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The deformation of the intermetallic compound TlBi2
THE DEFORMATION
OF THE INTERMETALLIC
P. M. ROBINSON?
COMPOUND
TlBi2*
and M. B. BEVER$
The deformation behavior of the intermetallic compound TlBi, at 25”C, which is equivalent to a~~rox~ately 0.6 of its absolute melting point, has been investigated. The changes in electrical resistivity of specimens of two grain sizes after deformation in torsion have been measured as a function of &rain and strain rate. The tensile properties of specimens of three grain sizes at different strain rates have been measured. Metallographic examinations and microhardness measurements have also been carried out. The energy stored in specimens of one gram size after deformation in torsion has been measured by liquid metal solution calorimetry. ‘Ibe compound TlBi, deformed at 25°C may behave in either a ductile or a brittle manner depending on the strain rate and the grain size of the specimens. At low strain rates the compound is ductile, a yield hump is observed in the stress-strain curves and the resistivity after defo~ation in torsion reaches nearly constant values with increasing strain. These results are consistent with the indications of gram bom&x-y sliding observed by metallographic examination of specimens deformed at low strain rates. At high strain rates, the compound is brittle, no yield hump is observed and the resistivity after deformation in torsion continues to increase with strain, Metallographic examination indicated that at high strain rates the compound deforms primarily by slip within the grains with negligible gram boundary sliding. An increase in the grain size of the specimens affects the change in resistivity on deformation in a similar way as an increase in the strain rate, but it affects the yield stress in the opposite way. The energy st,ored in the compound TIBi, after deformation by slip is lower than that stored in the ordered in~rme~~llic compounds Cu,Au and AgMg deformed to the same strain. LA
DEFORMATION
DU
COMPOSE
INTERMETALLIQUE
TlBi,
Les auteurs one Btudie le comportement it la deformation du compose intermetallique TlBi, k 25’C, temperature Bquivalant it peu pres it 0,6 de son point de fusion absolu. Les variations de la resistiviti: electrique pour deux grosseurs de grains apres une deformation par torsion ont ete mesurees en fonction de la deformation et de la vitesse de d&formation. Des essais de traction ont Bte effect&s a dif%rents taux de deformation pour trois grosseurs de grains. Des examens m~tallographiques et des mesures de L’&ergie emmagasinee apres nne deformation de torsion microdurete ont Bgalement ete effect&s. dans des Bprouvettes ayant une certaine grosseur de grains a Bt6 mesuree par calorimetric de solutions metalliques liquides. Le comportement du compose TlBi, deform& it 25°C peut etre soit ductile, soit fragile, selon la vitesse de deformation et le diametre des grains. Pour les faibles vitesses de deformation, le compose est ductile, la courbe tension-deformation presente un accident a la limite Blastique et la resistivite, apres une deformation en torsion atteint une valeur relativement constante pour des deformations croissantes. Ces resultats sont en accord aveo le glissement des joints de grains observe en metallographie pour des 6prouvettes deform&s sous de faibles vitesses de dbformation. Pour ies vitesses de deformation elevees, le compose devient fragile, la eourbe tension~d~fo~lation ne presente plus d’accident et la resistivitti apres une deformation de torsion augmente continuellement aveo la dbformation. Les examens metallographiques indiquent que le compose se deforme alors principalement par glissement a l’interieur des grains et que le glissement des joints est negligeable. IJne augmentation de la grosseur des grains affecte la resistivite d’une fapon analogue a un accroissement de la vitesse de d&formation et affecte la limite elastique dans le sens oppose. L’energie emmagasinee dans le compose TlBi, apr&s deformation par glissement est plus faible que eelle emmagasin&e dans les composes inte~~talllques ordonnes C&Au et AgMg ayant subi la meme deformation. DIE
VERFORMUNG
DER
I~TERMETA~LISCHE~
VERBINDUNG
TlBi,
Das Verformungsverhalten der intermetallischen Verbindung TIBi, wurde bei 25°C (entsprechend etwa 0,6 der absoluten Schmelztemperatur) untersucht. Anderungen des elektrischen Widerstandes von Proben mit zwei verschiedenen KorngrBOen werden nach Torsionsvorformung in Abhilngigkeit von Dehnung und Dehnungsgeschwindigkeit gemessen. Die mechanischen Eigenschaften wurden an Proben mit drei versobiedenen Korngrijfien bei verschiedenen Dehnungsgeschwindigkeiten gcmessen. Ferner wurden metallographische Untersuchungen und ~~rtemessungen durchgefiihrt. Die gespeicherte Energie wurde fiir eine Korngr66e nach ~o~ionsverformuxlg mittels Metall~sungskalorimetrie gemeasen. Die Verbindung TlBl., ist bei 25°C duktil oder spriide, je nach Dehn~mgsgeschwindigkeit und Korngr613e der Proben. Bei klemen Dehnungsgeschwindigkeiten ist die Verbindung duktil, es wird eine FlieDgrenze in der Verfestigungskurve beobachtet, und der elektrische Widerstand nach Torsionsverfocmung erreicht mit zunehmender Dehnung fast konstante Werte. Diese Ergebnisse sind konsistent mit den Hinweisen fur Korngrenzengleiten bei der metallographischen Untersuchung von Proben, die bei kleinen Dehnungsgeschwindigkeiten verformt wurden. Bei hohen Verform~in~gesehwindigkeiten ist die Verbindung sprode, man beobachtet keine FlieSgrenze, und der elektrische Widerstand nach Torsions~Brfo~ung nimmt mit der Dehnung ZU. ~~etallographis~he Un~rsu~hungen deuten an, daf3 bei hohen De~~gsgesc~windigkeiten die Verbindrmg haupts5chlich durch Abgleiten innerhalb der Korner und nur wenig durch Korngrenzcngleitung verformt wird. Eine Zunahme der KorngrGBe der Probe beeinfluBt die Widerstands&ndorung bei Verformung iihnlich wie eine Zunahme der Dehnungsgescbwindigkeit. Sie beeinflul3t die Fliellspannung jedooh in entgegengesetzter Richtung. Die in der Verbindung TlBi, nach Verformung durch Abgleitung gespeicherte Energie ist kleiner als diojenige in den geordneten intermetallischen Verbindungen Cu,Au und AgMg bei gleichem Verformungsgrad. -_ ._ * Received August 13, 1965; revised October 27, 1965. i Division of Sponsored Research, Massachusetts Institute of Technology. $ Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts. ACTA
METALLURGICA,
VOL.
14, JUNE
1966
693
694
ACTA
METALLURGICA,
1. INTRODUCTION
The mechanical behavior of intermetahio compounds is greatly influenced by the ~mperature. They tend to be brittle at temperatures below approximately 0.6 of their absolute melting point, but become ductile at higher temperatures.(l) Possible explanations of the transition from ductile to brittle behavior are the effects of ~mperature on (1) the degree of order in the compound, (2) the ease of dislocation generation and movement, (3) the number of operative slip systems and (4) localized deformation at grain boundaries. In the research reported here, the relative contributions of these factors to the deformation of the intermeta~ie compound TlBi, at room temperature have been investigated. The melting point of the congruently melting composition of TlBi, is 213YY and room temperature, therefore, is approximately 0.6 of the absolute melting point, On deforming the oompound in this critical temperat~e range, changes in such variables as the strain rate and grain size can determine whether the compound behaves in a brittle or ductile manner. The compound TlBi, exists over a composition range extending from 56.0 to 61.4 at. ‘4 bismuth at 20°C; its stoic~ometric composition lies outside the homogeneity range at room temperature.t2t The structure of TlBi, is now believed to be of the N&In (B8) type@a4)rather than the AlB, (C32) type reported earlier.(6) Bismuth atoms probably form a hexagonal sublattice while the thallium atoms and the bismuth atoms in excess of those required to form the sublattice occupy the octahedral and trigonal sites at random.(4) The compound TlBi, can be formed into wire by extrusion at room temperature.@) Tensile tests at 27“G on wire specimens armealed for one hour at 75°C have shown that the yield stress and elongation depend strongly on the strain rate. For example, the yield strength and elongation change from approximately 6,000 psi and 55 % at a strain rate of 0.005 per min to 8,000 psi and 5 % at a strain rate of 0.02 per min.@J) In the investigation reported here, the tensile properties of the compound and the changes in electrical resistivity have been measured at different strain rates and with specimens of different grain sizes. Metallographic examinations and microhardness measurements have been carried out. The energy stored in specter of one grain size has been measured as a function of strain at one strain rate. 2. MATERIALS
Samples of the compound TlBi, containing 60 at. % bismuth were prepared by melting 99.99% bismuth
VOL.
