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Microstraining in αCuAl single crystals
MICROSTRAINING
IN aCu-Al
SINGLE
CRYSTALS*
T. J. KOPPENAALt The early stage of plastic deformation in c&u-Al single crystals has been studied at room temperature using a strain sensitivity of 1 x lo- B. The stress corresponding to this strain increases from 75 g/mm2 in a 0.5 at.% Al alloy to 394 g/mm2 in a 14 at.% Al crystal; the easy glide stresses for the same alloys are During microstraining, the stress is generally proportional to the 415 and 1550 g/mma, respectively. square root of the plastic strain. Assuming a dislocation generation mechanism, independent calculations with the microstrain work-hardening behavior and the 1 x 1O-B “yield stress” give approximately the same value for the unpinned length of dislocation for each alloy. If the pinning is due to forest dislocations, the forest density increases with solute concentration. The barrier density is calculated to be about an order of magnitude smaller than the forest density and this observation is explained with a model given by Meakin and Wilsdorf (formation of Cottrell-Lomer dislocations). Sub-grain boundaries may also be acting as barriers. Slip lines were examined with a light microscope in a 14 at.% Al crystal during various stages of microstraining. The coarse primary and cross slip lines characteristic of easy glide deformation in this “a-brass type” crystal are observed at a stress of about 2/3 the easy glide stress. MICRODEFORMATIONS DANS LES MONOCRISTAUX DE C&Ala L’auteur a etudie le premier stade de la deformation plastique de monocristaux de Cu-Ala Q la temperature ambiante en utilisant une sensibilite Q la deformation de 1 x lo- O. La contrainte correspondent a cette deformation croit depuis 75 g/mm2 dans un alliage a 0,5 at. o/0Al jusqu’b 394 g/mm* dans un cristal a 14 at.% Al; les contraintes de glissement facile pour les memes alliages sont respectivement 45 et 1550 g/mm2. Pendant la microdeformation, la contrainte est generalement proportionnelle a la racine car&e de la deformation plastique. En admettant un mecanisme de generation de dislocations, des calouls independants faits sur la base du comportement a la consolidation en microdeformation et de la “limite Blastique” 111 x 10e6 donnent approximativement la meme valeur de la longueur non ancree de dislocation pour chaque alliage. Si l’ancrage est db aux for&s de dislocations, la densite des for&s augmente avec la concentration en solute. La densite des barrieres a Bte trouvee inferieure d’environ un ordre de grandeur Q la densite des for&s; l’auteur explique cette observation a l’aide d’un modele propose par Meakin et Wilsdorf (formation de dislocations de Cottrell-Lomer). Des joints de sousgrains peuvent Qgalement agir comme barrieres. Les lignes de glissement ont ete examinees en microscopic optique sur un cristal a 14 at y0 Al pendant Les lignes de glissement primaires et les lignes de glissement differents stades de la microdeformation. croisees caract&isant la deformation par glissement facile dans ce cristal “du type laiton a” s’observent pour une contrainte valant environ les deux tiers de la contrainte de glissement facile. MIKRODEHNUNG BE1 a-Cu-Al-EINKRISTALLEN Das Anfangsstadium der plastischen Verformung von a-Cu-Al-Einkristallen wurde bei Raumtemperatur mit einer Dehnungsempfindlichkeit von 1 x 10e6 untersucht. Die dieser Dehnung entsprechende Spannung wachst von 75 g/mm* bei einer Legierung mit 0.5 At.% Al auf 394 g/mm2 bei einem Kristall mit 14 At.% Al; die Spannungen im easy-glide-Bereich betragen fur dieselben Legierungen 415 bezw. 1550 g/mm%. Wahrend der Mikrodehnung ist die Spannung im allgemeinen proportional der QuadratNimmt man einen Versetzungserzeugungsmechanismus an und wurzel der plastischen Dehnung. berechnet die Versetzungsliinge zwischen Verankerungspunkten einmd aus dem Verfestigungsverhalten bei Mikrodehnung, dann aus der 1 x 10-6-“FlieBgrenze”, so ergibt sich bei den einzelnen Kristallen beidemal derselbe Wert. Wird die Verandkenmg durch Waldversetzungen hervorgerufen, so mu13deren Dichte mit der Verunreinigungskonzentration zunehmen. Die Hindernisdichte ergibt sich aus der diese Beobachtung Rechnung urn etwa eine GrijDenordnung kleiner als die Dichte der Waldversetzungen; wird erkliirt durch ein von Meakin und Wilsdorf stammendes Model1 (Bildung von Cottrell-LomerVersetzungen). Auch Subkorngrenzen konnten als Hindernisse wirken. Gleitlinien wurden bei einem Kristall mit 14 At.% Al wahrend verschiedener Stadien der Mikrodehnung lichtmikroskopisch beobachtet. Die groben Haupt-und Quergleitlinien, die fur die easy-glide charakteristisch sind, wnrden bei einer Spannung Verformung dieses Kristalls vom “a-Messing-Typ” beobachtet, die etwa 213 der easy-glide-Spannung betrug.
INTRODUCTION
In theory,
solutes can strengthen
In the past few years, studies of microstraining (plastic deformation beginning at strains of ~1
two
x 10T6) have Investigations
the stress necessary
irradiation
been made in a number of metals. have been made with single crystals
technique
measurements
for studying
should
solid solution
be
a
investigation
useful
strengthening.
* Received September 10, 1962; revised November 13, 1962. t Metallurgy Division, Argonne National Laboratory, Argonne, Illinois. Formerly associated with the Armour Research Foundation. ACTA
METALLURGICA,
VOL.
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1963
similar
to
a solvent in one of current
concepts
of
“hardening,”
strengthening.
to a few specific alloys such as silicon-iron’s)
and CU,AU.(~) Microstrain
ways,
e.g. solutes could increase to initiate plastic deformation,
source strengthening, or increase the stress necessary to move dislocations through various barriers, friction
of Cue) and Al,(l) and polycrystalline Cu,W) Al,(l) Fe(n and Zn.c4) Studies with solid solutions have been restricted
general
The application in this respect
of a microstraining
could help to clarify the
strengthening mechanism. If plastic deformation starts at or near the easy glide stress (the initial horizontal portion of the stress-plastic strain curve), this might indicate a type of source strengthening, while the presence of plastic deformation at stresses well below easy glide could indicate a type of friction Thus, the purpose of the present study strengthening.
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was to investigate the early stage of plastic deformation in alloy crystals in hopes of distinguishing between these two general mechanisms, and, if possible, establish a clearer understanding of how and why solutes strengthen a solvent. Single crystals of the a&--Al system were chosen for investigation. EXPERIMENTAL
PROCEDURE
The Cu-base single crystals, confining from 0.5 to 14 at.% Al, reported upon here were from the same group used in previous investigations;(‘ys) the details concerning the growing and preparation of the specimens are given in these reports. Prior to testing, each crystal was annealed at 900°C for 24 hr, furnace cooled, and ele~trol~ic&~y polished in a 60% phosphoric acid solution. Two SR-4 electrical resistance strain gages were diametrically mounted at the center of each crystal, wired in series, andconnected toa strain indicator with s, strain sensitivity 1 x iO--6. Tension testing was performed on an Instron testing machine at room temperature with s, strain rate of ~5 x 1O-4 set-l. The stress-plastic strain data was obtained by the load-unload procedure.c2) The readings were taken immediately after unloading to zero stress. Anelastic recovery was observed, but the amount of the recovery w&s quite small; in a 14 at.% Al crystal strained to 0.040487, the indicated strain after 10 min was 0.040177, representing a recovery of less than 1 per cent. In reporting the strain data, the problem arose as to whether to treat the observed strain as a normal or a shear strain. An analysis of the sensing and computing stages with the employed experimentation, shows that the strain indicator is actually reporting sheer strain in single crystals. The electrical circuitry of the strain gages and strain indicator is such that the relative change in resistance of the gage wires, AR is proportional to the relative change in length R’ AL of the gage wires, , which is strain. Fig. 1 shows L %Ldisplacement of the gage wires across a slip plane in a single crystal. It is evident that the change in length, AL, of the strain gage wires is equivalent to the shear vector AB. Hence, AL has the significance AL of shear, and , the “output” ofthe strain indicator, L is shear strain. In Fig. 1, the strain in the gage wires is assumed to be exactly the same as the shear on the slip plane. While there could easily be small deviations of this behavior around sharp corners, the relative change in length of the gage wires is morecloselyrelated
WIRES
FIU. 1. Illustration of the change in length, AId, of the strain gage wires in relation to the shear, AB, in a single crystal.
to a shear strain than a normal strain. Thus, all strain values reported upon here are the values observed with the strain indicator and are at least very close to the actual shear strains in the specimens. In order to investigate the accuracy of the strain measurements, Young’s Modulus was measured by microstrain methods (within the purely elastic range of defo~ation) in Cu-12 at.% Al ~lycrys~l~e specimens and compared to values previously determinedcg) by dynamic measurement (electrostatic excitation and detection). In three samples that were examined, the variation between the two values was about 14, 3 and 5 per cent. RESULTS
Originally, strain gages with an l/16 in. gs,ge length were used on specimens with a gage length of about 0.7 in.; by defining a parameter R as L,/L,, where L, is the gage length of the strain gage and L, the gage length of the specimen, these tests were done with R N 0.1. The results obtained with three 12 at.% Al single crystals where R N 0.1 are shown in Fig. 2 (solid objects), and a number of features are evident. Plastic deformation starts at stresses well below easy glide (the resolved easy glide stress was between 1.430 and 1.485 kg/mm2 for all specimens in Fig. 2). The stress, 7*, corresponding to the initial detection of plastic strain (3 1 x 10e6) was 363, 548 and 670 g/mm2 in specimens F2-5, Fl-I and F2-4, respectively; samples F2-4 and F2-5 were of the same orientation (cut from the same single crystal). The variation in Q-~is exceedingly large compared to the accuracy of the measurements. For reasons that will be discussed later, the microstraining behavior in another 12 at.% Al crystal was determined in a sample with R = 1.0 using gages with a, longer gage
KOPPENAAL:
I.2
MICROSTRAINING
IX
UCU-Al
SINGLE
CRYSTALS
539
-
1.0 -
9
-
I
0.8
-
,” ., % g
0.6
-
0.4
-
iz 2 w 8
.,a-HIWEST
e 3 0
l . 0 -STRAIN 0.2
SlBE88 L+ I I IO*
FOR STRAIN
-
SHEAR STRAIN ,x IO 6
Fm. 2. Microstraining in Cu-12 at.% Al single crystals. See t,ext for meaning of R.
