspannung zu; der hiichste Wert, 360 g/mm2, war etwa das Vierfache des fur nichtbehandeltes Material gemessenen Wertes. Je griil3er der Konzentrationsgradient in der N&he der Oberflache war, desto grol3er was die gemessene kristische Schubspannung. Die die Verfestigung begleitenden Strukturanderungen wurden in den meisten Fallen als ein Netzwerk von Anpassungsversetzungen in oberfliichennahen Bereichen identifiziert. Mit abnehmendem Konzentrationsgradienten nahm die ZellgroBe dieser Netzerke zu. Bei der Untersuohung des Mechanismus der Oberfliichenverfestigung wurde der EinfluB des Schubmoduls, der Kristallorientierung und der Ordnung beriicksichtigt. Aus diesen Experimenten wurde geschlossen, da13 der wichtigste Verfestigungsmechanismus die Behinderung der Gleitversetzungen durch das Netzwerk der Anpassungsversetzungen in der oberfliichennahen Schicht ist.
1. INTRODUCTION
About thirty years ago R. Roscoe’l) surface
oxide
film caused
a marked
surface region in the deformation observed that a
The
increase
investigated
in the
* Received February 24 1969; revised April 22 1969. This work was performed by L. C. D. as a partial fulfihnent for the Degree of Masters of Applied Science at the University of Delaware. t Now at: Department of Materials Science and Engineering, University of California, Berkeley, California. 94720. $ Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, Delaware 197 11. ?
METALLURGICA,
VOL.
17, DECEMBER
1969
process of materials.
of the strengthening
in experiments
tance of environment,(2)
strength of cadmium single crystals. This work initiated other interest in the study of the role of the
ACTA
mechanisms
that involved
effects
were
the impor-
coatings,(3,4) diffusion
layer
of impurities(5s6J and removal of the surface layer.(‘) Strengthening was interpreted as being due to changes in the activation stress of the dislocation sources in in the surface,‘5ss) prevention of dislocation egress by the altered surface layer,(‘) or by a decrease in image forces that attract the dislocation to the surface.(s) Unambiguous analysis was not always possible since
1411
1412
ACTA
some aspects
of the altered
experimentally coatings,
revealed.
dislocation
METALLURGICA,
surface layers were not
In
the
networks
case
of diffusion
were found to develop
in the region of the composition gradient, even when the impurity is completely soluble in the matrix crystal. This was first observed by H. J. QueisseP) diffusion
of boron
and phosphorus
later by M. J. Marcinkowski E.
Levine,
J. Washburn
dislocation
structures
were considered of
and
and R. M. FishernO) and and G. Thornas.
developed
The
in the diffusion zone
to be accommodating
lattice spacing in the composition ical analysis
for the
in silicon,
the behavior
the misfit in
gradient. of misfit
A theoretdislocations
VOL.
Ii’,
1969
torr) at a temperature near the melting point of copper. They were then electropolished
in a 60%
acid solution,
were covered
and both
concentration lO”C/min. vacuum
each crystal
All annealing
of an
sponge
after
at a rate of
were made in a
getter.
The starting
purity of the copper was 99.999 per cent. For
the
profiles
calculations
of
after diffusion,
thickness
with
a
platinum
concentration
it is necessary
of the deposited
uring
the influence
was cooled
treatments
with titanium
the platinum deposition
investigation,
with a
gradient in the subsurface region;
this treatment
made by J. S. Vermaak In the present
phosphoric
layer of electrodeposited platinum.05) Each plated crystal was heated to develop a certain platinum
during diffusion in a binary solid solution system was and J. H. van der Merwe.n2)
faces
platinum
to know layers;
rate was determined
multiple
beam
the
hence, by meas-
interferometer
the
of plastic
thicknesses of the deposited layers after a given time. Transmission-electron-microscopical observa-
deformation of copper single crystals was studied. The subsurface region of a specimen was changed by
tions were made of the surface layers of the diffusionannealed undeformed single crystals, of annealed
from a thin electrodeposited diffusing platinum coating into a single crystal so that a platinum con-
polycrystalline
centration
prepared
altered
subsurface
layer on the initiation
gradient was developed
to 2000 A from the surface, subsurface
gradient
mentally
since
which extended up
The actual profile of the
could not be determined
present
analyzing
experi-
techniques
are
specimens.