14, 1966
(Mallinckrodt Chemical Works) and 99.99 % thallium (Amend Drug and Chemical Co.) in sealed, evacuated Vyoor tubes of 0.6 in. dia. This composition, rather than that of highest melting point, was chosen bectause the latter does not lie within the homogeneity range at room temperature.cz) The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The ingots were crushed and melted again in sealed, evacuated Vycor tubes of 0.2 in. dia. in order to obtain ingots of suitable diameter for extrusion. The melts were held for approximately one hour and quenched into iced brine. The ingots were homogenized for 48 hr at 100°C. Metallographic examination of repre~n~tive sections did not reveal any evidence of second phases or segregation. Rods of 1 in. length and 0.185 in. dia. machined from the ingots were extruded in one pass at room temperature to 0.040 in. dia. wire. Molybdenum ~sulphide was used as a lubricant. The extrusion load was 8,500 psi and the ram speed approximately 0.2 in. per min. Room temperature is above the recrystallization temperature of the compound TlBi, after heavy deformation. The extruded wire which had been annealed at room temperature consisted of equi-axed recrystallized grains with an average diameter of 37 ,LL. Annealing for 1 hr at 75°C and annealing for 1 hr at 150°C produced grains of 50 and 190 ,u dia., respectively. The grain diameters were determined by m~tiplying the average linear intercept in a plane section by 1.65.f’) 3. ELECTRICAL
RESISTIVITY SPECIMENS
OF ANNEALED
The electrical resistivity of specimens of 0.040 in. dia. wire of the compound TlBi, was measured by a po~ntiometric method with a precision of 0.2 %. The resistivity, at -.l95*C, of specimens extruded and annealed at room temperature was 41.50 &J-cm and that of specimens annealed for one hour at 75% was 41.25 $&cm. A resistivity of this magnitude is to be expected for a compound containing bismuth, which has only few conduction electrons in the second Brillouin zone.(s) The temperature coefficient of resistivity of the compound TlBi,, unlike that of elemental bismuth, increased slightly with increasing temperature over the range -195’ to 200°C. The average temperature coefficient of resistivity over this range was 0.15 pi&cm per “C. In order to determine whether the annealing treatment affected the degree of order in the compound, specimens were annealed for one hour at IQO’C and either quenched to -195°C 01‘ slowly
ROBINSON
AND
BEVER:
cooled in 52 hr to -195°C. Their resistivity was measured on heating to various temperatures between -195’ and 200°C. The resistivities of the quenched and slowly cooled specimens were not sig~fi~ntly different. It is unlikely, therefore, that the degree of order in the compound was affected by the annealing treatments at 75” and 150°C used to produce specimens of different grain sizes. The resistivity, at -195”C, of specimens of TlBi, which had been placed in liquid nitrogen immediately after extrusion did not change during annealing at room temperature for 2 to 3 days. The resistivity of extruded specimens annealed at room temperature was in close agreement with that of specimens annealed for one hour at 75°C. It is probable that the compound recrystallizes immediately at room temperature after the reduction in area of approximately 78 % received during extrusion. 4. ELECTRICAL
RESISTIVITY SPECIMENS
OF DEFORMED
The electrical resistivity of specimens of the compound TlBi, with a grain size of 37 and 50 p average dia. was measured as a fun&ion of strain in torsion after deformation at 25°C at different strain rates. Specimens with larger grain sizes could not be deformed appreciably in torsion because they were too brittle. The resistance of each specimen was measured before and after deformation. The specimens were immersed in liquid nitrogen immediately after deformation at 25%. The shear strain at the surface of the specimen was measured as nnd/l and the corresponding strain rate as godly, where n is the number of turns, *Gthe number of turns per min, d the diameter of the specimen and 1 its length. The resistivity of specimens of 50 p grain dia. deformed at strain rates exceeding 0.10 per min increased with increasing strain at 25°C up to the largest strains used. After deformation at a strain rate of 0.03 per min, however, the resistivity as a function of strain reached a nearly constant value at strains larger than approximately 0.06 (Fig. I). The specimens of 37 p grain dia. showed the same general dependence of the resistivity on strain as the specimens of 50 p grain dia., but nearly constant values of the resistivity were reached at the ~omparatiyely high strain rate of 0.22 per min (Fig. 2). The increment’ in the resistivity of specimens of the two grain sizes after a given strain increased rapidly wit#han increase in the strain rate, as shown in Fig. 3 for a strain of 0.63. At a given strain rate, the change in resistivity was greater for the specimens with large than specimens with small grain size (Fig. 3). The change in resistivity on deforming the compound
DEFORMATION
OF
695
TlBi,
TlBi, at 25”C, therefore, is a function of the strain, the strain rate and the grain size of the specimen. The changes in resistivity after deformation at 25°C may be attributed to an increase in the dislocation density within the grains. The attainment of nearly constant values of the resistivity after deformation at low strain rates suggests that the dislocation density
$
48.0
; .C 2 .u E i, .t .> z z a”
0.15 46.0 0 IO
44.0
0.03
42.0 Average of undeformed
._.-a_/_ 0.2
0
0.4
0.6 Strom,
-
specimens 0.8 vnd/l
..A 1.0
12
FIG. 1. The resistivity, measured at
-195X’, of the compound TlBi, after deformation in torsion at different strain rates at 25°C aa a function of the shear strain at the surface of the specimens. Average grain diameter of specimens: 50 p.
48’orl-=-l
42.0 FAverage
40.0 ’ 0
I 0.2
of undeformed
I 0.4
I I 0.6 0.8 Strain, wnd/P
specimens
I 1.0
1.2
2. The resistivity, measured at -195W, of the compound TlBi, after deformation in torsion et different strain rates at 25°C as a function of the shear strain at the surface of the specimens. Average grain diameter of specimens: 37 ,u.
FIG.
ACTA 80
I
I
I
Grain
Strain
0.2 rate,
0.3 rlid/X,
diameter:
0.4 per mln
VOL.
14,
1966 5. TENSILE
I
diameter:
Grain
0. I
METALLURGICA,
I 0.5
FIG. 3. The change in resistivity on deforming the compound TlBi, in torsion, at 25”C, to a shear strain, mad/E, of 0.63 as a function of strain rate for specimens of two different grain sizes.
does not increase appreciably above a critical value of the strain. If this behavior were associated with recovery or recrystallization, the change in resistivity would depend on the time the specimen is at room temperature during deformation; this time is longer for deformation at low than at high strain rates. The time at room temperature during deformation at the low strain rates was less than 10 min except for the specimens deformed to strains of 0.63 and 0.94 at a rate of 0.03 per min, which were at room temperature for 20 and 30 min, respectively. The resistivity of specimens which had been deformed to a strain of 0.82 at a strain rate of 0.22 per min, however, did not change on holding for 40 min at 25°C. On annealing at 75°C after the same deformation, the change in resistivity with time indicated that the specimens did not completely recrystallize until after 60 min at this temperature. Under the experimental conditions used, therefore, the change in resistivity was not affected by recrystallization occurring during deformation at room temperature. The deformation process is aided by thermal fluctuations. On deforming at high homologous temperatures, a decrease in strain rate is equivalent to an increase in temperature. It is possible, therefore, that on deforming at low strain rates the mutual annihilation of dislocations occurs to a greater extent than at high strain rates. Grain boundary sliding may also take place at the low strain rates. These processes would account for the nearly constant values of the resistivity as a function of strain on deforming at low
TESTS
Wire specimens (0.040 in. dia., 1.0 in. gauge length) of the compound TlBi, with average grain diameters of 37,50 and 190 ,Mwere tested on an Instron machine. The tests were carried out at 25’ f 1°C with crosshead speeds ranging from 0.002 to 0.100 in. per min. The stress is reported as the true stress and the strain as the true strain; the strain rates are reported as the increase in length of the specimen per unit length per min. The estimated precision was f40 psi. Typical curves of the true stress versus true strain at different strain rates are shown in Fig. 4 for specimens with an average grain diameter of 50 p. At strain rates of 0.020, 0.050 and 0.100 per min, the specimens fractured soon after the yield stress had been reached. At strain rates of 0.010 per min and slower rates a “yield hump” was observed after an initial period of rapid work hardening. Only slight work hardening occurred in the region beyond the yield hump and the specimens deformed to elongations of up to 70%. The general form of these curves for specimens of the compound TlBi, deformed at low strain rates was similar to that of published curves for specimens of the compound In,Bi, which has the same structure,(3*4) deformed under similar conditions.@) The yield stress at 0.2 % strain offset for specimens of TlBi, is plotted in Fig. 5 as a function of strain rate. The specimens with an average grain diameter of 190 ,U were too brittle to be tested at strain rates exceeding 0.020 per min. The yield stress of specimens of different grain sizes increased rapidly with an
True
strain
Fm. 4. Typical true stress-true strain curves, at 25% for the compound TlBi, at different strain rates. Average prain diameter of snecimens: 50 u.
ROBINSON 9,500
r 1!
I
1
/
/Y,eld
AND
BEVER:
DEFORMATION
697
40
I
I
OF TlBi,
stress
b” 3.8 -B
Groin
diameter,
37
36
I
I
log
\
I
/
a02
0.04 Strain
4,000 0
t, ---_-_a.Elongation ---------0-e
I
0.06 rote,
per
I
/
008 rmn
0.10
I 0.12
These results obey the equation proposed which
predicts
a linear relation
stress a, and the quantity at strain rates in the
range of 0.002 to 0.020 per min.
For example,
CT?/ =
the
yield stress of specimens with a grain diameter of 50 ,u
where
increased
constants.
from
approximately
-3 i
FIG. 6. The logarithm of the yield stress at 0.2% offset of the compound TlBi, plotted against the logarithm of the strain rate for specimens of different grain sizes.