.-----QH _/--
12at.%AlfR*l.O)
7.5at.%AI(R.l.o)
SHEAR
o__-L-*-
*y
STRAIN,
Y IO'
FIG. 3. Microstraining in aCu-Al single crystals. Symbols have s&me meaning es in Fig. 2.
length. The results obtained with this specimen, F4-4, are also shown in Fig. 2 (open objects) and 70 was found to be 358 g/mm2. The amount of strain present at the onset of easy glide was the largest in F4-4 where B = 1.0. The orientation of all of the 12 at.% Al crystals is also shown in Fig. 2 and the possibility exists that the microstrain behavior could be orientation dependent. This variable was not investigated in the present work, but a comparison of the data of specimens F2-4, F2-5 and F4-4 seems to indicate that r0 is probably not orientation dependent. However, the stress-strain relationships during microstraining could be orientation dependent and this effect will be discussed later. Unless otherwise stated,
all future discussion of the 12 at.% Al alloy will refer to data obtained with crystal F4-4. The microstraining behavior was investigated in 7.5 and 14 at.% Al crystals where R = 1.0, and in a 0.5 at.% Al specimen where R ~0.4. The results axe shown in Fig, 3 along with the previous data of the 12 at.% Al crystal. The data for pure Cu single crystals reported by RosenGeld and Averbach is also shown. Q-~and the resolved easy glide stress,* * The term “resolved easy glide stress” is being adopted rather than the customary “critical resolved shear stress,” CRSS, generally quoted in the literature. Both terms refer to the s&me mechenicel property, but the letter is now seen to be misleeding since the word “critical” implies the initiation of plastic deformation.
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METALLURGICA,
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2
6
VOL.
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1963
I2
IO
14
ATOMIC PERCENT ALUMINUM
Fm. 4. Stress at which plastic deformation is initially observed, T,,, and the resolved easy glide stress, 7@, vs. solute content in c&u-Al single crystals. Cu values from Rosenfield and Averbach.cf)
rerr,for all of the crystals are given in Table 1, and plotted vs. Al con~nt in Fig. 4. The addition of 14 at.% Al to pure Cu increases T,, by Alfactor of-21, and increases T,~ by ~22. Thus, the relative degree of strengthening of the two properties is about the same. TABLE 1. T,, and 7sofor c&u-Al single crystak
at. o/O Al
crystal
R*
(g~xJ2”)
cut 0.5 7.5 12 12 12 12 14
11-l Cl-3 F2-4 F2-5 El-1 F4-4 4B 3-2
-0.4 1.0 NO.1 No.1 NO. 1 1.0 1.0
:: 209 363 670 548 358 394
(g&P) 4:: 1170 x450 1485 1450 1430 1550
shown in Fig. 6 along with their data for Cu single cry&&. In this figure, the lower bracket represents the maximum stress for which the plastic strain was ~1 x 10-s, and the upper bracket is the stress level of the subsequent loading where the strain was > 1 x 10W6. Thus, meis within this stress range. As in the case of copper, re increases with prior strain and reaches a steady value. Slip lines were examined at various stages of microstrain in a 14 at.% AI crystal. The specimen was initially loaded to 1.00 kg/mm2 (No.65 of Tag); the amount of strain recorded on a similar specimen, 483-2, at this stress was about 350 x 1OW (see Fig. 3).
L
I
* R = L,jL,, see text. $ Data from Rosenfield and Averbach.
The amount of strain present at the onset of easy glide also increases with Al content. The exact value of this strain is difficult to determine because of the somewhat asymptotic manner in which the curves approach Tag. However, the amount of strain present at 90 per cent of T,~ is more easily determined and values so obtained are shown vs. Al content in Fig. 5. The amount of strain appears to increase N parabolically with Al content except that positive strain deviations are seen in the two highest solute alloys. For the 14 at.oh Al alloy, this deviation represents a ~80 per cent increase from the extrapolated (dotted) curve. The effect of prior plastic strain on re was measured for 0.5 and 14 at.% Al crystals in the same manner as used by Rosenfield and Averbach. The results are
I
ax
.
t-j 6
20 ‘I
Of 0
I
I
I
I
I
1
2
4
6
8
IO
I2
ATOMIC PERCENT
I
14
ALUMINUM
FKJ. 5. Shear strain at 90 per cent of the easy glide stress vs. sol&o content in aCu-Al single crystals. Cu value from Rosenfield and Averbach.“)
KOPPENAAL:
MICROSTRAINING
IN
UCU-Al
SINGLE
CRYSTALS
541
0.5 at.% Al
0.411
-II0.2 cu (ROSENFIELD AND AVERBACH)
k-, 0
,
0
500
1000
1500
,
2000
PRIOR PLASTIC
I IOOW
I
I 30000
1 50000
SHEAR STRAIN, X IO”
FIG. 6. 70 vs. prior plastic strain in 14 and 0.5 at.% Al single crystals.
An example of the slip lines observed at this stage is shown in Fig. 7. Generally, single isolated lines were observed. Infrequently, a few lines in a band were found, as seen to the right of Fig. 7. In a very few cases, cross-slip appeared within a band, Fig. 8. The crystal was then reloaded to 1.25 kg/mm2 (-0.8 of 7eU where the strain on specimen 4B3-2 was about 1650 x 1O-6 (not shown in Fig. 3). Bands of slip lines now appeared where the single slips were previously observed, and many cross-slips were found connected to the primary lines, Fig. 9. In a few instances, profuse cross-slip was observed within a fairly small area, Fig. 10. DISCUSSION
The microstraining behavior of c&u-Al single crystals has been investigated at room temperature using a strain sensitivity of 1 x 1OV. T,,, the stress corresponding to the minimum observable plastic strain of ~1 x lOV, increases with solute additions, but this stress is only a small portion of 7es, the easy
glide stress. The properties which need evaluating are ro, reg, and the rate of work-hardening between 7. and rer. Before proceeding to these discussions, the effect of the R parameter seen in Fig. 2 should be commented upon. When this investigation was initiated, the assumption was made (incorrectly) that the microstraining in all of these alloy crystals would be homogeneous throughout their gage length, and strain gages were used where only a small portion of the specimen gage length was covered. However, when the results of specimens F2-5, Fl-I and F2-4 in Fig. 2 became known, the conclusion was reached that the microstraining is not homogeneous. In order to detect the minimum or true r. in these crystals, strain gages must cover the entire gage length. Observations of slip lines after 0.01 shear strain in aCu-Al single crystals with 5 or more at.% Al have shown the presence of coarse slip lines generally concentrated at one end of the gage length.(lO) During easy glide,
I,:
FIG. 7. Slip lines in a 14 at.% 1 .OOk&me.
Al single crystal loaded to x 150.
542
METALLURGICA,
FIG. 8. Primary crystal
VOL.
11,
1963
and cross-slip lines in a 14 at.% Al single x 700. loaded to 1.00 kg/mn?.
these coarse slips propagate
through
the gage length
in a manner similar to that observed in u-brass single crystals.(ll)
From the appearance
of the slip lines at
fairly small strains, Fig. 7, some of the coarse slip lines characteristic of easy glide deformation in these alloy single crystals are formed prior to reaching easy glide.
Thus, as easy glide begins, more strain should
FIG. 10. Profuse cross-slip in a 14 at.%Al single crystal loaded to 1.25 kg/mm*. x 500.
to move
“unlocked”
(pre-strained)
dislocations
was
be present at one end of the crystal gage length, and
found to be only 20-25 per cent of the stress necessary
tests conduction
R = 1.0should in general show R - 0.1. The observa-
to move
this conclusion.
copper(l)
with
larger strains than those with tions, Fig. 2, support which deform
in-homogeneously
ing (easy glide) microstraining.
also deform
Thus, crystals
during macrostrainin this manner
during
“locked”
dislocations. In
(as-recrystallized
This behavior
in either
or the alloy single crystals, Fig. 6.
interpreting
the
copper
single
crystals,
discuss
and
eliminate
frictional
effects,
proportional extended if any,
or strain-aged)
is not observed
microstraining Rosenfield a
behavior
and
mechanism
see their equation
(1).
in
Averbach based
upon
Here 7. is
to (exp-pu), where w is the width of the
dislocations with
(the other variables vary little,
composition).