sheet specimens and of deformed tensile
These electron microscope by electropolishing
specimens were
from
one side of the
crystal. Table
1 is a list of the thicknesses
deposited
layers of platinum,
of the electro-
the diffusion
annealing
It was found insensitive to these small changes. useful, however, to relate the diffusion treatments to
treatments and the calculated VC,,,,, for the specimens.
the maximum concentration a parameter, VC,,,, was calculated by using the method gradient. VC,,, of Stefan and Kawalkin3) for the diffusion of a thin
versal Testing Machine at a strain rate of 5.5 x 10-s
coating into an infinite matrix. experimental
diffusion
data
assumed that the diffusion
Because of a lack of
on this system, coefficient
by C. Matanod4)
( -55,700/RT)cm2
set-l].
The
[D = 0.048 exp
maximum
gradient
is expressed in this paper in units of atom fraction platinum
per micron @u-l).
For as-deposited
of
coatings
for long diffusion times, VC,,, V%l,X is infinite; approaches zero. For short diffusion anneals at low temperatures, steep concentration gradients are produced. Since a finite thickness of platinum was electrodeposited
on the surface, a diffusion
decrease in the surface concentration
per sec.
anneal leads to a of the platinum
with an Instron
Special grips, reported on elsewhere,
developed to allow uniaxial deformation specimens.
it was
is independent
of concentration and that it can be extrapolated to the temperatures of the present treatments by using the values determined
Tensile tests were performed
Uniwere
of the tensile
3. RESULTS
3.1 Xtructures The as-plated observed
electrodeposited
in the electron
the copper-crystal typical pattern
structure from
platinum
microscope
substrate
layer was
after removing
by electropolishing.
A
is shown in Fig. 1. The diffraction
this area indicates
that
the electro-
deposited layer is single crystal. The small regions of varying contrast in Fig. 1 are a result of subgrains formed during the growth of the electrodeposited layer.
Accommodation
in transmission between
dislocations
specimens
the as-deposited
are not observed
that contain
the interface
surface layer and the bulk
Copper single crystals in the form of tensile specimens 1 mm thick, with a reduced test section 30 mm
copper, although other investigators obtained evidence of dislocation arrays at the interface between two different materials.‘17-1s) If the lattice parameters for platinum and copper are considered, the misfit dislocation spacing’20’ is expected to be about
long and 3 mm wide were grown in random orientations by using a Bridgeman technique. The crystals were annealed for about 40 hr in a high vacuum ( 1O-6
30 A. Tt is possible that in the present experiments, critical diffraction conditions necessary to observe these closely spaced dislocations’21) were not satisfied.
in addition
to the decrease of VC,,,,,.
2. EXPERIMENTAL
PROCEDURE
DE JONGHE
AND GREENFIELD: TABLE
Spec.
Deposited thickness (4
903 108 903d
675 595
9Old 114 102 119
113 112 104 901 902a 120 96
BY
DIFFUSION
IN Cu
1413
5: :: 14 15 108 15 15 52 55 51 -
-
Observations Dislocation Moire network spacing spacing (A) (iu)
Profile 8 urface vGn,x cone W’) -0.96; -0.93
0
559
600 615 704 672 645 705 705 675 675 695
HARDENING
1. Summary of treatments and results
Diffusion anneal Time Temp. (min) (“C)
200 200 250 200 200 460 140 460 450 150 120 200 200 200
902
SURFACE
No.85* 0.33 0.29 0.31 0.15 0.28 0.31 0.10 0.07 0.13 0.07 1.0 0
-
70 55 100 -
>500 > 500 -55
*
0.04 0.035 0.04 0.10 0.22 not determined 0.17 0.20 0.27 0.28 0.32 -
::: 3.3 33:: 2.9 1.8 1.1 1.0 0.01 co 0
* Interpolated.