FIG. 5. The yield stress at 0.2 ‘A offset and the elongation of the compound TIBi,, at 25”C, as functions ofstrainrate.
increase in strain rate, especially
._._A
-2
-I
5,600 psi at a strain
d is the grain
by Petchdl)
between
the yield
d--1i2
k, f
k2d-1’2
diameter
The compliance
and
k, and
of the yield
k, are
stress with
rate of 0.002 per min to 8,300 psi at a strain rate of
this equation
shows that at the strain levels
0.100
sponding
the
70%
per min; and 2%,
be consistent
the corresponding respectively.
At high homologous
to
intragranular
yield
stress
the movement
the yield stress
on the strain rate since
slip is aided by thermal fluctuations.
The stress and
strain rate at constant
and strain are
temperature
related by the equation
the
of dislocations.
I
r--T
Stroln
Rate, ‘1
0.050
0.020 where ay is t’he flow stress, k a constant, coefficient.
d the strain
1
0.0 IO
A plot of
log a, versus log 8 (Fig. 6) shows that the change in the flow stress of TlBi, rate conforms other
at 0.2%
to this equation.
intermetallic
compounds
offset
0.005
with strain
The flow stress of changes
0.002
with strain
rate in the same general manner at high homologous temperatures, although the strain rate dependence may be smaller, as for AgMg,(lO) or larger, as for In,Bi,@) than for TlBi At a given strain fate, the yield stress increased with a decrease The
yield
in the grain size of the specimens.
st’ress at 0.2%
offset
at different
strain
rates is plotted in Fig. 7 as a function of the reciprocal of the square
root
of the average
grain diameter.
-__I
0.05
0.10
0.15
is
play a major
8,000 -
rate and m the work hardening
corre-
deformation
and that grain boundaries
role in inhibiting
by Wood.cQ
temperatures
to depend
were
These results appear
with those obtained
may be expected
elongations
to
0.20
d -~Z,in1cro”s-~2
FIG. 7. The yield stress at 0.2% offset of the compound TlBi,, at 25’C, as a function of the average grain diameter at various strain rates.
698
ACTA
METALLURGICA,
The unusual feature of the tensile behavior of the TIBi, is that at low strain rates, a yield hump is observed, followed by a region in which extensive elongation occurs with only slight work hardening. A similar yield hump has been observed on testing the compound In,Bi.(Q) In some respects, however, the tensile properties of these compounds differ. In contrast to TlBi,, an increase in the yield stress with increasing grain size has been observed for 1nzBi.u’) These observations have been explained on the assumption that dislocation generation is difficult in InQBi and that grain boundaries act as sources of dislocations rather than as barriers to their movement. The activation of many dislocation sources at grain boundaries once a critical stress level has been reached has been cited as the reason for the yield hump in 1nsBi.c’) If the yield hump in TlBi, is due to an initial di~culty of generating dislocations, the subsequent generation of dislocations must occur at sources other than those at grain boundaries. In the compound TlBi,, the difficulty of dislocation generation probably accounts only partly for the yield hump. The tensile results indicate that, at low strain rates, the mechanism of deformation changes in the region of the yield hump. It is possible that beyond the yield stress, work hardening occurs until the stress level is sufficiently high to cause grain boundary sliding. The specimens then deform with only slight work hardening to elongations of up to 70 %.
VOL.
14,
1966
compound
6. METALLOGRAPHY AND MICROHARDNESS MEASUREMENTS
~eta~o~aphic examinations were carried out on flat specimens which were prepared by casting into a mould machined in the shape of a tensile test piece 2.0 in. long, 0.25 in. wide and 0.125 in. thick. The cast specimens were heat treated to produce different grain sizes. The preparation of specimens of TlBi, for metallographic examination is difficult because the compound is soft. In addition, the time available for examination of the prepared surface is limited by the formation of an oxide film to approximately 15 min after polishing. Examination of the surfaces of flat tensile specimens which had been polished before deformation showed that the grain boundaries were in relief in the unetched specimens after deformation at 25’33 and at strain rates below 0.020 per min. This observation indicates that sliding of the grains on either side of the boundary relative to one another had taken place. Figure 8(a) shows the ~splacement of two scratches crossing a grain boundary in an unetched specimen deformed at a strain rate of 0.010 per min. Since the scratches remained straight within the grains, the
FIU. S(a). Dis&wmwnt of scratches crossina a erain bound& in in nnetohed specimen of the Gomp&md TlBi, after tensile deform&ion of approximately 20% at a strttin r&e of 0.010 per min. Fold at the grain boundary at bottom left of photo~cro~~ph should be noted. x 320
deformation was probably confined to a narrow region along the grain boundary. A further indication of localized defo~ation was given by the formation of folds at the grain boundaries in specimens which were deformed at low strain rates; an example is shown in Fig. 8(a). The formation of folds is a common mechanism of accommodati~ grain bounds strains in metals deformed at low strain rates and high homologous temperatures.(is) In specimens of the compound TlBi,, the formation of voids at grain boundaries occurred during deformation at low strain rates (Fig. 8(b)). These voids were similar to those which have been observed at the grain boundaries of metals after creep testing at
FIG. 8(b). Voids and folds at the grain boundary in an unetched specimen of the compound TlBi, after tensile deformation of approximately 45 % at a strain rate of 0.005 per min. x 320
ROBINSON
AND BEVER:
temperatures. (13) The formation
elevated metals
has been attributed
vacancies
of voids in
to the condensation
at the grain bounclaries.(14)
DEFORMATION
of
On the other
OF
Microhardness
699
TIBi,
measurements
were carried out with
a load of 100 g on a series of polished
different grain sizes which had not been etched.
hand, it has been concluded from some experiments that the formation of voids occurs as the result of
results show that the compound
grain
on the grain size.
boundary
intermetallic
sliding.(15*16)
compound
in the vicinity
strain
the
case
occurred
which was usually
by
initiated meet,
photomicrograph
illustrates
to be expected
of TlBi,
intercrystalline
grain boundaries
the that
The
is soft;
the
hardness values range from 14 to 22 V.P.N. depending In contrast
metals at low homologous of TlBi,
increased
to the behavior
temperatures,
of
the hardness
with an increase in the grain size
at low
cracking,
at a triple point
as shown
where
in Fig. 8(c).
This
typical
intercrystalline
if extensive
grain boundary
sliding takes place during cleformation.(17) case, large
of
of folds
TlBi,
of
associated with grain boundary
of the tensile specimens
rates
cracking
In
the formation
of the voids (Fig. S(b)) indicates
the voids are probably sliding. Fracture
TlBi,,
specimens
tensile stresses develop
In such a
at the triple point
owing to shear stresses acting along the grain boundaries.(ls)
Figure 8(c) shows that, before the fracture
of this specimen
of TlBi,,
some
relieved by plastic deformation
of the stress was
and the formation
of
101
Slip bands deformation
were observed
the grains after
at strain rates greater than 0.020 per min.
Markings observed than
deformation
visible
after repolishing
twins
as they
and etching.
to occur on the pyramidal temperatures.
were
Slip may
not be
and basal planes
of TlBi,, both of which are close-packed, at high homologous
FIG. 9. The microhardness of the compound TIBi, as a function of the grain size of the specimens. Load 100 g.
within the grains were slip bands
rather expected
within
200 100 Groin diameter, microns
0
folds within the grains around the triple point.
on deforming
Grain boundary
Boundaries
of equi-axed,
recrystallized
grains were
observed around the hardness indentations and
unetched
diameter
specimens
with
an
in polished
average
of 37 and 50 ,U (Fig. 10(a)).
grain
These bound-
aries were placed in relief by grain boundary
sliding in
sliding did not appear to be the primary mechanism
of
the deformed region around the hardness indentation.
deformation
of
The
specimens
at the higher strain rates. deformed
Fracture
at high strain rates occurred
cleavage and intercrystalline
by
cracking.
grain
boundary
sliding
leads
to the irregular
outlines of the hardness indentations Localized
deformation
seen in Fig. 10(a).
at the grain boundaries
also
occurred in specimens having average grain diameters of 190 and 252 p, but only the sections of the boundaries in the vicinity visible.
of the indentations
An illustration
Slip bands
were made
of this is shown in Fig. 10(b).
were also observed
with
the hardness
in
grain
sizes
(Fig. 10(b)).
The increase in hardness of TlBi,
with
increasing
specimens
around
indentations
large
grain size (Fig. 9) is consistent
observations
of grain boundary
sliding
with these around
the
hardness indentations. 7. STORED
ENERGY
The energy stored in the compound TlBi, after deformation by torsion at 25°C at a strain rate of 0.22 per min was measured metry FIG. 8(c). Crack at a triple point and folds at the grain boundaries after tensile deformation to fracture at a strain rate of 0.005 per min. x 320
with bismuth
experiments
described
by metal solution
as solvent.
As shown
in the preceding
caloriby the
sections,
compound deforms at these strain rates primarfly slip rather than by grain boundary slicling.
the by
700
ACTA
METALLURGICA,
VOL.
14.