This is also easily
dis-
regarded for the c&u-Al
crystals.
Since the stacking
fault
with
content,(13)
energy
decreases
Al
w in-
creases(14) and 7. should decrease whereas an increase FIG. 9. Primary and cross-slip lines in a 14 at.% x 500. single crystal loaded to 1.25 kg/mm*.
The test on the 0.5 at.% performed validity
before
these facts
of the observed
However,
Al crystal,
is observed.
Al
Fig. 3, was
were known,
and the
The generation of sources with the unpinned length of dislocation controlling 7. is another possibility. Using the line tension approximation,
results might be questioned.
70=-,
since this alloy shows a high density of very
fine slip lines completely
covering
the gage length of
the crystal after 0.01 shear atrain, is probably
homogeneous
the following
the microstraining
along the gage length.
discussions,
the observed
In
data in this
crystal are assumed to be the “true” values, although this is a point which requires confirmation. With respect to an interpretation
of the magnitude
Gh
where G is the shear modulus the Burgers vector of unpinned
(1)
1 (4.9 x lo3 kg/mms),
b
(2.6 x 1OV cm), and 1 the length
dislocation,
values
of 1 are obtained
varying from 1.7 x 10-s cm for the 0.5 at.%
Al alloy
to 3.2 x 10W4cm for the 14 at.% Al alloy. If the pinning is due to forest dislocations, calculated forest densities,
pr( = E2), increase
from
3 x lo5 crnm2 to
of -ro, Fig. 6 shows that r. increases with prior plastic
9.9 x lo6 crnA2 for the same two alloys, respectively.
strain and eventually
pinning
These values are reasonable numbers based upon etch pit densities of 1-6 x lo6 cm-2 found in a-brass single
mechanism, such as Cottrell locking, for controlling Once plastic deformation begins, the stress neces70. sary to move what might be considered as “unlocked”
crystals.(15) In a similar manner, Rosenfield and Averbach calculate a I value of ~6 x 1O-3 cm for their observed 7. in copper single crystals. The
dislocations does not decrease as would be expected. In a recent microstraining investigation in polycrystalline niobium,u2) which is b.c.c. and amenable
authors felt that this value was too large, and concluded that overcoming the line tension of a dislocation was not the mechanism controlling 70. In addi-
to interstitial
tion, the temperature
This
behavior
should
(elastic)
becomes
independent
eliminate
locking,
any solute
of strain.
the stress necessary
dependency
of r. was greater
KOPPENAAL:
MICROSTRAINING
IN a&-Al
SINGLE CRYSTALS
543
than could be accounted for from the temperature dependency of the shear modulus by equation (1). Rosenfield and Averbach explained their results with an alternate mechanism based upon the stress necessary to move the leading partial of an extended dislocation. The application of this theory to the temperature dependency of the NIO-~ “yield stress” gave reasonable stacking fault energies for Cu and Al, and was later?@ used to calculate both the stacking fault energy of disordered CusAu and the anti-phase domain boundary energy of ordered CusAu. However, an argument against the application of the Rosenfield and Averbach theory has been made(16j with an analysis of the dislocation density, amount of motion per dislocation, and resulting strain. For example, using the previously calculated dislocation density of ~10’ cm-2 for the 14 at.76 Al crystal, the dislocation density on the primary slip system would be ~10~ cm-2. Using the relationship, y = BLN,
(2)
where y is the shear strain, L the length of travel per dislocation, and N the number of moving dislocations per unit area, the motion of a single Burgers vector by each of the primary dislocations would produce a strain of ~5 x 10-lo. Since the minimum measurable strain in these investigations is 1 x lC@, 70 does not represent the stress corresponding to the initial stage of plastic deformation, and the Rosenfield and Averbach theory is not applicable. Thus, plastic deformation begins at some stress Too, but this stress can not be measured with available strain detection equipment. Once plastic deformation starts, Fig. 3 shows that an -parabolic relationship exists between stress and strain. The data in this figure are ~plot~d in Fig. 11 as the square root of the plastic strain vs. stress, and linear relationships are found for each curve with the exception of two general areas. Deviations are observed at low strains for alloys of 7.5-14 at.% Al and at high strains for the 12 and 14 at.% Al alloys. These deviations will be discussed later. Using the slopes of the straight lines in Fig. 11 and the workhardening relationship given by Blott,(l’)
-0
0.2
0.4
RESOLVED
0.6
0.8
1.0
SHEAR STRESS, kg -
rn&*
FIU. 11. Squareroot of plastic shear strain vs. stressfor curves from Fig. 4.
the agreement appears to be fairly good, and supports the concept of dislocation generation at r0 since the values are obtained with independent sets of experimental data. In the past, researchers have not used equation (3) to explain work-hardening relationships in single crystals; the ray112 dependency exists only when 1 is constant, and this is not expected during stage II in the deformation process. However, I should be constant during the initial microstraining stage, and equation (3) is seen to be applicable to the present me~~ments. Since the microstraining in the higher solute crystals has already been established as being inhomogeneous, the use of equation (3) for these alloys However, a was initially viewed with caution. comparison of the work-hardening parameter ~+i/~/d~ for the data in Fig. 2 tends to eliminate the exclusion of equation (3). The value of dyi12/& for crystal F4-4, where R = 1.0, is 5.0 x 10m2mm2/kg (slope of the 12 at.% Al crystal shown in Fig. 12). The data for the other three crystals in Fig. 2 where R - 0.1 was plotted on a {st~in)1’2-stress basis, and ~~~~=I~T TABLE2. Length of unpinned dislocation at.% Al
an independent calculation of t can be made. Values of 1 are obtained varying from 2.2 x IO-3 cm to 0.85x lop4 cm in the 0.5 and 14 at.% Al alloys, respectively. Table 2 shows the E distance for all alloys obtained by equations (1) and (3). Considering the approximations used in equations (1) and (3),
CkI*
0.5 1.5 12 14
1, em equation (1) 6.7 1.7 6.1 3.6 3.2
x x x x x
1O-3 10-z 10-a 10-d lo-*
1, cm equation (3) 2.2 0.49 8.5 2.5 0.85
x x x x x
10-a lo-* 10-t 10-a lo-’
* Values calculsted from data of Rosenfield and Aver-
b&&W
544
ACTA
METALLURGICA,
values of 2.8 x 10-2, 5.2 x 10-2, and 3.1 x 10-r mm2/kg were obtained for crystals F2-4, F2-5 and Fl-1, respectively. Thus, even though the strain for a particular stress varied in these tests, the .uyils dependency is still observed, and the work-hardening parameters, o$J/~/G!T,varied by less than a factor of two. Some of the difference in these observed workhardening parameters could easily be orientation effects. Crystals F2-4 and F4-4 both showed approximately the same 7,, (363 and 358 g/mm2, respectively) but F2-4 displayed a lower dy1f2/& parameter. The resolved shear stress on the conjugate slip system in F2-4 is 86 per cent of the primary system, while in F4-4 it is only 42 per cent. Thus, if it takes ~360 g/mm 2 to activate a source in these 12 at.% Al crystals, sources on the conjugate system would become active at a resolved shear stress on the primary system of -430 and ~850 g/mm2 in crystals F2-4 and F4-4, respectively. Hence, small amounts of conjugate slip are presumably occurring much earlier in the deformation of crystal F2-4, which in turn would lead to higher work-hardening rate (smaller dy1J2/& parameter) through the formation of CottrellLomer sessile dislocations. Returning to Fig. 11, the deviations from the straight lines at small strains could represent the activation of sources over a small range of stress due to variations in the actual 1 distance. With regards to the deviations at high strains, a number of observations indicate that this is caused by the cross slip which occurs in the high alloy crystals. A previous investigationoO) showed that the amount of cross slip seen in Figs. 8,9 and 10 is about an order of magnitude larger in 14 at.% Al crystals than in 7.5 at.% Al alloys. This supports the behavior in Fig. 11 since the former shows deviations at high strains while the latter does not. Further, the deviations from the curve shown in Fig. 5 are in a similar fashion. In addition, the deviation in the 14 at.% Al crystal begins at about 0.9 kg/mm2, Fig. 11, and very limited amounts of cross slip were observed after stressing to 1.00 kg/mm2, Fig. 10. Finally, 7. in the 14 at.% Al alloy becomes independent of strain at a value of about 0.95 kg/mm2, Fig. 6, and since this is about the same stress level as the other two observations, it may represent the stress at which limited amounts of cross slip can take place. At a resolved shear stress of 1.00 kg/mm2 on the primary slip system for the crystal shown in Fig. 9, the resolved shear stress on the cross slip system was 200 g/mm2. Since a resolved shear stress of 394 g/mm2 appears to be the stress necessary to activate a source, the difference, 194 g/mm2, must have been supplied by interactions of
VOL.