lb) Cu,Pt and CuPt.(221 As a consequence tion pattern seen.
in Fig. 2 superlattice
Moreover,
moire fringe contrast at two orienta-
tions are noted in this electron imposed Fra. 1. (a) Electrodeposited platinum layer. The copper substrate has been removed. The foil contains many defects: some of the contrast is due to slight misorientation of the subgrains. The diffraction pattern (b) indicates that the film is single crystalline. After veloped
diffusion
annealing,
in the subsurface
various layers
st’ructures
de-
of the specimens.
The typical patterns that were revealed by transmission electron microscopy are listed in Table 1 and will be discussed in the following section. For short annealing treatments, as with specimens 902 and 903, the surface concentration of platinum is high and the profile of platinum in copper contains compositions which include the ordered structures
in the diffrac-
spots are clearly
111 and 332 diffraction
that the orientation
micrograph.
Super-
patterns
indicate
of the surface normal is between
[ill] and [332]. The moire fringe contrast in area A corresponds to the operating vector [113] ; whereas in area B it corresponds
to the operating vector [OB].
The average moire fringe spacing was measured to be 70 A (0. = 2&.* The appearance of the subsurface layer of a specimen heated for 2 min at 595°C (Fig. 3) is basically the same as the previous figure, but with a smaller moire fringe spacing of 55 A (u = 24. The moire fringes were always irregular, a geometry which indicates the presence of lattice imperfections. It was * Standard deviation.
ACTA
METALLURGICA,
VOL.
17,
1969
FIG. 2. Surface layer of specimen 902. In region A the fringes are Ferpendicular to [113] and in B they are perpendicular to [022]. The diffraction pattern shows diffraction spots due to ordering and double diffraction. The fringes have a 70 A spacing.
estimated
that VC,,,
was greater
than 500 ,~-l for
the above specimens. At lower VC,,, in addition
values of 55 ,~-l, as in specimen 108,
to moire fringes, a dislocation
seen, see Fig. 4.
These dislocation
more clearly demonstrated network
is
graphs.
The diffraction
networks
in subsequent
will be
photomicro-
pattern of this area contains
superlattice spots as well as spots resulting from double diffraction. Network
dislocations
in the affected
zone of the
subsurface are separated by larger distances for the more extensive diffusion treatments which produce lower
VC,,,
Specimen
values.
An
electron
903d with the calculated
is shown in Fig. 5. The dislocations imperfect
network.
Tilting
microscope
demonstrated
distributed
throughout
micrograph VC,,,,
of
of 7.3 ,L-I
are arranged in an
of foils in the electron
that the dislocation
nets are
the diffused region at various
distances from the surface.
There is also a tendency
for some of the dislocations
to be spatially arranged parallel to each other in ribbons. An example of these ribbons can be seen in Fig. 5 at R. The mesh size, which is determined by counting the average number of mesh boundaries intersecting a unit length of lines drawn at random on the micrograph was found for FIG. 3. Specimen 903. has produced
The diffusion annealing treatment moire fringes with a spacing of 55 A.
this specimen
to be 0.035 ,u. Some ordering
Cu,Pt type was also observed
of the
in these specimens.
DE
JONGHE
&ND GREE~FI~L~:
SURFACE
HARDENING
BY
(a)
DIFFUSION
IN
Cu
(b)
Fro. 4. For VC,,,,, of about 55 p-i (specimen 108) both moire fringes (A) and a dislocation net (B) are observed. The diffraction pattern of this area contains many super-lattice reflections.
The general aspect of the subsurface of specimens of 1.0 ,u-l is shown in Fig. 6. Since with VC,,, multiple-beam diffracting conditions existed in this area all the dislocations are expected to be in contrast. The observed dislocation network (mesh size 0.28 ,u) with ribbon-lil~e arrays in this figure is quite uniform; the Burgers vector of the dislocations in the ribbons were found to be the same (42 (110)). For VC,,, of 0.01 p-l, the dislocation density is much lower in the diffusion zone. This change in density is apparent in
Fig. 7. The appearance of Kikuohi lines in the diffraction pattern indicates that the foil was rather thick so that the apparent low dislocation density cannot be interpreted as a foil thickness effect.