1966
In contrast to previous invesfigations of the stored energy of cold work in metals and intermetallic compounds, in the present investigation the compound TlBi, was worked at a temperature equivalent to approximately 0.6 of the absolute melting point. The values of the energy stored after deformation in torsion to different strains at a strain rate of 0.22 per minute are given below.
FIG. 10(a). Grain boundary sliding around hardness indentations in an unetched specimen of the compound TlBi,. Grain diameter: 150 /J. Load: 100 g x80
FIQ. 10(b). Grain boundary sliding and slip lines around hardness indentations in unetched specimens of the comGrain diameter: 190 ~1. Load: 1OOg. pound TlBi,. x 120
The stored energy was determined as the difference in the heat effects on solution of alternate additions of deformed and undeformed samples. The heat capacity of the calorimeter was determined by calibrating with bismuth. The values of the stored energy are based on a difference in the heat content of bismuth between 0” and 350°C of 4.96 kcal/g-atom. The calorimetric procedure and the method of calculation have been described elsewhere.czO) The specimens intended for the stored energy measurements were annealed for one hour at 75°C before deformation and had an average grain diameter of 50 ,u. Immediately after deformation the specimens were immersed in liquid nitrogen; all additions to the calorimeter were made from this temperature. In a typiml calorimetric run, three additions each of the deformed and undeformed compound were made.
Shear strain at the surface, m&/l
Stored energy Cal/g-atom
0.06 0.31 0.44
5 20 26
These values are higher than the energy stored in metals deformed at room temperature to comparable strains(21) but considerably lower than the energy stored in ordered phases such as CU,AU(~~)or AgMg.t23) This is to be expected for two reasons : the compound TlBi, appears to be only partially ordered and the temperature of deformation (room temperature) is a high homologous temperature. It is of interest to consider the ratio of the stored energy to the change in electrical resistivity after deforming TlBi, to a given strain with this ratio for other intermetallic compounds deformed to the same strain. In contrast. to metals, the energy stored in deformed intermetallic compounds depends not only on the dislocation density but also on the number of A-B bonds replaced by A-A and B-B bonds and on the associated energy effects. The change in resistivity due to the deformation of compounds depends mainly on the dislocation density and on the disorder produced by replacing the A-B bonds by A-A and B-B bonds. It depends only indirectly on the strength of the A-B bond. This dependence arises because the bond strength affects the degree of order in the compound and thus the type of line defect produced during deformation. In an ordered compound the stable line defect is a superdislocation. During deformation a minimum destruction of order occurs as the trailing dislocation of the superdislocation tends to reorder the material disordered by the leading dislocation. As the net destruction of order is relatively small, the change in resistivity is low. The stored energy, on the other hand, may be high because the energy associated with the A-B bonds broken may be large, although their number is small.
ROBINSON In a disordered
or partially
BEVER:
AND
ordered compound
stable line defect is a unit dislocation.
the
The change in
resistivity
on deforming
paratively
large, but the stored energy is low because
such a compound
of the small energy associated The ratio resistivity
of the stored
on deforming
energy
compounds
A relation
should
exist between
of the compound
which is a measure of the bond strength. and TlBi,
for the compounds
after deformation
heats
of
by torsion
by wire drawing formation.(24-26)
In Fig. 11,
CU,AU,(~~) AgMg’23)
strain at the surface of the specimen equivalent
in
to a
depends on the bond strength
this ratio and the heat of formation the ratio E,/Ap
bonds.
to the change
intermetallic
given strain, therefore, in the compound.
with the A-B
is com-
is plotted In
to a shear
of 0.31 or its against
agreement
their
with
the
DEFORMATION
701
OF TlBi,
1. The changes in electrical resistivity on deforming the compound
TlBi, in torsion at 0.6 of the absolute
melting point (25°C) depend on the strain, the strain rate and the grain size of the specimens. 1.1 On deforming at high strain rates sistivity the
increases with strain.
resistivity
as a function
nearly constant annihilation
of
values, probably
of
dislocations
the
re-
At low strain rates strain
reaches
owing to mutual
or
grain
boundary
sliding. 1.2 The
change
increases
in resistivity
rapidly
at a given
with an increase
strain
in strain rate
(except at very low strains). 1.3 At a given strain and strain rate, the change in resistivity
is greater in specimens of large grain size
than in specimens of small grain size. 2. The tensile behavior depends
of the compound
at 25°C
on the strain rate and the grain size of the
specimens. 2.1 At high strain rates the specimens fracture soon after the yield stress has been reached. 2.2 At low strain rates a yield hump is observed beyond
which only slight work hardening occurs.
2.3 The yield stress at a given strain rate is higher for
specimens
specimens
with
a small
grain
with a large grain size.
size than
the yield stress with grain size complies equation
due to Petch indicating
with the
that, at least in
the region of the yield stress, the deformation the compound 4.0
kcol/g
5.0
given grain size with strain rate tends to confirm
-o+om
FIG. 11. The ratio of the energy stored to the change
in electrical resistivitv for comnounds deformed at 25°C plotted against their geats of formation. The compounds TIBi, and AgMg were deformed in torsion to a shear strain of 0.31. The compound Cu,Au was deformed by wire drawing to an equivalent strain. See text for references.
arguments ratio
set forth in the preceding
increases
with
an
increase
paragraphs, in
the
heat
the of
that the compound 2.5 The elongation
but at low strain rates elongations 3. Metallographic
deforms
is a different
the melting point of each compound,
fraction
of
It would be of
interest to obtain the corresponding
data for a series
of compounds of the same structure same fraction of the melting point.
deformed
8. SUMMARY
The
main
conclusions
results
AND
of
at the
investigation
and
the
that can be drawn from them are sum-
marized below.
of up to 70 % are
indicates
examination
specimens
that
at high
polished strain
of the surfaces before rates
compound
by slip but at low strain rates appreciable
grain boundary
sliding takes place.
4. The hardness of the compound increase
the
of
deformation
increases with an
in the grain size of the specimens.
Grain boundary sliding takes place around the hardness indentations in specimens of all grain sizes tested. 5. The energy stored in the compound TlBi, after hot working in torsion at 25°C at a strain rate of 0.22
CONCLUSIONS
this
on the strain
is brittle at high strain rates
observed.
It should be noted that the results plotted in Fig. 11 are for compounds of different structures deformed at which
depends strongly
rate ; the compound
formation.
temperature,
deforms by slip in the region of
the yield stress.
flat tensile
room
of
is intragranular.
2.4 The change of the yield stress of specimens of a
-kTk-k--
0
-AH,
for
The change of
per min increases with increasing strain.
The energy
stored is considerably smaller than that stored in the ordered compounds Cu,Au and AgMg cold worked to
702
ACTA
METALLURGICA,
the same strains, but larger than the energy stored in metals cold worked to the same strains. 6. The results of the tensile tests indicate that up to a stress level corresponding to the maximum of the yield hump, the compound deforms at low strain rates and high homologous temperatures by slip within the grains. On deforming at these strain rates to strains in excess of the yield hump, however, grain boundary sliding appears to be a major mechanism of deformation. Mutual annihilation of dislocations may also occur under these conditions. At low strain rates and at strains in excess of the yield hump, therefore, the compound d&forms with slight work hardening and little change in electrical resistivity. 7. An increase in the strain rate tends to suppress the onset of grain boundary sliding. At high strain rates, therefore, the compound deforms at all strain levels by slip within the grains and work hardens after yielding until fracture occurs after small elongations. Under these conditions, the resistivity continues to increase with increasing strain in torsion. An increase in the grain size of the specimens affects the change in resistivity on deformation in a similar way as an increase in the strain rate, but it affects the yield stress in the opposite way. ACKNOWLEDGMENTS
The authors thank Dr. K. C. Chuang and Mr. Praveen Chaudhari for many helpful discussions. They are indebted to Dr. M. D. Banus of Lincoln Laboratory, Massachusetts Institute of Technology, for providing facilities for extrusion. The assistance of Mr. L. I. Sudenfield with the experimental work is gratefully acknowledged. This work was supported by the U.S. Atomic Energy Commission under Contract ATI30-lj-1002. I I
VOL.