11, 1963
the cross slip sources and primary dislocations. The quantitative relationship for the activation of cross slip sources given by Avery and Backofenos) was used to calculate the dislocation spacing on the primary slip system necessary to activate these sources. This spacing is calculated to be 0.6 p. Meakin and Wilsdorfug) measured the distance between dislocations in isolated pileups in a-brass single crystals deformed into easy glide and obtained values of about 0.1-0.5 ,U at the leading end of the pileups. The Meakin and Wilsdorf spacings are expected to be smaller since the resolved shear stress under which the pileups were formed was ~60-100 per cent larger for their determinations. Thus, the constant 7. level in Fig. 6 could represent the stress necessary to activate sources on the cross slip system, at least in the high solute crystals. The same explanation could also be given for Cu and the dilute alloys; cross slip is not observed in these cases, but this may be due to resolution limitations (including observations made with an electron microscope). Thus, cross slip is concluded to be cause of the deviations at high strains in the 12 and 14 at.% Al crystals seen in Fig. 11. Equation (3) is seen to be independent of the distance between the barriers which leads to the ~uyl’~ behavior. Using the relationship I, =
2n G% reg 7T(7,,2-
To2) ’
(4)
where 1, is the spacing of the barriers and n the number of dislocations piled up at the barriers during easy glide, the barrier spacing can be calculated by assuming a value for n. From the work of Meakin and Wilsdorf,09) n is ~25 in u-brass single crystals, and this value is used for the 14 at.% Al crystal because of the similarities in mechanical properties of the two alloys. With this assumption, 1, in equation (4) is calculated to be 14 x 1O-4 cm, and pb, the barrier density, becomes 5.1 x lo5 cm-2. Thus, pf N 2Op,. In the easy-glide deformation of u-brass single crystals, Meakin and Wilsdorf(15) experimentally observed a pb of ~5 x lo5 cm2, and pr N lop,. Their explanation, which explains the present results, is that the barriers are sessile Cottrell-Lomer dislocations formed by reactions of the glidingprimarydislocations and the forest dislocations which have the appropriate Burgers vector. With this model, the barrier density is expected to be about an order of magnitude less than the forest dislocation density. As also pointed out by these researchers, the strength of the barriers in u-brass are expected to be stronger than in pure copper because of the decrease in stacking fault energy with solute additions (wider extended dislocations).
KOPPENAAL:
MICROSTRAINING
IN
ctCu-Al
SINGLE
CRYSTALS
545
Thus, the easy glide stress, which (for a particular replacing N by 2np,, where ps is the density of distemperature and strain rate) represents the stress location sources, the source density computes to necessary for steady-state motion of dislocations 4.6 x IO5 cm-2. Since the primary dislocation density through or around these barriers, increases with was ~10~ cm-2, this calculation indicates that approxisolute content because there are more and stronger mately one-half of the primary dislocations have barriers. Whereas the Meakin and Wilsdorf report acted as sources at a stress of 0.80 kg/mm2 describes the steady-state condition, the present Finally, it is felt that additional measurements of investigation yields information about the pre-steady the microstrain behavior in aCu-Al single crystals are state condition. The two reports are seen to be necessary before any definite conclusions can be made. compatible. Included in these are the variables of testing temperaIn a previous investigation dealing with the solid ture and degree of local order, the effects of which solution strengthening mechanism in aCu-Al single have already(718) been evaluated on the flow stress in crystals,(s) the strengthening in T,~ at temperatures these alloy single crystals. < 296°K was presumed to arise from the cutting of SUMMARY forest dislocations, which become wider with Al The following information has been obtained in this content through the decrease in stacking fault energy. On the basis of the present investigation, this needs investigation regarding microstraining in ~cu-Al to be modified only to the extent of considering the single crystals. (1) Plastic deformation begins at some stress T’~, forest dislocations capable of forming Cottrell-Lomer barriers with the gliding dislocations rather than the but due to limitations in strain detection, TO,,is not measurable. Hence, the effect of solutes on the very entire forest. initial “yielding” is not known. were noted to show the same relative T,, and re9 (2) The stress, ~a, corresponding to the minimum degree of strengthening (Fig. 4) and both of these mechanical properties have been explained with a observable strain of 1 x 1OV increases with solute additions and has been explained on the basis of a single physical property, the number of dislocations dislocation generation mechanism. Calculations from present, see equations (1) and (4). Thus, the effect two independent sets of data for the unpinned length of solutes in producing more barriers could be a more of dislocation of each alloy are in reasonable agreement. important feature than that of resulting in stronger (3) Forest dislocations are presumed to control the barriers. length of unpinned dislocation, since reasonable In addition to the Meakin-Wilsdorf model, subdensities of the former can be calculated from the grain boundaries might also be effective dislocation latter. barriers. The calculated distance between barriers, (4) Beyond T,,, the microstrain follows a stress 14 ,D,in the 14 at.% Al alloy is also in the range of the a(strain)li2 dependency, and the barriers responsible probable sub-grain size. Meakin and Wilsdorfo5) for this behavior are thought to be sessile Cottrellfound an average sub-grain diameter of about 20 ,u Lomer dislocations and/or sub-grain boundaries. in a-brass single crystals, and observed sub-boundaries (5) In the high solute alloys, 12-14 at.% Al, acting as barriers in a similar fashion to the randomly pileups at these barriers assist in activating cross slip distributed barriers. Youngc21) and Livingston(22) sources at stresses about 213 of the easy glide stress; have reported upon pileups at sub-grain boundaries when this occurs, the ray112 dependency is no longer in Cu single crystals; however, Youngc21) also finds observed. evidence for Cottrell-Lomer barriers. The possibility (6) In classifying the effects of solutes as either of sub-grain size strengthening in c&u-Al single source or friction strengthening mechanisms, the crystals at high temperatures, >296”K, has been largest contribution to the easy glide stress is a previously(a) noted. frictional effect although a smaller source effect is In either case, the distance between the barriers can also present. be used to estimate the source density. Referring to Fig. 11, the ray1l2 dependency is maintained up to Note added in proof about 0.9 kg/mm2 in the 14 at.% Al crystal. Below Since the original submission of this report, the this stress, the generated dislocations are being held author has become aware of some recent work by up at the barriers. Using equation (a), -9 dislocations are in each pileup at a stress of 0.80 kg/mm2, and the Kingf2a) on dislocation etch-pit studies in aCu-Al amount of strain at this stress was 75 x 1OW (Fig. 3). single crystals after cycling at stresses below the easy Using equation (2) and approximating L as 1,/4 and glide stress. King’s results support the present
546
ACTA
investigation dislocations
in two ways.
METALLURGICA,
He observes
motion
of
at stresses below easy glide in the alloy
crystals (up to 14.8 at.% Al), and still more important, King
finds
numerous
pile
cycles at stresses of about Thus,
the concept
formed
after
three
of pile ups being formed
the initial microstrain
region of plastic
which is an “assumption” least qualitatively
ups
213 the easy glide stress. during
deformation,
in the present
work, is at
confirmed.
ACKNOWLEDGMENTS
The author Brittain,
would
like to thank
Professors
J. 0.
J. B. Cohen, and M. E. Fine for somewhat
simultaneously
suggesting the importance
strain investigation
in these alloys.
of a micro-
Professor
Fine
and Dr. T. H. Blewitt were kind enough to read this manuscript The
and offer valuable
experimental
work
suggestions.
reported
accomplished
while the author
the
Research
Armour
supported by Commission.
the
Foundation,
United
upon
here was
was associated
States
where Atomic
it
with was
Energy
REFERENCES 1. A. R. ROSENFIELD and B. L. AVERBACH, Beta Met. 8,624 (1960).
VOL.
11,
1963
D. A. THOMASand B. L. AVERBACH,Acta Met. 7,69 (1969). N. BROWN and K. F. LUKENS, JR., Acta Met. 9,106(1961). J. M. ROBERTS, see Ref. (3). J. C. SUITS and B. CKALMERS, Acta Met. 9. 854 (1961). W. J. WAQNER, JR., A. R. ROSENFIELD and-B. L. ‘A&BACH, Acta Met. 10, 256 (1962). 7. T. J. KOPPENAAL and M. E. FINE, Trans. Amer. Inst. Min. (Metall.) Engrs. 221, 1178 (1961). 8. T. 5. KOPPENAAL and M. E. FINE, Trans. Amer. Inst. Min. (MetalE.) Engrs. 224, 347 (1962). 9. T. 5. KOPPENAAL, PhD. Thesis, Northwestern Universit,y, 1961. 10. T. J. KOPPENAAL, Trans. Amer. Inst. Min. (Metall.) Engrs., 227, 257 (1963), 11. G. R. PIERCY, R. W. CAHN and A. H. COTTRELL,Acta Met. 3, 331 (1955). 12. T. J. KOPPENAAL and P. R. V. EVANS. submitted to Acta Met. 13. A. HOWIE and P. R. SWANN, Phil. Mag. 6, 1215 (1961). 14. A, H. COTTRELL,D&locations and Plastic Flow in Crystals, p. 74. Clarendon Press, Oxford (1953). 15. 5. D. MEAKIN and H. G. F. WILSDORF, Trans. Amer. Inst. Min. (M&all.) Engrs. 218, 737 (1960). 16. T. J. KOPPENAAL, Acta Met., 11, 85 (1963). N. F. MOTT, Proc. Phys. Sot. Lond. 43, 1151 (1952). ::: D. H. AVERY and W. A. BACKOFEN, Trans. Amer. Inst. Min. (Metall.) Engrs. in press. 19. J. D. MEAKIN and H. G. F. WILSDORF. Trans. Amer. Inst. Min. (Met&Z.) Engrs. 212, 745 (1960).’ 20. T. VREELAND, JR., D. S. WOOD and D. S. CLARK, Acta Met. 1, 414 (1953). 21. F. W. YOUNG. JR.. J. Avvl. Phvs. 33. 963 (1962). 22. J. D. LIVIN&ON,~J. A&Z. Ph&. 31,1076 ‘(1966). 23. A. H. KING, submitted to Nature, Lond. 2. 3. 4. 5. 6.