The treated single crystal specimens were deformed at room temperature up to 2 ‘A in tension. The orientations of tensile axis and the resolved-stress-strain curves are shown in Fig. 8. A resolved-stress-strain curve of an untreated, pure copper crystal is also included in Fig. 8 so that comparisons of the mechanical behavior can be made. In general the slope of the easy-glide region is not significantly affected by the surface treatment. Crystals 119 and 102, on the other hand, are near a symmetrical orientation where double slip occurs; consequently, easy glide is not seen. The critical-resolved-shear stress in these experiments is defined as the stress at which the linearelastic portion of the resolved-stress-strain curve terminated. Table 2 is a list of these experimental values. The strain resolution in these experiments was about 1 x 10-5. The critical-resolved-shear stress ranges from less than 100 g/mm2 for the untreated t_
TABLE
2
---
Specimen
FIQ. 5. Subsurface region for a specimen whom V&,, is 7.3 ,a-i. A distinct network aspect appears, while in certain directions dislocations tend to cluster in ribbons R.
1% 104 108 112 113 114 119 120
Critical-resolvedshear stress (g/mmz) 97 255 115 360 215 176 204 227 180
ACTA
1416
FIG. 6. VC,,,
~ETALLURGICA,
VOL.
17,
1969
is 1.0 cc-’ in this specimen (104). The dislocation ribbons are quite clear in this uniform network.
crystal to about 360 g/mm2 for specimen 108 with a gradient of about 55 ,L-l. All surface treatments produce increases in the critical-resolved-shear stress. The strengthening effect for steeper gradients than 55 p-r were not investigated at this time. IIowever, in the as-plated condition (no diffusion annealing treatment) where the gradient may be considered as being infinite, the critical-resolved-sheer stress was only 180 g/mm =. This value is considerably lower than that measured for the specimen with a gradient of 55 p-r. It is interesting to note that Ruddle and Wilsdorf(2s) observed a decrease in critical-resolved-shear stress for copper crystals with as-plated nickel or gold. Electron microscope examinations of diffusion annealed specimens deformed up to 2% have not indicated any significant change in the accommodation dislocation network structure near the surface.
concentration gradient will be produced over the range of the composition for which ordering occurs. Hence, for this condition the shape of the concentration gradient can be predicted from the phase diagram. For example, after a diffusion anneal at a given temperature T (Fig. 9a) the concentration gradient from the surface (Fig. 9b) will be relatively shallow to cr ; the slope will be steep in the ordered region to ea. Above this composition the slope will be relatively shallow again. Moire contrast can result from this type of discontinuity in a transmission-electron-microscope specimen because of the difference in the lattice parameters on each side of the thin ordered layer. For a given temperature these lattice parameters can be determined by considering the concentrations c1 and c, and by converting these values into a, and aa by using data of A. Sehneider and U. Esch.(25) The calculated and measured moire fringe spacing for two treatments agree well and are listed in Table 3.
4. DISCUSSION
4.1 lMoirdfriqe
TABLE 3. Moir6 fringe spacing (f)).