14, 1966 REFERENCES
1. J. H. WESTBROOK,Mechanical Properties of Intermetallic Compounds--a Review of the Literature, in: Mechalzdcal Properties of Intermetallic Compound8 (edited by J. H. Westbrook). John Wiley, New York (1960). 2. M. HANSEN and K. ANDERKO, Constitution of Binary Alloys, 2nd ed. McGraw-Hill, New York (1958). 3. E. S. MAKAROV,Soviet Phys. Crystallogr. 3, 3 (1958). 4. B. GIESSEN, private communication, Massachusetts Institute of Technology, May 1965. 6. E. S. MAKAROV, Dokl. Akad. Naukuzbet. S.S.R. 74, 936 (1950). 6. D. L. WOOD, Extrusion of Intermetallic Compounds, in: Mechanical Properties of Intermetallic Compounds (edited by J. H. Westbrook) John Wiley, New York (1960). 7. C. S. SMITH and L. GUTTMAN, Trans. Am. Inst. Min. Metall. Engrs 197, 81 (1953). 8. N. F. MOTTand H. JONES. The T’heorvof the Proverties of Metals and Alloys, Chap& 7, p. 30% *Clarend& Presi, Oxford (1936). 9. R. GRIERSONand R. N. PARKINS, Trans. Met. Sot. AIME 253, 1000 (1965). 10. D. L. WOOD and J. H. WESTBROOK, Trans. Met. Sot. AIME 224. 1024 (19621. 11. N. J. PETCH,J. ITon &eel Inst. 174, 25 (1953). 12. H. C. CHANT and N. J. GRANT, Trans. Am. Inst. Min. Metal.!. Engrs. 206, 169 (1956). 13. N. J. GRANT and A. R. CHAUDHURI.CreeD and Fracture in: Creep and Recovery. Amer. Soo.‘Metafs, Metals Park, Ohio (1957). 14. R. W. BALLUFFI and L. L. SEIQLE, Acta Met. 5, 449 (1957). 15. C. W. CHEN and E. S. MACHLIN. Trans. Am. Inst. Min. ’ Metall. Engrs 209, 829 (1957). 16. J. INTRATERand E. S. MACHLIN,Acta Met. 7, 140 (1969). 17. H. C. CHANQ and N. J. GRANT, Trans. Am. Inst. Min. Metall. Engrs 206, 544 (1956). 18. C. ZENER, Micromechanism of Fracture in: B’nzcturing of Metals. Amer. Sot. Metals, Metals Park, Ohio (1948). 19. R. HULTQREN,R. L. ORR, P. D. ANDERSON,and K. K. KELLEY, Selected Values of Thermodynamic Properties of Metals and Alloys. John Wiley, New York (1963). 20. B. W. HOWLETT, J. S. LL. LEACH, L. B. TICKNOR,and M. B. BEVER, Rev. Scient. Ins&urn. 83, 619 (1962). 21. A. L. TITCEIENER and M. B. BEVER, Progr. Metal Phys. 7, 247 (1958). 22. J. B. COHENand M. B. BEVER, Trans. Met. Sot. AIME 218, 155 (1960). 23. P. M. ROBINSONand M. B. BEVER, Acta Met. 18, 647 (1965). 24. L. R. RUBIN, J. S. LL. LEACH and M. B. BEVER, Trans. Am. Inst. Min. Metall. Enars 208. 421 (1955). 25. P. M. ROBINSON and M.“B. B&ER, ‘Trak8. Met. Sot. AIME 230, 1487 (1964). 26. P. -_M. and M. B. BEVER, Trans. Met. Sot. __ ROBINSON _-- ..~_ ..^^_. AIM,8 ZBB,1908 (lYti5).
OF THE INTERMETALLIC
P. M. ROBINSON?
COMPOUND
TlBi2*
and M. B. BEVER$
The deformation behavior of the intermetallic compound TlBi, at 25”C, which is equivalent to a~~rox~ately 0.6 of its absolute melting point, has been investigated. The changes in electrical resistivity of specimens of two grain sizes after deformation in torsion have been measured as a function of &rain and strain rate. The tensile properties of specimens of three grain sizes at different strain rates have been measured. Metallographic examinations and microhardness measurements have also been carried out. The energy stored in specimens of one gram size after deformation in torsion has been measured by liquid metal solution calorimetry. ‘Ibe compound TlBi, deformed at 25°C may behave in either a ductile or a brittle manner depending on the strain rate and the grain size of the specimens. At low strain rates the compound is ductile, a yield hump is observed in the stress-strain curves and the resistivity after defo~ation in torsion reaches nearly constant values with increasing strain. These results are consistent with the indications of gram bom&x-y sliding observed by metallographic examination of specimens deformed at low strain rates. At high strain rates, the compound is brittle, no yield hump is observed and the resistivity after deformation in torsion continues to increase with strain, Metallographic examination indicated that at high strain rates the compound deforms primarily by slip within the grains with negligible gram boundary sliding. An increase in the grain size of the specimens affects the change in resistivity on deformation in a similar way as an increase in the strain rate, but it affects the yield stress in the opposite way. The energy st,ored in the compound TIBi, after deformation by slip is lower than that stored in the ordered in~rme~~llic compounds Cu,Au and AgMg deformed to the same strain. LA
DEFORMATION
DU
COMPOSE
INTERMETALLIQUE
TlBi,
Les auteurs one Btudie le comportement it la deformation du compose intermetallique TlBi, k 25’C, temperature Bquivalant it peu pres it 0,6 de son point de fusion absolu. Les variations de la resistiviti: electrique pour deux grosseurs de grains apres une deformation par torsion ont ete mesurees en fonction de la deformation et de la vitesse de d&formation. Des essais de traction ont Bte effect&s a dif%rents taux de deformation pour trois grosseurs de grains. Des examens m~tallographiques et des mesures de L’&ergie emmagasinee apres nne deformation de torsion microdurete ont Bgalement ete effect&s. dans des Bprouvettes ayant une certaine grosseur de grains a Bt6 mesuree par calorimetric de solutions metalliques liquides. Le comportement du compose TlBi, deform& it 25°C peut etre soit ductile, soit fragile, selon la vitesse de deformation et le diametre des grains. Pour les faibles vitesses de deformation, le compose est ductile, la courbe tension-deformation presente un accident a la limite Blastique et la resistivite, apres une deformation en torsion atteint une valeur relativement constante pour des deformations croissantes. Ces resultats sont en accord aveo le glissement des joints de grains observe en metallographie pour des 6prouvettes deform&s sous de faibles vitesses de dbformation. Pour ies vitesses de deformation elevees, le compose devient fragile, la eourbe tension~d~fo~lation ne presente plus d’accident et la resistivitti apres une deformation de torsion augmente continuellement aveo la dbformation. Les examens metallographiques indiquent que le compose se deforme alors principalement par glissement a l’interieur des grains et que le glissement des joints est negligeable. IJne augmentation de la grosseur des grains affecte la resistivite d’une fapon analogue a un accroissement de la vitesse de d&formation et affecte la limite elastique dans le sens oppose. L’energie emmagasinee dans le compose TlBi, apr&s deformation par glissement est plus faible que eelle emmagasin&e dans les composes inte~~talllques ordonnes C&Au et AgMg ayant subi la meme deformation. DIE
VERFORMUNG
DER
I~TERMETA~LISCHE~
VERBINDUNG
TlBi,
Das Verformungsverhalten der intermetallischen Verbindung TIBi, wurde bei 25°C (entsprechend etwa 0,6 der absoluten Schmelztemperatur) untersucht. Anderungen des elektrischen Widerstandes von Proben mit zwei verschiedenen KorngrBOen werden nach Torsionsvorformung in Abhilngigkeit von Dehnung und Dehnungsgeschwindigkeit gemessen. Die mechanischen Eigenschaften wurden an Proben mit drei versobiedenen Korngrijfien bei verschiedenen Dehnungsgeschwindigkeiten gcmessen. Ferner wurden metallographische Untersuchungen und ~~rtemessungen durchgefiihrt. Die gespeicherte Energie wurde fiir eine Korngr66e nach ~o~ionsverformuxlg mittels Metall~sungskalorimetrie gemeasen. Die Verbindung TlBl., ist bei 25°C duktil oder spriide, je nach Dehn~mgsgeschwindigkeit und Korngr613e der Proben. Bei klemen Dehnungsgeschwindigkeiten ist die Verbindung duktil, es wird eine FlieDgrenze in der Verfestigungskurve beobachtet, und der elektrische Widerstand nach Torsionsverfocmung erreicht mit zunehmender Dehnung fast konstante Werte. Diese Ergebnisse sind konsistent mit den Hinweisen fur Korngrenzengleiten bei der metallographischen Untersuchung von Proben, die bei kleinen Dehnungsgeschwindigkeiten verformt wurden. Bei hohen Verform~in~gesehwindigkeiten ist die Verbindung sprode, man beobachtet keine FlieSgrenze, und der elektrische Widerstand nach Torsions~Brfo~ung nimmt mit der Dehnung ZU. ~~etallographis~he Un~rsu~hungen deuten an, daf3 bei hohen De~~gsgesc~windigkeiten die Verbindrmg haupts5chlich durch Abgleiten innerhalb der Korner und nur wenig durch Korngrenzcngleitung verformt wird. Eine Zunahme der KorngrGBe der Probe beeinfluBt die Widerstands&ndorung bei Verformung iihnlich wie eine Zunahme der Dehnungsgescbwindigkeit. Sie beeinflul3t die Fliellspannung jedooh in entgegengesetzter Richtung. Die in der Verbindung TlBi, nach Verformung durch Abgleitung gespeicherte Energie ist kleiner als diojenige in den geordneten intermetallischen Verbindungen Cu,Au und AgMg bei gleichem Verformungsgrad. -_ ._ * Received August 13, 1965; revised October 27, 1965. i Division of Sponsored Research, Massachusetts Institute of Technology. $ Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts. ACTA
METALLURGICA,
VOL.