IN aCu-Al
SINGLE
CRYSTALS*
T. J. KOPPENAALt The early stage of plastic deformation in c&u-Al single crystals has been studied at room temperature using a strain sensitivity of 1 x lo- B. The stress corresponding to this strain increases from 75 g/mm2 in a 0.5 at.% Al alloy to 394 g/mm2 in a 14 at.% Al crystal; the easy glide stresses for the same alloys are During microstraining, the stress is generally proportional to the 415 and 1550 g/mma, respectively. square root of the plastic strain. Assuming a dislocation generation mechanism, independent calculations with the microstrain work-hardening behavior and the 1 x 1O-B “yield stress” give approximately the same value for the unpinned length of dislocation for each alloy. If the pinning is due to forest dislocations, the forest density increases with solute concentration. The barrier density is calculated to be about an order of magnitude smaller than the forest density and this observation is explained with a model given by Meakin and Wilsdorf (formation of Cottrell-Lomer dislocations). Sub-grain boundaries may also be acting as barriers. Slip lines were examined with a light microscope in a 14 at.% Al crystal during various stages of microstraining. The coarse primary and cross slip lines characteristic of easy glide deformation in this “a-brass type” crystal are observed at a stress of about 2/3 the easy glide stress. MICRODEFORMATIONS DANS LES MONOCRISTAUX DE C&Ala L’auteur a etudie le premier stade de la deformation plastique de monocristaux de Cu-Ala Q la temperature ambiante en utilisant une sensibilite Q la deformation de 1 x lo- O. La contrainte correspondent a cette deformation croit depuis 75 g/mm2 dans un alliage a 0,5 at. o/0Al jusqu’b 394 g/mm* dans un cristal a 14 at.% Al; les contraintes de glissement facile pour les memes alliages sont respectivement 45 et 1550 g/mm2. Pendant la microdeformation, la contrainte est generalement proportionnelle a la racine car&e de la deformation plastique. En admettant un mecanisme de generation de dislocations, des calouls independants faits sur la base du comportement a la consolidation en microdeformation et de la “limite Blastique” 111 x 10e6 donnent approximativement la meme valeur de la longueur non ancree de dislocation pour chaque alliage. Si l’ancrage est db aux for&s de dislocations, la densite des for&s augmente avec la concentration en solute. La densite des barrieres a Bte trouvee inferieure d’environ un ordre de grandeur Q la densite des for&s; l’auteur explique cette observation a l’aide d’un modele propose par Meakin et Wilsdorf (formation de dislocations de Cottrell-Lomer). Des joints de sousgrains peuvent Qgalement agir comme barrieres. Les lignes de glissement ont ete examinees en microscopic optique sur un cristal a 14 at y0 Al pendant Les lignes de glissement primaires et les lignes de glissement differents stades de la microdeformation. croisees caract&isant la deformation par glissement facile dans ce cristal “du type laiton a” s’observent pour une contrainte valant environ les deux tiers de la contrainte de glissement facile. MIKRODEHNUNG BE1 a-Cu-Al-EINKRISTALLEN Das Anfangsstadium der plastischen Verformung von a-Cu-Al-Einkristallen wurde bei Raumtemperatur mit einer Dehnungsempfindlichkeit von 1 x 10e6 untersucht. Die dieser Dehnung entsprechende Spannung wachst von 75 g/mm* bei einer Legierung mit 0.5 At.% Al auf 394 g/mm2 bei einem Kristall mit 14 At.% Al; die Spannungen im easy-glide-Bereich betragen fur dieselben Legierungen 415 bezw. 1550 g/mm%. Wahrend der Mikrodehnung ist die Spannung im allgemeinen proportional der QuadratNimmt man einen Versetzungserzeugungsmechanismus an und wurzel der plastischen Dehnung. berechnet die Versetzungsliinge zwischen Verankerungspunkten einmd aus dem Verfestigungsverhalten bei Mikrodehnung, dann aus der 1 x 10-6-“FlieBgrenze”, so ergibt sich bei den einzelnen Kristallen beidemal derselbe Wert. Wird die Verandkenmg durch Waldversetzungen hervorgerufen, so mu13deren Dichte mit der Verunreinigungskonzentration zunehmen. Die Hindernisdichte ergibt sich aus der diese Beobachtung Rechnung urn etwa eine GrijDenordnung kleiner als die Dichte der Waldversetzungen; wird erkliirt durch ein von Meakin und Wilsdorf stammendes Model1 (Bildung von Cottrell-LomerVersetzungen). Auch Subkorngrenzen konnten als Hindernisse wirken. Gleitlinien wurden bei einem Kristall mit 14 At.% Al wahrend verschiedener Stadien der Mikrodehnung lichtmikroskopisch beobachtet. Die groben Haupt-und Quergleitlinien, die fur die easy-glide charakteristisch sind, wnrden bei einer Spannung Verformung dieses Kristalls vom “a-Messing-Typ” beobachtet, die etwa 213 der easy-glide-Spannung betrug.
INTRODUCTION
In theory,
solutes can strengthen
In the past few years, studies of microstraining (plastic deformation beginning at strains of ~1
two
x 10T6) have Investigations
the stress necessary
irradiation
been made in a number of metals. have been made with single crystals
technique
measurements
for studying
should
solid solution
be
a
investigation
useful
strengthening.
* Received September 10, 1962; revised November 13, 1962. t Metallurgy Division, Argonne National Laboratory, Argonne, Illinois. Formerly associated with the Armour Research Foundation. ACTA
METALLURGICA,
VOL.
11, JUNE
1963
similar
to
a solvent in one of current
concepts
of
“hardening,”
strengthening.
to a few specific alloys such as silicon-iron’s)
and CU,AU.(~) Microstrain
ways,
e.g. solutes could increase to initiate plastic deformation,
source strengthening, or increase the stress necessary to move dislocations through various barriers, friction
of Cue) and Al,(l) and polycrystalline Cu,W) Al,(l) Fe(n and Zn.c4) Studies with solid solutions have been restricted
general
The application in this respect
of a microstraining
could help to clarify the
strengthening mechanism. If plastic deformation starts at or near the easy glide stress (the initial horizontal portion of the stress-plastic strain curve), this might indicate a type of source strengthening, while the presence of plastic deformation at stresses well below easy glide could indicate a type of friction Thus, the purpose of the present study strengthening.
537
ACTA
538
METALLURGICA,
VOL.
11,
1963
was to investigate the early stage of plastic deformation in alloy crystals in hopes of distinguishing between these two general mechanisms, and, if possible, establish a clearer understanding of how and why solutes strengthen a solvent. Single crystals of the a&--Al system were chosen for investigation. EXPERIMENTAL
PROCEDURE
The Cu-base single crystals, confining from 0.5 to 14 at.% Al, reported upon here were from the same group used in previous investigations;(‘ys) the details concerning the growing and preparation of the specimens are given in these reports. Prior to testing, each crystal was annealed at 900°C for 24 hr, furnace cooled, and ele~trol~ic&~y polished in a 60% phosphoric acid solution. Two SR-4 electrical resistance strain gages were diametrically mounted at the center of each crystal, wired in series, andconnected toa strain indicator with s, strain sensitivity 1 x iO--6. Tension testing was performed on an Instron testing machine at room temperature with s, strain rate of ~5 x 1O-4 set-l. The stress-plastic strain data was obtained by the load-unload procedure.c2) The readings were taken immediately after unloading to zero stress. Anelastic recovery was observed, but the amount of the recovery w&s quite small; in a 14 at.% Al crystal strained to 0.040487, the indicated strain after 10 min was 0.040177, representing a recovery of less than 1 per cent. In reporting the strain data, the problem arose as to whether to treat the observed strain as a normal or a shear strain. An analysis of the sensing and computing stages with the employed experimentation, shows that the strain indicator is actually reporting sheer strain in single crystals. The electrical circuitry of the strain gages and strain indicator is such that the relative change in resistance of the gage wires, AR is proportional to the relative change in length R’ AL of the gage wires, , which is strain. Fig. 1 shows L %Ldisplacement of the gage wires across a slip plane in a single crystal. It is evident that the change in length, AL, of the strain gage wires is equivalent to the shear vector AB. Hence, AL has the significance AL of shear, and , the “output” ofthe strain indicator, L is shear strain. In Fig. 1, the strain in the gage wires is assumed to be exactly the same as the shear on the slip plane. While there could easily be small deviations of this behavior around sharp corners, the relative change in length of the gage wires is morecloselyrelated
WIRES
FIU. 1. Illustration of the change in length, AId, of the strain gage wires in relation to the shear, AB, in a single crystal.
to a shear strain than a normal strain. Thus, all strain values reported upon here are the values observed with the strain indicator and are at least very close to the actual shear strains in the specimens. In order to investigate the accuracy of the strain measurements, Young’s Modulus was measured by microstrain methods (within the purely elastic range of defo~ation) in Cu-12 at.% Al ~lycrys~l~e specimens and compared to values previously determinedcg) by dynamic measurement (electrostatic excitation and detection). In three samples that were examined, the variation between the two values was about 14, 3 and 5 per cent. RESULTS
Originally, strain gages with an l/16 in. gs,ge length were used on specimens with a gage length of about 0.7 in.; by defining a parameter R as L,/L,, where L, is the gage length of the strain gage and L, the gage length of the specimen, these tests were done with R N 0.1. The results obtained with three 12 at.% Al single crystals where R N 0.1 are shown in Fig. 2 (solid objects), and a number of features are evident. Plastic deformation starts at stresses well below easy glide (the resolved easy glide stress was between 1.430 and 1.485 kg/mm2 for all specimens in Fig. 2). The stress, 7*, corresponding to the initial detection of plastic strain (3 1 x 10e6) was 363, 548 and 670 g/mm2 in specimens F2-5, Fl-I and F2-4, respectively; samples F2-4 and F2-5 were of the same orientation (cut from the same single crystal). The variation in Q-~is exceedingly large compared to the accuracy of the measurements. For reasons that will be discussed later, the microstraining behavior in another 12 at.% Al crystal was determined in a sample with R = 1.0 using gages with a, longer gage
KOPPENAAL:
I.2
MICROSTRAINING
IX
UCU-Al
SINGLE
CRYSTALS
539
-
1.0 -
9
-
I
0.8
-
,” ., % g
0.6
-
0.4
-
iz 2 w 8
.,a-HIWEST
e 3 0
l . 0 -STRAIN 0.2
SlBE88 L+ I I IO*
FOR STRAIN
-
SHEAR STRAIN ,x IO 6
Fm. 2. Microstraining in Cu-12 at.% Al single crystals. See t,ext for meaning of R.