colztrm7t
S. D. Gertariken and I. Ya DekhtyaP) reported that the self-diffusion coefficients decrease diacontinuously when disordered f.c.c. alloys are ordered. Thus as a result of the diffusion annealing treatments, in the present experiments, it is expected that a steep
Temperature Platinum concentration (“C) 675 595
0% 0.34
0% 0.80
Lattice parameter (A) 3.%4 3.730
3.27 3.856
D talc (A)
D ohs (A)
69 57
70 (0 = 2) 55(cr = 2)
DE
JONGHE
AND
GREENFIELD:
SURFACE
HARDENING
BY
DIFFUSION
IN
Cu
1417
VC maxis high, the dislocation spacing was calculated to be about 30 ,!I; this spacing was too small for dislooation imaging. For longer diffusion treatments, the average dislocation separation increases and at a VC,,, of about 65 ,u-l dislocations are observed in networks (Fig. 4). Hence, 8s VC,,, increases the average mesh size decreases 8s shown in Pig. 10. Apparently between VC,, of 7 ,t-’ to 55 y-1 little change in mesh size of the network occurred. The distribution of the accommodation dislocations in a ~oneentration gradient was investigated theoretically by J. S. Vermaak and J. H. van der Merwe.(28) They proposed that for a given change in lattice parameter a given number of dislocations results and the dislocations are redistributed by the diffusioninduced stresses into several parallel subinterfaces located throughout the diffusion zone. Since in the present case, the as-deposited platinum layer is of the order of 200 8, some accommodation dislocations are likely to reach the free surface by climb@O) during the I
I
119 700 FIG. 7. For VC,,,,, = 0.01 p-l, the network size has increased, while the apparent dislocation density has decreased. Kikuchi lines in the diffraction pattern indicate that the foil is rather thick.
The moir6 fringes observed are not parallel over the entire areas in Fig. 3; moreover, examination of the patterns rcvea,la many terminating fringes. Deviations of small groups of fringes can come from slight rotational misfit of the two layers as a result of subgrain structure probably introduced upon deposition of the platinum layer on the surface; terminating fringes are indicative of the presence of dislocations, (see S. Amelinckx@@). Moire fringe contrast is not observed in specimens with concentration profiles that contained only the Cu,Pt type ordering. It is expected that, at the diffusion annealing temperatures used in these experiments, the decrease in diffusion coefficient for Cu,Pt type ordering is much smaller than the decrease for CuPt type ordering,(27,2s) and hence the eomposition profile does not contain a large discontinuity. This conclusion is also supported by the fact that moir6 fringe contrast is absent when only Cu,Pt type ordering is found in the subsurface layer, 4.2 Dislocations in the diffmion
zone
Electron microscope observations of transmission specimens revealed that the sizes of the dislocation networks in the diffusion zone were related to the calFor short diffusion treatments, where culated VC,,,.
600i
0 .02
.Oi
0 Shear
strain
Fro. 8. Resolved-shear stress as a function of shear strain. The treatments are described in Table 1. The curve for Specimen 90 is typical for pure copper. Spocimen 120 is an as-plated specimen.
ACTA
METALLURGICA,
VOL.
17,
1969
the antiphase-domain size could not be determined while an increase in critical-resolved-shear stress was observed for all gradients whether ordering was or was not detected by diffraction. Thus, it is concluded that a thin layer oforder phase in the subsurface region is not an important source of strengthening. 4.4 The effect of surface orientation
C2
cI At %
When a dislocation leaves a crystal a ledge of new surface on the crystal surface is created. The energy associated with formation of the new surface area for a unit length of dislocation is ~/sbsin 8, where ys is the surface energy and 0 is angle that the Burgers vector makes with the trace of the primary slip plane on the surface. If the egress of the dislocation were dependent upon the area of the new surface energy, the critical resolved shear stress should increase with sin 8 ; this effect has been discussed by F. R. N. Nabarro.(3b) In the present experiments there was no correlation between the initial-resolve-shear stress and sin 8.
Platinum (4
disordered --II---
4.5 Effect of elastic m~odulus and lattice parameter
ordered
on ~mechanicalproperties
Distance
from surface, (b)
x.
FIG. 9. (a) Platinum concentration profile near surface region. Annealing treatment carried out at temperature T. (b) Orderingregions in CuPt phase d&ram.
annealing treatment. The egress of dislocations are assisted, moreover, by the image forces attracting the dislocations to the surface. This reduction of the total number of dislocations in the diffusion zone is seen in the sequence of photomicro~aphs since the entire diffusion gradient with the misfit dislocations was contained in the foils viewed for VC,,,,, larger than 0.5 p-1. A tendency for dislocations to form ribbon-like networks parallel to the surface is shown in Figs. 5,6 and 7. Since the Burgers vectors of the parallel dislocations in ribbons were observed to be the same, the arrangement of dislocations is similar to that observed in subgrain formation (see J. Friedel(31)).