14, JUNE
1966
693
694
ACTA
METALLURGICA,
1. INTRODUCTION
The mechanical behavior of intermetahio compounds is greatly influenced by the ~mperature. They tend to be brittle at temperatures below approximately 0.6 of their absolute melting point, but become ductile at higher temperatures.(l) Possible explanations of the transition from ductile to brittle behavior are the effects of ~mperature on (1) the degree of order in the compound, (2) the ease of dislocation generation and movement, (3) the number of operative slip systems and (4) localized deformation at grain boundaries. In the research reported here, the relative contributions of these factors to the deformation of the intermeta~ie compound TlBi, at room temperature have been investigated. The melting point of the congruently melting composition of TlBi, is 213YY and room temperature, therefore, is approximately 0.6 of the absolute melting point, On deforming the oompound in this critical temperat~e range, changes in such variables as the strain rate and grain size can determine whether the compound behaves in a brittle or ductile manner. The compound TlBi, exists over a composition range extending from 56.0 to 61.4 at. ‘4 bismuth at 20°C; its stoic~ometric composition lies outside the homogeneity range at room temperature.t2t The structure of TlBi, is now believed to be of the N&In (B8) type@a4)rather than the AlB, (C32) type reported earlier.(6) Bismuth atoms probably form a hexagonal sublattice while the thallium atoms and the bismuth atoms in excess of those required to form the sublattice occupy the octahedral and trigonal sites at random.(4) The compound TlBi, can be formed into wire by extrusion at room temperature.@) Tensile tests at 27“G on wire specimens armealed for one hour at 75°C have shown that the yield stress and elongation depend strongly on the strain rate. For example, the yield strength and elongation change from approximately 6,000 psi and 55 % at a strain rate of 0.005 per min to 8,000 psi and 5 % at a strain rate of 0.02 per min.@J) In the investigation reported here, the tensile properties of the compound and the changes in electrical resistivity have been measured at different strain rates and with specimens of different grain sizes. Metallographic examinations and microhardness measurements have been carried out. The energy stored in specter of one grain size has been measured as a function of strain at one strain rate. 2. MATERIALS
Samples of the compound TlBi, containing 60 at. % bismuth were prepared by melting 99.99% bismuth
VOL.
14, 1966
(Mallinckrodt Chemical Works) and 99.99 % thallium (Amend Drug and Chemical Co.) in sealed, evacuated Vyoor tubes of 0.6 in. dia. This composition, rather than that of highest melting point, was chosen bectause the latter does not lie within the homogeneity range at room temperature.cz) The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The ingots were crushed and melted again in sealed, evacuated Vycor tubes of 0.2 in. dia. in order to obtain ingots of suitable diameter for extrusion. The melts were held for approximately one hour and quenched into iced brine. The ingots were homogenized for 48 hr at 100°C. Metallographic examination of repre~n~tive sections did not reveal any evidence of second phases or segregation. Rods of 1 in. length and 0.185 in. dia. machined from the ingots were extruded in one pass at room temperature to 0.040 in. dia. wire. Molybdenum ~sulphide was used as a lubricant. The extrusion load was 8,500 psi and the ram speed approximately 0.2 in. per min. Room temperature is above the recrystallization temperature of the compound TlBi, after heavy deformation. The extruded wire which had been annealed at room temperature consisted of equi-axed recrystallized grains with an average diameter of 37 ,LL. Annealing for 1 hr at 75°C and annealing for 1 hr at 150°C produced grains of 50 and 190 ,u dia., respectively. The grain diameters were determined by m~tiplying the average linear intercept in a plane section by 1.65.f’) 3. ELECTRICAL
RESISTIVITY SPECIMENS
OF ANNEALED
The electrical resistivity of specimens of 0.040 in. dia. wire of the compound TlBi, was measured by a po~ntiometric method with a precision of 0.2 %. The resistivity, at -.l95*C, of specimens extruded and annealed at room temperature was 41.50 &J-cm and that of specimens annealed for one hour at 75% was 41.25 $&cm. A resistivity of this magnitude is to be expected for a compound containing bismuth, which has only few conduction electrons in the second Brillouin zone.(s) The temperature coefficient of resistivity of the compound TlBi,, unlike that of elemental bismuth, increased slightly with increasing temperature over the range -195’ to 200°C. The average temperature coefficient of resistivity over this range was 0.15 pi&cm per “C. In order to determine whether the annealing treatment affected the degree of order in the compound, specimens were annealed for one hour at IQO’C and either quenched to -195°C 01‘ slowly
ROBINSON
AND
BEVER:
cooled in 52 hr to -195°C. Their resistivity was measured on heating to various temperatures between -195’ and 200°C. The resistivities of the quenched and slowly cooled specimens were not sig~fi~ntly different. It is unlikely, therefore, that the degree of order in the compound was affected by the annealing treatments at 75” and 150°C used to produce specimens of different grain sizes. The resistivity, at -195”C, of specimens of TlBi, which had been placed in liquid nitrogen immediately after extrusion did not change during annealing at room temperature for 2 to 3 days. The resistivity of extruded specimens annealed at room temperature was in close agreement with that of specimens annealed for one hour at 75°C. It is probable that the compound recrystallizes immediately at room temperature after the reduction in area of approximately 78 % received during extrusion. 4. ELECTRICAL
RESISTIVITY SPECIMENS
OF DEFORMED
The electrical resistivity of specimens of the compound TlBi, with a grain size of 37 and 50 p average dia. was measured as a fun&ion of strain in torsion after deformation at 25°C at different strain rates. Specimens with larger grain sizes could not be deformed appreciably in torsion because they were too brittle. The resistance of each specimen was measured before and after deformation. The specimens were immersed in liquid nitrogen immediately after deformation at 25%. The shear strain at the surface of the specimen was measured as nnd/l and the corresponding strain rate as godly, where n is the number of turns, *Gthe number of turns per min, d the diameter of the specimen and 1 its length. The resistivity of specimens of 50 p grain dia. deformed at strain rates exceeding 0.10 per min increased with increasing strain at 25°C up to the largest strains used. After deformation at a strain rate of 0.03 per min, however, the resistivity as a function of strain reached a nearly constant value at strains larger than approximately 0.06 (Fig. I). The specimens of 37 p grain dia. showed the same general dependence of the resistivity on strain as the specimens of 50 p grain dia., but nearly constant values of the resistivity were reached at the ~omparatiyely high strain rate of 0.22 per min (Fig. 2). The increment’ in the resistivity of specimens of the two grain sizes after a given strain increased rapidly wit#han increase in the strain rate, as shown in Fig. 3 for a strain of 0.63. At a given strain rate, the change in resistivity was greater for the specimens with large than specimens with small grain size (Fig. 3). The change in resistivity on deforming the compound
DEFORMATION
OF
695
TlBi,
TlBi, at 25”C, therefore, is a function of the strain, the strain rate and the grain size of the specimen. The changes in resistivity after deformation at 25°C may be attributed to an increase in the dislocation density within the grains. The attainment of nearly constant values of the resistivity after deformation at low strain rates suggests that the dislocation density
$
48.0
; .C 2 .u E i, .t .> z z a”
0.15 46.0 0 IO
44.0
0.03
42.0 Average of undeformed
._.-a_/_ 0.2
0
0.4
0.6 Strom,
-
specimens 0.8 vnd/l
..A 1.0
12
FIG. 1. The resistivity, measured at
-195X’, of the compound TlBi, after deformation in torsion at different strain rates at 25°C aa a function of the shear strain at the surface of the specimens. Average grain diameter of specimens: 50 p.
48’orl-=-l
42.0 FAverage
40.0 ’ 0
I 0.2
of undeformed
I 0.4
I I 0.6 0.8 Strain, wnd/P
specimens
I 1.0
1.2
2. The resistivity, measured at -195W, of the compound TlBi, after deformation in torsion et different strain rates at 25°C as a function of the shear strain at the surface of the specimens. Average grain diameter of specimens: 37 ,u.
FIG.
ACTA 80
I
I
I
Grain
Strain
0.2 rate,
0.3 rlid/X,
diameter:
0.4 per mln
VOL.