.-----QH _/--
12at.%AlfR*l.O)
7.5at.%AI(R.l.o)
SHEAR
o__-L-*-
*y
STRAIN,
Y IO'
FIG. 3. Microstraining in aCu-Al single crystals. Symbols have s&me meaning es in Fig. 2.
length. The results obtained with this specimen, F4-4, are also shown in Fig. 2 (open objects) and 70 was found to be 358 g/mm2. The amount of strain present at the onset of easy glide was the largest in F4-4 where B = 1.0. The orientation of all of the 12 at.% Al crystals is also shown in Fig. 2 and the possibility exists that the microstrain behavior could be orientation dependent. This variable was not investigated in the present work, but a comparison of the data of specimens F2-4, F2-5 and F4-4 seems to indicate that r0 is probably not orientation dependent. However, the stress-strain relationships during microstraining could be orientation dependent and this effect will be discussed later. Unless otherwise stated,
all future discussion of the 12 at.% Al alloy will refer to data obtained with crystal F4-4. The microstraining behavior was investigated in 7.5 and 14 at.% Al crystals where R = 1.0, and in a 0.5 at.% Al specimen where R ~0.4. The results axe shown in Fig, 3 along with the previous data of the 12 at.% Al crystal. The data for pure Cu single crystals reported by RosenGeld and Averbach is also shown. Q-~and the resolved easy glide stress,* * The term “resolved easy glide stress” is being adopted rather than the customary “critical resolved shear stress,” CRSS, generally quoted in the literature. Both terms refer to the s&me mechenicel property, but the letter is now seen to be misleeding since the word “critical” implies the initiation of plastic deformation.
540
ACTA
METALLURGICA,
4
2
6
VOL.
8
II,
1963
I2
IO
14
ATOMIC PERCENT ALUMINUM
Fm. 4. Stress at which plastic deformation is initially observed, T,,, and the resolved easy glide stress, 7@, vs. solute content in c&u-Al single crystals. Cu values from Rosenfield and Averbach.cf)
rerr,for all of the crystals are given in Table 1, and plotted vs. Al con~nt in Fig. 4. The addition of 14 at.% Al to pure Cu increases T,, by Alfactor of-21, and increases T,~ by ~22. Thus, the relative degree of strengthening of the two properties is about the same. TABLE 1. T,, and 7sofor c&u-Al single crystak
at. o/O Al
crystal
R*
(g~xJ2”)
cut 0.5 7.5 12 12 12 12 14
11-l Cl-3 F2-4 F2-5 El-1 F4-4 4B 3-2
-0.4 1.0 NO.1 No.1 NO. 1 1.0 1.0
:: 209 363 670 548 358 394
(g&P) 4:: 1170 x450 1485 1450 1430 1550
shown in Fig. 6 along with their data for Cu single cry&&. In this figure, the lower bracket represents the maximum stress for which the plastic strain was ~1 x 10-s, and the upper bracket is the stress level of the subsequent loading where the strain was > 1 x 10W6. Thus, meis within this stress range. As in the case of copper, re increases with prior strain and reaches a steady value. Slip lines were examined at various stages of microstrain in a 14 at.% AI crystal. The specimen was initially loaded to 1.00 kg/mm2 (No.65 of Tag); the amount of strain recorded on a similar specimen, 483-2, at this stress was about 350 x 1OW (see Fig. 3).
L
I
* R = L,jL,, see text. $ Data from Rosenfield and Averbach.
The amount of strain present at the onset of easy glide also increases with Al content. The exact value of this strain is difficult to determine because of the somewhat asymptotic manner in which the curves approach Tag. However, the amount of strain present at 90 per cent of T,~ is more easily determined and values so obtained are shown vs. Al content in Fig. 5. The amount of strain appears to increase N parabolically with Al content except that positive strain deviations are seen in the two highest solute alloys. For the 14 at.oh Al alloy, this deviation represents a ~80 per cent increase from the extrapolated (dotted) curve. The effect of prior plastic strain on re was measured for 0.5 and 14 at.% Al crystals in the same manner as used by Rosenfield and Averbach. The results are
I
ax
.
t-j 6
20 ‘I
Of 0
I
I
I
I
I
1
2
4
6
8
IO
I2
ATOMIC PERCENT
I
14
ALUMINUM
FKJ. 5. Shear strain at 90 per cent of the easy glide stress vs. sol&o content in aCu-Al single crystals. Cu value from Rosenfield and Averbach.“)
KOPPENAAL:
MICROSTRAINING
IN
UCU-Al
SINGLE
CRYSTALS
541
0.5 at.% Al
0.411
-II0.2 cu (ROSENFIELD AND AVERBACH)
k-, 0
,
0
500
1000
1500
,
2000
PRIOR PLASTIC
I IOOW
I
I 30000
1 50000
SHEAR STRAIN, X IO”
FIG. 6. 70 vs. prior plastic strain in 14 and 0.5 at.% Al single crystals.
An example of the slip lines observed at this stage is shown in Fig. 7. Generally, single isolated lines were observed. Infrequently, a few lines in a band were found, as seen to the right of Fig. 7. In a very few cases, cross-slip appeared within a band, Fig. 8. The crystal was then reloaded to 1.25 kg/mm2 (-0.8 of 7eU where the strain on specimen 4B3-2 was about 1650 x 1O-6 (not shown in Fig. 3). Bands of slip lines now appeared where the single slips were previously observed, and many cross-slips were found connected to the primary lines, Fig. 9. In a few instances, profuse cross-slip was observed within a fairly small area, Fig. 10. DISCUSSION
The microstraining behavior of c&u-Al single crystals has been investigated at room temperature using a strain sensitivity of 1 x 1OV. T,,, the stress corresponding to the minimum observable plastic strain of ~1 x lOV, increases with solute additions, but this stress is only a small portion of 7es, the easy
glide stress. The properties which need evaluating are ro, reg, and the rate of work-hardening between 7. and rer. Before proceeding to these discussions, the effect of the R parameter seen in Fig. 2 should be commented upon. When this investigation was initiated, the assumption was made (incorrectly) that the microstraining in all of these alloy crystals would be homogeneous throughout their gage length, and strain gages were used where only a small portion of the specimen gage length was covered. However, when the results of specimens F2-5, Fl-I and F2-4 in Fig. 2 became known, the conclusion was reached that the microstraining is not homogeneous. In order to detect the minimum or true r. in these crystals, strain gages must cover the entire gage length. Observations of slip lines after 0.01 shear strain in aCu-Al single crystals with 5 or more at.% Al have shown the presence of coarse slip lines generally concentrated at one end of the gage length.(lO) During easy glide,
I,:
FIG. 7. Slip lines in a 14 at.% 1 .OOk&me.
Al single crystal loaded to x 150.
542
METALLURGICA,
FIG. 8. Primary crystal
VOL.
11,
1963
and cross-slip lines in a 14 at.% Al single x 700. loaded to 1.00 kg/mn?.
these coarse slips propagate
through
the gage length
in a manner similar to that observed in u-brass single crystals.(ll)
From the appearance
of the slip lines at
fairly small strains, Fig. 7, some of the coarse slip lines characteristic of easy glide deformation in these alloy single crystals are formed prior to reaching easy glide.
Thus, as easy glide begins, more strain should
FIG. 10. Profuse cross-slip in a 14 at.%Al single crystal loaded to 1.25 kg/mm*. x 500.
to move
“unlocked”
(pre-strained)
dislocations
was
be present at one end of the crystal gage length, and
found to be only 20-25 per cent of the stress necessary
tests conduction
R = 1.0should in general show R - 0.1. The observa-
to move
this conclusion.
copper(l)
with
larger strains than those with tions, Fig. 2, support which deform
in-homogeneously
ing (easy glide) microstraining.
also deform
Thus, crystals
during macrostrainin this manner
during
“locked”
dislocations. In
(as-recrystallized
This behavior
in either
or the alloy single crystals, Fig. 6.
interpreting
the
copper
single
crystals,
discuss
and
eliminate
frictional
effects,
proportional extended if any,
or strain-aged)
is not observed
microstraining Rosenfield a
behavior
and
mechanism
see their equation
(1).
in
Averbach based
upon
Here 7. is
to (exp-pu), where w is the width of the
dislocations with
(the other variables vary little,
composition).