Cslculationst32) and experimental evidence(3s*s*) indicate that the maximum strengthening as a result of ordering should occur in a narrow range of a domain size in the vicinity of 30 A. In the present experiments
Associated with a platinum concentration profile near the surface are gradients in shear modulus and lattice parameter. A change in lattice parameter results in a change in the magnitude of the Burgers vector of a dislocation. The shear modulus and the lattice parameter for platinum-copper alloys are larger than those for pure copper. Thus, the self energy of a dislocation located in the alloy is increased when the platinum concentration is increased. On the other hand, the self energy decreases as the dislocation approaches the surface.c3i) Based on these energy considerations a calculation of the force acting on a
FIG. 10. Mesh size, L, as a function of concentration gradient Vb,,,.
DE
JONGHE
AND
GREENFIELD:
SURFACE
dislocation in the gradients with VC,,, greater than 20 p-r indicated that the hardening due to the change in shear modulus and lattice parameter was not significant. If gold is used instead of platinum as the solute, the image force should attract the dislocations more strongly to the surface since the modulus for gold is less than that for platinum. However, experiments with gold still show a hardening effect ;(36) and consequently with diffused layers the modulus and lattice parameter effects appear to have a secondary influence to surface strengthening. 4.6 The effect of the accommodatio~~~slo~utio?z. network on the glide dislocations Accommodation dislocations were observed in a limited three dimensional network near the surface. The glide dislocations initiated either in the surface layer or in the bulk of the crystal will be influenced by the presence of this dislocation network. Nabarro and Basinskit3Q in a recent, review have considered modes of strengthening ; they noted that several strengthening mechanisms can be described by the relation LYr= ,41-” where AT is the increase in critical-resolved-shear stress, A and n are parameters which depend on the model, and 1 is a characteristic distance between the obstacles to the glide dislocations. When it is assumed that the sources of the glide dislocations are in the surface layer, then I is about equal to L, the observed mesh size. Also, for this model n = -I, and A = J&/O>, where o is a constant related t,o the geometry and the nature of the pinning points. In the present case, comparison with the experiments shown that cr)is in order of 50 to 100, a value which is more than an order of magnitude above the theoretical value. Friedel(3x) considered the interaction between a pile-up of glide dislocations and a dislocation network, For this model n in the above relationship is equal to -3. The observed data is in better agreement with the Friedel model if there are three to six dislocations in the pile-up. More experiments are necessary to determine the details of the surface hardening mechanism, but on the basis of the present results a pile-up model is more appropriate. Because of solution hardening at the surface and because of the accommodation- dislocation network near the surface, surface sources are impeded. Thus, glide dislocations originating in the bulk can reach the surface only after cutting through the accommodation-dislocation network.
HARDENING
BP
DIFFUSION
IN
Cu
1419
5. CONCLUSION
1. Platinum deposits epitaxially on copper single crystals in the electropolishing process. 2. A very steep platinum concentration gradient exists during diffusion over the range of composition for which CuPt type ordering occurs. 3. For longer diffusion annealing treatments the gradient in lattice parameter induces an accommodation dislocation network arranged throughout the diffusion zone in the surface layer of the crystal. There is also a tendency for groups of dislocations to form parallel arrangements similar to low angle boundaries. 4. Correlation between the size of the network and the maximum steepness of the platinum concentration gradient was found. 5. Correlation between the critical-resolved-shear stress and the size of the network was found. The strengthening increases as the net size decreases. 6. In these experiments it was found that a gradient in elastic modulus, in solute concentration and in lattice parameter are not important cont~butors to the surface hardening effect. 7. Surface sources are impeded by the surface treatment. 8. Initiation of deformation occurs by dislocations being pushed through the network by dislocation pile-ups. ACKNOWLEDGEMENT
We are grateful to the National Science Foundation for support of this program. REFERENCES I. 2. 3. 4.
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