14,
1966 5. TENSILE
I
diameter:
Grain
0. I
METALLURGICA,
I 0.5
FIG. 3. The change in resistivity on deforming the compound TlBi, in torsion, at 25”C, to a shear strain, mad/E, of 0.63 as a function of strain rate for specimens of two different grain sizes.
does not increase appreciably above a critical value of the strain. If this behavior were associated with recovery or recrystallization, the change in resistivity would depend on the time the specimen is at room temperature during deformation; this time is longer for deformation at low than at high strain rates. The time at room temperature during deformation at the low strain rates was less than 10 min except for the specimens deformed to strains of 0.63 and 0.94 at a rate of 0.03 per min, which were at room temperature for 20 and 30 min, respectively. The resistivity of specimens which had been deformed to a strain of 0.82 at a strain rate of 0.22 per min, however, did not change on holding for 40 min at 25°C. On annealing at 75°C after the same deformation, the change in resistivity with time indicated that the specimens did not completely recrystallize until after 60 min at this temperature. Under the experimental conditions used, therefore, the change in resistivity was not affected by recrystallization occurring during deformation at room temperature. The deformation process is aided by thermal fluctuations. On deforming at high homologous temperatures, a decrease in strain rate is equivalent to an increase in temperature. It is possible, therefore, that on deforming at low strain rates the mutual annihilation of dislocations occurs to a greater extent than at high strain rates. Grain boundary sliding may also take place at the low strain rates. These processes would account for the nearly constant values of the resistivity as a function of strain on deforming at low
TESTS
Wire specimens (0.040 in. dia., 1.0 in. gauge length) of the compound TlBi, with average grain diameters of 37,50 and 190 ,Mwere tested on an Instron machine. The tests were carried out at 25’ f 1°C with crosshead speeds ranging from 0.002 to 0.100 in. per min. The stress is reported as the true stress and the strain as the true strain; the strain rates are reported as the increase in length of the specimen per unit length per min. The estimated precision was f40 psi. Typical curves of the true stress versus true strain at different strain rates are shown in Fig. 4 for specimens with an average grain diameter of 50 p. At strain rates of 0.020, 0.050 and 0.100 per min, the specimens fractured soon after the yield stress had been reached. At strain rates of 0.010 per min and slower rates a “yield hump” was observed after an initial period of rapid work hardening. Only slight work hardening occurred in the region beyond the yield hump and the specimens deformed to elongations of up to 70%. The general form of these curves for specimens of the compound TlBi, deformed at low strain rates was similar to that of published curves for specimens of the compound In,Bi, which has the same structure,(3*4) deformed under similar conditions.@) The yield stress at 0.2 % strain offset for specimens of TlBi, is plotted in Fig. 5 as a function of strain rate. The specimens with an average grain diameter of 190 ,U were too brittle to be tested at strain rates exceeding 0.020 per min. The yield stress of specimens of different grain sizes increased rapidly with an
True
strain
Fm. 4. Typical true stress-true strain curves, at 25% for the compound TlBi, at different strain rates. Average prain diameter of snecimens: 50 u.
ROBINSON 9,500
r 1!
I
1
/
/Y,eld
AND
BEVER:
DEFORMATION
697
40
I
I
OF TlBi,
stress
b” 3.8 -B
Groin
diameter,
37
36
I
I
log
\
I
/
a02
0.04 Strain
4,000 0
t, ---_-_a.Elongation ---------0-e
I
0.06 rote,
per
I
/
008 rmn
0.10
I 0.12
These results obey the equation proposed which
predicts
a linear relation
stress a, and the quantity at strain rates in the
range of 0.002 to 0.020 per min.
For example,
CT?/ =
the
yield stress of specimens with a grain diameter of 50 ,u
where
increased
constants.
from
approximately
-3 i
FIG. 6. The logarithm of the yield stress at 0.2% offset of the compound TlBi, plotted against the logarithm of the strain rate for specimens of different grain sizes.
FIG. 5. The yield stress at 0.2 ‘A offset and the elongation of the compound TIBi,, at 25”C, as functions ofstrainrate.
increase in strain rate, especially
._._A
-2
-I
5,600 psi at a strain
d is the grain
by Petchdl)
between
the yield
d--1i2
k, f
k2d-1’2
diameter
The compliance
and
k, and
of the yield
k, are
stress with
rate of 0.002 per min to 8,300 psi at a strain rate of
this equation
shows that at the strain levels
0.100
sponding
the
70%
per min; and 2%,
be consistent
the corresponding respectively.
At high homologous
to
intragranular
yield
stress
the movement
the yield stress
on the strain rate since
slip is aided by thermal fluctuations.
The stress and
strain rate at constant
and strain are
temperature
related by the equation
the
of dislocations.
I
r--T
Stroln
Rate, ‘1
0.050
0.020 where ay is t’he flow stress, k a constant, coefficient.
d the strain
1
0.0 IO
A plot of
log a, versus log 8 (Fig. 6) shows that the change in the flow stress of TlBi, rate conforms other
at 0.2%
to this equation.
intermetallic
compounds
offset
0.005
with strain
The flow stress of changes
0.002
with strain
rate in the same general manner at high homologous temperatures, although the strain rate dependence may be smaller, as for AgMg,(lO) or larger, as for In,Bi,@) than for TlBi At a given strain fate, the yield stress increased with a decrease The
yield
in the grain size of the specimens.
st’ress at 0.2%
offset
at different
strain
rates is plotted in Fig. 7 as a function of the reciprocal of the square
root
of the average
grain diameter.
-__I
0.05
0.10
0.15
is
play a major
8,000 -
rate and m the work hardening
corre-
deformation
and that grain boundaries
role in inhibiting
by Wood.cQ
temperatures
to depend
were
These results appear
with those obtained
may be expected
elongations
to
0.20
d -~Z,in1cro”s-~2
FIG. 7. The yield stress at 0.2% offset of the compound TlBi,, at 25’C, as a function of the average grain diameter at various strain rates.
698
ACTA
METALLURGICA,
The unusual feature of the tensile behavior of the TIBi, is that at low strain rates, a yield hump is observed, followed by a region in which extensive elongation occurs with only slight work hardening. A similar yield hump has been observed on testing the compound In,Bi.(Q) In some respects, however, the tensile properties of these compounds differ. In contrast to TlBi,, an increase in the yield stress with increasing grain size has been observed for 1nzBi.u’) These observations have been explained on the assumption that dislocation generation is difficult in InQBi and that grain boundaries act as sources of dislocations rather than as barriers to their movement. The activation of many dislocation sources at grain boundaries once a critical stress level has been reached has been cited as the reason for the yield hump in 1nsBi.c’) If the yield hump in TlBi, is due to an initial di~culty of generating dislocations, the subsequent generation of dislocations must occur at sources other than those at grain boundaries. In the compound TlBi,, the difficulty of dislocation generation probably accounts only partly for the yield hump. The tensile results indicate that, at low strain rates, the mechanism of deformation changes in the region of the yield hump. It is possible that beyond the yield stress, work hardening occurs until the stress level is sufficiently high to cause grain boundary sliding. The specimens then deform with only slight work hardening to elongations of up to 70 %.
VOL.
14,
1966
compound
6. METALLOGRAPHY AND MICROHARDNESS MEASUREMENTS
~eta~o~aphic examinations were carried out on flat specimens which were prepared by casting into a mould machined in the shape of a tensile test piece 2.0 in. long, 0.25 in. wide and 0.125 in. thick. The cast specimens were heat treated to produce different grain sizes. The preparation of specimens of TlBi, for metallographic examination is difficult because the compound is soft. In addition, the time available for examination of the prepared surface is limited by the formation of an oxide film to approximately 15 min after polishing. Examination of the surfaces of flat tensile specimens which had been polished before deformation showed that the grain boundaries were in relief in the unetched specimens after deformation at 25’33 and at strain rates below 0.020 per min. This observation indicates that sliding of the grains on either side of the boundary relative to one another had taken place. Figure 8(a) shows the ~splacement of two scratches crossing a grain boundary in an unetched specimen deformed at a strain rate of 0.010 per min. Since the scratches remained straight within the grains, the
FIU. S(a). Dis&wmwnt of scratches crossina a erain bound& in in nnetohed specimen of the Gomp&md TlBi, after tensile deform&ion of approximately 20% at a strttin r&e of 0.010 per min. Fold at the grain boundary at bottom left of photo~cro~~ph should be noted. x 320
deformation was probably confined to a narrow region along the grain boundary. A further indication of localized defo~ation was given by the formation of folds at the grain boundaries in specimens which were deformed at low strain rates; an example is shown in Fig. 8(a). The formation of folds is a common mechanism of accommodati~ grain bounds strains in metals deformed at low strain rates and high homologous temperatures.(is) In specimens of the compound TlBi,, the formation of voids at grain boundaries occurred during deformation at low strain rates (Fig. 8(b)). These voids were similar to those which have been observed at the grain boundaries of metals after creep testing at
FIG. 8(b). Voids and folds at the grain boundary in an unetched specimen of the compound TlBi, after tensile deformation of approximately 45 % at a strain rate of 0.005 per min. x 320
ROBINSON
AND BEVER:
temperatures. (13) The formation
elevated metals
has been attributed
vacancies
of voids in
to the condensation
at the grain bounclaries.(14)
DEFORMATION
of
On the other
OF
Microhardness
699
TIBi,
measurements
were carried out with
a load of 100 g on a series of polished
different grain sizes which had not been etched.
hand, it has been concluded from some experiments that the formation of voids occurs as the result of
results show that the compound
grain
on the grain size.
boundary
intermetallic
sliding.(15*16)
compound
in the vicinity
strain
the
case
occurred
which was usually
by
initiated meet,
photomicrograph
illustrates
to be expected
of TlBi,
intercrystalline
grain boundaries
the that
The
is soft;
the
hardness values range from 14 to 22 V.P.N. depending In contrast
metals at low homologous of TlBi,
increased
to the behavior
temperatures,
of
the hardness
with an increase in the grain size
at low
cracking,
at a triple point
as shown
where
in Fig. 8(c).