This is also easily
dis-
regarded for the c&u-Al
crystals.
Since the stacking
fault
with
content,(13)
energy
decreases
Al
w in-
creases(14) and 7. should decrease whereas an increase FIG. 9. Primary and cross-slip lines in a 14 at.% x 500. single crystal loaded to 1.25 kg/mm*.
The test on the 0.5 at.% performed validity
before
these facts
of the observed
However,
Al crystal,
is observed.
Al
Fig. 3, was
were known,
and the
The generation of sources with the unpinned length of dislocation controlling 7. is another possibility. Using the line tension approximation,
results might be questioned.
70=-,
since this alloy shows a high density of very
fine slip lines completely
covering
the gage length of
the crystal after 0.01 shear atrain, is probably
homogeneous
the following
the microstraining
along the gage length.
discussions,
the observed
In
data in this
crystal are assumed to be the “true” values, although this is a point which requires confirmation. With respect to an interpretation
of the magnitude
Gh
where G is the shear modulus the Burgers vector of unpinned
(1)
1 (4.9 x lo3 kg/mms),
b
(2.6 x 1OV cm), and 1 the length
dislocation,
values
of 1 are obtained
varying from 1.7 x 10-s cm for the 0.5 at.%
Al alloy
to 3.2 x 10W4cm for the 14 at.% Al alloy. If the pinning is due to forest dislocations, calculated forest densities,
pr( = E2), increase
from
3 x lo5 crnm2 to
of -ro, Fig. 6 shows that r. increases with prior plastic
9.9 x lo6 crnA2 for the same two alloys, respectively.
strain and eventually
pinning
These values are reasonable numbers based upon etch pit densities of 1-6 x lo6 cm-2 found in a-brass single
mechanism, such as Cottrell locking, for controlling Once plastic deformation begins, the stress neces70. sary to move what might be considered as “unlocked”
crystals.(15) In a similar manner, Rosenfield and Averbach calculate a I value of ~6 x 1O-3 cm for their observed 7. in copper single crystals. The
dislocations does not decrease as would be expected. In a recent microstraining investigation in polycrystalline niobium,u2) which is b.c.c. and amenable
authors felt that this value was too large, and concluded that overcoming the line tension of a dislocation was not the mechanism controlling 70. In addi-
to interstitial
tion, the temperature
This
behavior
should
(elastic)
becomes
independent
eliminate
locking,
any solute
of strain.
the stress necessary
dependency
of r. was greater
KOPPENAAL:
MICROSTRAINING
IN a&-Al
SINGLE CRYSTALS
543
than could be accounted for from the temperature dependency of the shear modulus by equation (1). Rosenfield and Averbach explained their results with an alternate mechanism based upon the stress necessary to move the leading partial of an extended dislocation. The application of this theory to the temperature dependency of the NIO-~ “yield stress” gave reasonable stacking fault energies for Cu and Al, and was later?@ used to calculate both the stacking fault energy of disordered CusAu and the anti-phase domain boundary energy of ordered CusAu. However, an argument against the application of the Rosenfield and Averbach theory has been made(16j with an analysis of the dislocation density, amount of motion per dislocation, and resulting strain. For example, using the previously calculated dislocation density of ~10’ cm-2 for the 14 at.76 Al crystal, the dislocation density on the primary slip system would be ~10~ cm-2. Using the relationship, y = BLN,
(2)
where y is the shear strain, L the length of travel per dislocation, and N the number of moving dislocations per unit area, the motion of a single Burgers vector by each of the primary dislocations would produce a strain of ~5 x 10-lo. Since the minimum measurable strain in these investigations is 1 x lC@, 70 does not represent the stress corresponding to the initial stage of plastic deformation, and the Rosenfield and Averbach theory is not applicable. Thus, plastic deformation begins at some stress Too, but this stress can not be measured with available strain detection equipment. Once plastic deformation starts, Fig. 3 shows that an -parabolic relationship exists between stress and strain. The data in this figure are ~plot~d in Fig. 11 as the square root of the plastic strain vs. stress, and linear relationships are found for each curve with the exception of two general areas. Deviations are observed at low strains for alloys of 7.5-14 at.% Al and at high strains for the 12 and 14 at.% Al alloys. These deviations will be discussed later. Using the slopes of the straight lines in Fig. 11 and the workhardening relationship given by Blott,(l’)
-0
0.2
0.4
RESOLVED
0.6
0.8
1.0
SHEAR STRESS, kg -
rn&*
FIU. 11. Squareroot of plastic shear strain vs. stressfor curves from Fig. 4.
the agreement appears to be fairly good, and supports the concept of dislocation generation at r0 since the values are obtained with independent sets of experimental data. In the past, researchers have not used equation (3) to explain work-hardening relationships in single crystals; the ray112 dependency exists only when 1 is constant, and this is not expected during stage II in the deformation process. However, I should be constant during the initial microstraining stage, and equation (3) is seen to be applicable to the present me~~ments. Since the microstraining in the higher solute crystals has already been established as being inhomogeneous, the use of equation (3) for these alloys However, a was initially viewed with caution. comparison of the work-hardening parameter ~+i/~/d~ for the data in Fig. 2 tends to eliminate the exclusion of equation (3). The value of dyi12/& for crystal F4-4, where R = 1.0, is 5.0 x 10m2mm2/kg (slope of the 12 at.% Al crystal shown in Fig. 12). The data for the other three crystals in Fig. 2 where R - 0.1 was plotted on a {st~in)1’2-stress basis, and ~~~~=I~T TABLE2. Length of unpinned dislocation at.% Al
an independent calculation of t can be made. Values of 1 are obtained varying from 2.2 x IO-3 cm to 0.85x lop4 cm in the 0.5 and 14 at.% Al alloys, respectively. Table 2 shows the E distance for all alloys obtained by equations (1) and (3). Considering the approximations used in equations (1) and (3),
CkI*
0.5 1.5 12 14
1, em equation (1) 6.7 1.7 6.1 3.6 3.2
x x x x x
1O-3 10-z 10-a 10-d lo-*
1, cm equation (3) 2.2 0.49 8.5 2.5 0.85
x x x x x
10-a lo-* 10-t 10-a lo-’
* Values calculsted from data of Rosenfield and Aver-
b&&W
544
ACTA
METALLURGICA,
values of 2.8 x 10-2, 5.2 x 10-2, and 3.1 x 10-r mm2/kg were obtained for crystals F2-4, F2-5 and Fl-1, respectively. Thus, even though the strain for a particular stress varied in these tests, the .uyils dependency is still observed, and the work-hardening parameters, o$J/~/G!T,varied by less than a factor of two. Some of the difference in these observed workhardening parameters could easily be orientation effects. Crystals F2-4 and F4-4 both showed approximately the same 7,, (363 and 358 g/mm2, respectively) but F2-4 displayed a lower dy1f2/& parameter. The resolved shear stress on the conjugate slip system in F2-4 is 86 per cent of the primary system, while in F4-4 it is only 42 per cent. Thus, if it takes ~360 g/mm 2 to activate a source in these 12 at.% Al crystals, sources on the conjugate system would become active at a resolved shear stress on the primary system of -430 and ~850 g/mm2 in crystals F2-4 and F4-4, respectively. Hence, small amounts of conjugate slip are presumably occurring much earlier in the deformation of crystal F2-4, which in turn would lead to higher work-hardening rate (smaller dy1J2/& parameter) through the formation of CottrellLomer sessile dislocations. Returning to Fig. 11, the deviations from the straight lines at small strains could represent the activation of sources over a small range of stress due to variations in the actual 1 distance. With regards to the deviations at high strains, a number of observations indicate that this is caused by the cross slip which occurs in the high alloy crystals. A previous investigationoO) showed that the amount of cross slip seen in Figs. 8,9 and 10 is about an order of magnitude larger in 14 at.% Al crystals than in 7.5 at.% Al alloys. This supports the behavior in Fig. 11 since the former shows deviations at high strains while the latter does not. Further, the deviations from the curve shown in Fig. 5 are in a similar fashion. In addition, the deviation in the 14 at.% Al crystal begins at about 0.9 kg/mm2, Fig. 11, and very limited amounts of cross slip were observed after stressing to 1.00 kg/mm2, Fig. 10. Finally, 7. in the 14 at.% Al alloy becomes independent of strain at a value of about 0.95 kg/mm2, Fig. 6, and since this is about the same stress level as the other two observations, it may represent the stress at which limited amounts of cross slip can take place. At a resolved shear stress of 1.00 kg/mm2 on the primary slip system for the crystal shown in Fig. 9, the resolved shear stress on the cross slip system was 200 g/mm2. Since a resolved shear stress of 394 g/mm2 appears to be the stress necessary to activate a source, the difference, 194 g/mm2, must have been supplied by interactions of
VOL.
11, 1963
the cross slip sources and primary dislocations. The quantitative relationship for the activation of cross slip sources given by Avery and Backofenos) was used to calculate the dislocation spacing on the primary slip system necessary to activate these sources. This spacing is calculated to be 0.6 p. Meakin and Wilsdorfug) measured the distance between dislocations in isolated pileups in a-brass single crystals deformed into easy glide and obtained values of about 0.1-0.5 ,U at the leading end of the pileups. The Meakin and Wilsdorf spacings are expected to be smaller since the resolved shear stress under which the pileups were formed was ~60-100 per cent larger for their determinations. Thus, the constant 7. level in Fig. 6 could represent the stress necessary to activate sources on the cross slip system, at least in the high solute crystals. The same explanation could also be given for Cu and the dilute alloys; cross slip is not observed in these cases, but this may be due to resolution limitations (including observations made with an electron microscope). Thus, cross slip is concluded to be cause of the deviations at high strains in the 12 and 14 at.% Al crystals seen in Fig. 11. Equation (3) is seen to be independent of the distance between the barriers which leads to the ~uyl’~ behavior. Using the relationship I, =
2n G% reg 7T(7,,2-
To2) ’
(4)
where 1, is the spacing of the barriers and n the number of dislocations piled up at the barriers during easy glide, the barrier spacing can be calculated by assuming a value for n. From the work of Meakin and Wilsdorf,09) n is ~25 in u-brass single crystals, and this value is used for the 14 at.% Al crystal because of the similarities in mechanical properties of the two alloys. With this assumption, 1, in equation (4) is calculated to be 14 x 1O-4 cm, and pb, the barrier density, becomes 5.1 x lo5 cm-2. Thus, pf N 2Op,. In the easy-glide deformation of u-brass single crystals, Meakin and Wilsdorf(15) experimentally observed a pb of ~5 x lo5 cm2, and pr N lop,. Their explanation, which explains the present results, is that the barriers are sessile Cottrell-Lomer dislocations formed by reactions of the glidingprimarydislocations and the forest dislocations which have the appropriate Burgers vector. With this model, the barrier density is expected to be about an order of magnitude less than the forest dislocation density. As also pointed out by these researchers, the strength of the barriers in u-brass are expected to be stronger than in pure copper because of the decrease in stacking fault energy with solute additions (wider extended dislocations).
KOPPENAAL:
MICROSTRAINING
IN
ctCu-Al
SINGLE
CRYSTALS
545
Thus, the easy glide stress, which (for a particular replacing N by 2np,, where ps is the density of distemperature and strain rate) represents the stress location sources, the source density computes to necessary for steady-state motion of dislocations 4.6 x IO5 cm-2. Since the primary dislocation density through or around these barriers, increases with was ~10~ cm-2, this calculation indicates that approxisolute content because there are more and stronger mately one-half of the primary dislocations have barriers. Whereas the Meakin and Wilsdorf report acted as sources at a stress of 0.80 kg/mm2 describes the steady-state condition, the present Finally, it is felt that additional measurements of investigation yields information about the pre-steady the microstrain behavior in aCu-Al single crystals are state condition. The two reports are seen to be necessary before any definite conclusions can be made. compatible. Included in these are the variables of testing temperaIn a previous investigation dealing with the solid ture and degree of local order, the effects of which solution strengthening mechanism in aCu-Al single have already(718) been evaluated on the flow stress in crystals,(s) the strengthening in T,~ at temperatures these alloy single crystals. < 296°K was presumed to arise from the cutting of SUMMARY forest dislocations, which become wider with Al The following information has been obtained in this content through the decrease in stacking fault energy. On the basis of the present investigation, this needs investigation regarding microstraining in ~cu-Al to be modified only to the extent of considering the single crystals. (1) Plastic deformation begins at some stress T’~, forest dislocations capable of forming Cottrell-Lomer barriers with the gliding dislocations rather than the but due to limitations in strain detection, TO,,is not measurable. Hence, the effect of solutes on the very entire forest. initial “yielding” is not known. were noted to show the same relative T,, and re9 (2) The stress, ~a, corresponding to the minimum degree of strengthening (Fig. 4) and both of these mechanical properties have been explained with a observable strain of 1 x 1OV increases with solute additions and has been explained on the basis of a single physical property, the number of dislocations dislocation generation mechanism. Calculations from present, see equations (1) and (4). Thus, the effect two independent sets of data for the unpinned length of solutes in producing more barriers could be a more of dislocation of each alloy are in reasonable agreement. important feature than that of resulting in stronger (3) Forest dislocations are presumed to control the barriers. length of unpinned dislocation, since reasonable In addition to the Meakin-Wilsdorf model, subdensities of the former can be calculated from the grain boundaries might also be effective dislocation latter. barriers. The calculated distance between barriers, (4) Beyond T,,, the microstrain follows a stress 14 ,D,in the 14 at.% Al alloy is also in the range of the a(strain)li2 dependency, and the barriers responsible probable sub-grain size. Meakin and Wilsdorfo5) for this behavior are thought to be sessile Cottrellfound an average sub-grain diameter of about 20 ,u Lomer dislocations and/or sub-grain boundaries. in a-brass single crystals, and observed sub-boundaries (5) In the high solute alloys, 12-14 at.% Al, acting as barriers in a similar fashion to the randomly pileups at these barriers assist in activating cross slip distributed barriers. Youngc21) and Livingston(22) sources at stresses about 213 of the easy glide stress; have reported upon pileups at sub-grain boundaries when this occurs, the ray112 dependency is no longer in Cu single crystals; however, Youngc21) also finds observed. evidence for Cottrell-Lomer barriers. The possibility (6) In classifying the effects of solutes as either of sub-grain size strengthening in c&u-Al single source or friction strengthening mechanisms, the crystals at high temperatures, >296”K, has been largest contribution to the easy glide stress is a previously(a) noted. frictional effect although a smaller source effect is In either case, the distance between the barriers can also present. be used to estimate the source density. Referring to Fig. 11, the ray1l2 dependency is maintained up to Note added in proof about 0.9 kg/mm2 in the 14 at.% Al crystal. Below Since the original submission of this report, the this stress, the generated dislocations are being held author has become aware of some recent work by up at the barriers. Using equation (a), -9 dislocations are in each pileup at a stress of 0.80 kg/mm2, and the Kingf2a) on dislocation etch-pit studies in aCu-Al amount of strain at this stress was 75 x 1OW (Fig. 3). single crystals after cycling at stresses below the easy Using equation (2) and approximating L as 1,/4 and glide stress. King’s results support the present
546
ACTA
investigation dislocations
in two ways.
METALLURGICA,
He observes
motion
of
at stresses below easy glide in the alloy
crystals (up to 14.8 at.% Al), and still more important, King
finds
numerous
pile
cycles at stresses of about Thus,
the concept
formed
after
three
of pile ups being formed
the initial microstrain
region of plastic
which is an “assumption” least qualitatively
ups
213 the easy glide stress. during
deformation,
in the present
work, is at
confirmed.
ACKNOWLEDGMENTS
The author Brittain,
would
like to thank
Professors
J. 0.
J. B. Cohen, and M. E. Fine for somewhat
simultaneously
suggesting the importance
strain investigation
in these alloys.
of a micro-
Professor
Fine
and Dr. T. H. Blewitt were kind enough to read this manuscript The
and offer valuable
experimental
work
suggestions.
reported
accomplished
while the author
the
Research
Armour
supported by Commission.
the
Foundation,
United
upon
here was
was associated
States
where Atomic
it
with was
Energy
REFERENCES 1. A. R. ROSENFIELD and B. L. AVERBACH, Beta Met. 8,624 (1960).
VOL.
11,
1963
D. A. THOMASand B. L. AVERBACH,Acta Met. 7,69 (1969). N. BROWN and K. F. LUKENS, JR., Acta Met. 9,106(1961). J. M. ROBERTS, see Ref. (3). J. C. SUITS and B. CKALMERS, Acta Met. 9. 854 (1961). W. J. WAQNER, JR., A. R. ROSENFIELD and-B. L. ‘A&BACH, Acta Met. 10, 256 (1962). 7. T. J. KOPPENAAL and M. E. FINE, Trans. Amer. Inst. Min. (Metall.) Engrs. 221, 1178 (1961). 8. T. 5. KOPPENAAL and M. E. FINE, Trans. Amer. Inst. Min. (MetalE.) Engrs. 224, 347 (1962). 9. T. 5. KOPPENAAL, PhD. Thesis, Northwestern Universit,y, 1961. 10. T. J. KOPPENAAL, Trans. Amer. Inst. Min. (Metall.) Engrs., 227, 257 (1963), 11. G. R. PIERCY, R. W. CAHN and A. H. COTTRELL,Acta Met. 3, 331 (1955). 12. T. J. KOPPENAAL and P. R. V. EVANS. submitted to Acta Met. 13. A. HOWIE and P. R. SWANN, Phil. Mag. 6, 1215 (1961). 14. A, H. COTTRELL,D&locations and Plastic Flow in Crystals, p. 74. Clarendon Press, Oxford (1953). 15. 5. D. MEAKIN and H. G. F. WILSDORF, Trans. Amer. Inst. Min. (M&all.) Engrs. 218, 737 (1960). 16. T. J. KOPPENAAL, Acta Met., 11, 85 (1963). N. F. MOTT, Proc. Phys. Sot. Lond. 43, 1151 (1952). ::: D. H. AVERY and W. A. BACKOFEN, Trans. Amer. Inst. Min. (Metall.) Engrs. in press. 19. J. D. MEAKIN and H. G. F. WILSDORF. Trans. Amer. Inst. Min. (Met&Z.) Engrs. 212, 745 (1960).’ 20. T. VREELAND, JR., D. S. WOOD and D. S. CLARK, Acta Met. 1, 414 (1953). 21. F. W. YOUNG. JR.. J. Avvl. Phvs. 33. 963 (1962). 22. J. D. LIVIN&ON,~J. A&Z. Ph&. 31,1076 ‘(1966). 23. A. H. KING, submitted to Nature, Lond. 2. 3. 4. 5. 6.