This
typical
intercrystalline
if extensive
grain boundary
sliding takes place during cleformation.(17) case, large
of
of folds
TlBi,
of
associated with grain boundary
of the tensile specimens
rates
cracking
In
the formation
of the voids (Fig. S(b)) indicates
the voids are probably sliding. Fracture
TlBi,,
specimens
tensile stresses develop
In such a
at the triple point
owing to shear stresses acting along the grain boundaries.(ls)
Figure 8(c) shows that, before the fracture
of this specimen
of TlBi,,
some
relieved by plastic deformation
of the stress was
and the formation
of
101
Slip bands deformation
were observed
the grains after
at strain rates greater than 0.020 per min.
Markings observed than
deformation
visible
after repolishing
twins
as they
and etching.
to occur on the pyramidal temperatures.
were
Slip may
not be
and basal planes
of TlBi,, both of which are close-packed, at high homologous
FIG. 9. The microhardness of the compound TIBi, as a function of the grain size of the specimens. Load 100 g.
within the grains were slip bands
rather expected
within
200 100 Groin diameter, microns
0
folds within the grains around the triple point.
on deforming
Grain boundary
Boundaries
of equi-axed,
recrystallized
grains were
observed around the hardness indentations and
unetched
diameter
specimens
with
an
in polished
average
of 37 and 50 ,U (Fig. 10(a)).
grain
These bound-
aries were placed in relief by grain boundary
sliding in
sliding did not appear to be the primary mechanism
of
the deformed region around the hardness indentation.
deformation
of
The
specimens
at the higher strain rates. deformed
Fracture
at high strain rates occurred
cleavage and intercrystalline
by
cracking.
grain
boundary
sliding
leads
to the irregular
outlines of the hardness indentations Localized
deformation
seen in Fig. 10(a).
at the grain boundaries
also
occurred in specimens having average grain diameters of 190 and 252 p, but only the sections of the boundaries in the vicinity visible.
of the indentations
An illustration
Slip bands
were made
of this is shown in Fig. 10(b).
were also observed
with
the hardness
in
grain
sizes
(Fig. 10(b)).
The increase in hardness of TlBi,
with
increasing
specimens
around
indentations
large
grain size (Fig. 9) is consistent
observations
of grain boundary
sliding
with these around
the
hardness indentations. 7. STORED
ENERGY
The energy stored in the compound TlBi, after deformation by torsion at 25°C at a strain rate of 0.22 per min was measured metry FIG. 8(c). Crack at a triple point and folds at the grain boundaries after tensile deformation to fracture at a strain rate of 0.005 per min. x 320
with bismuth
experiments
described
by metal solution
as solvent.
As shown
in the preceding
caloriby the
sections,
compound deforms at these strain rates primarfly slip rather than by grain boundary slicling.
the by
700
ACTA
METALLURGICA,
VOL.
14.
1966
In contrast to previous invesfigations of the stored energy of cold work in metals and intermetallic compounds, in the present investigation the compound TlBi, was worked at a temperature equivalent to approximately 0.6 of the absolute melting point. The values of the energy stored after deformation in torsion to different strains at a strain rate of 0.22 per minute are given below.
FIG. 10(a). Grain boundary sliding around hardness indentations in an unetched specimen of the compound TlBi,. Grain diameter: 150 /J. Load: 100 g x80
FIQ. 10(b). Grain boundary sliding and slip lines around hardness indentations in unetched specimens of the comGrain diameter: 190 ~1. Load: 1OOg. pound TlBi,. x 120
The stored energy was determined as the difference in the heat effects on solution of alternate additions of deformed and undeformed samples. The heat capacity of the calorimeter was determined by calibrating with bismuth. The values of the stored energy are based on a difference in the heat content of bismuth between 0” and 350°C of 4.96 kcal/g-atom. The calorimetric procedure and the method of calculation have been described elsewhere.czO) The specimens intended for the stored energy measurements were annealed for one hour at 75°C before deformation and had an average grain diameter of 50 ,u. Immediately after deformation the specimens were immersed in liquid nitrogen; all additions to the calorimeter were made from this temperature. In a typiml calorimetric run, three additions each of the deformed and undeformed compound were made.
Shear strain at the surface, m&/l
Stored energy Cal/g-atom
0.06 0.31 0.44
5 20 26
These values are higher than the energy stored in metals deformed at room temperature to comparable strains(21) but considerably lower than the energy stored in ordered phases such as CU,AU(~~)or AgMg.t23) This is to be expected for two reasons : the compound TlBi, appears to be only partially ordered and the temperature of deformation (room temperature) is a high homologous temperature. It is of interest to consider the ratio of the stored energy to the change in electrical resistivity after deforming TlBi, to a given strain with this ratio for other intermetallic compounds deformed to the same strain. In contrast. to metals, the energy stored in deformed intermetallic compounds depends not only on the dislocation density but also on the number of A-B bonds replaced by A-A and B-B bonds and on the associated energy effects. The change in resistivity due to the deformation of compounds depends mainly on the dislocation density and on the disorder produced by replacing the A-B bonds by A-A and B-B bonds. It depends only indirectly on the strength of the A-B bond. This dependence arises because the bond strength affects the degree of order in the compound and thus the type of line defect produced during deformation. In an ordered compound the stable line defect is a superdislocation. During deformation a minimum destruction of order occurs as the trailing dislocation of the superdislocation tends to reorder the material disordered by the leading dislocation. As the net destruction of order is relatively small, the change in resistivity is low. The stored energy, on the other hand, may be high because the energy associated with the A-B bonds broken may be large, although their number is small.
ROBINSON In a disordered
or partially
BEVER:
AND
ordered compound
stable line defect is a unit dislocation.
the
The change in
resistivity
on deforming
paratively
large, but the stored energy is low because
such a compound
of the small energy associated The ratio resistivity
of the stored
on deforming
energy
compounds
A relation
should
exist between
of the compound
which is a measure of the bond strength. and TlBi,
for the compounds
after deformation
heats
of
by torsion
by wire drawing formation.(24-26)
In Fig. 11,
CU,AU,(~~) AgMg’23)
strain at the surface of the specimen equivalent
in
to a
depends on the bond strength
this ratio and the heat of formation the ratio E,/Ap
bonds.
to the change
intermetallic
given strain, therefore, in the compound.
with the A-B
is com-
is plotted In
to a shear
of 0.31 or its against
agreement
their
with
the
DEFORMATION
701
OF TlBi,
1. The changes in electrical resistivity on deforming the compound
TlBi, in torsion at 0.6 of the absolute
melting point (25°C) depend on the strain, the strain rate and the grain size of the specimens. 1.1 On deforming at high strain rates sistivity the
increases with strain.
resistivity
as a function
nearly constant annihilation
of
values, probably
of
dislocations
the
re-
At low strain rates strain
reaches
owing to mutual
or
grain
boundary
sliding. 1.2 The
change
increases
in resistivity
rapidly
at a given
with an increase
strain
in strain rate
(except at very low strains). 1.3 At a given strain and strain rate, the change in resistivity
is greater in specimens of large grain size
than in specimens of small grain size. 2. The tensile behavior depends
of the compound
at 25°C
on the strain rate and the grain size of the
specimens. 2.1 At high strain rates the specimens fracture soon after the yield stress has been reached. 2.2 At low strain rates a yield hump is observed beyond
which only slight work hardening occurs.
2.3 The yield stress at a given strain rate is higher for
specimens
specimens
with
a small
grain
with a large grain size.
size than
the yield stress with grain size complies equation
due to Petch indicating
with the
that, at least in
the region of the yield stress, the deformation the compound 4.0
kcol/g
5.0
given grain size with strain rate tends to confirm
-o+om
FIG. 11. The ratio of the energy stored to the change
in electrical resistivitv for comnounds deformed at 25°C plotted against their geats of formation. The compounds TIBi, and AgMg were deformed in torsion to a shear strain of 0.31. The compound Cu,Au was deformed by wire drawing to an equivalent strain. See text for references.
arguments ratio
set forth in the preceding
increases
with
an
increase
paragraphs, in
the
heat
the of
that the compound 2.5 The elongation
but at low strain rates elongations 3. Metallographic
deforms
is a different
the melting point of each compound,
fraction
of
It would be of
interest to obtain the corresponding
data for a series
of compounds of the same structure same fraction of the melting point.
deformed
8. SUMMARY
The
main
conclusions
results
AND
of
at the
investigation
and
the
that can be drawn from them are sum-
marized below.
of up to 70 % are
indicates
examination
specimens
that
at high
polished strain
of the surfaces before rates
compound
by slip but at low strain rates appreciable
grain boundary
sliding takes place.
4. The hardness of the compound increase
the
of
deformation
increases with an
in the grain size of the specimens.
Grain boundary sliding takes place around the hardness indentations in specimens of all grain sizes tested. 5. The energy stored in the compound TlBi, after hot working in torsion at 25°C at a strain rate of 0.22
CONCLUSIONS
this
on the strain
is brittle at high strain rates
observed.
It should be noted that the results plotted in Fig. 11 are for compounds of different structures deformed at which
depends strongly
rate ; the compound
formation.
temperature,
deforms by slip in the region of
the yield stress.
flat tensile
room
of
is intragranular.
2.4 The change of the yield stress of specimens of a
-kTk-k--
0
-AH,
for
The change of
per min increases with increasing strain.
The energy
stored is considerably smaller than that stored in the ordered compounds Cu,Au and AgMg cold worked to
702
ACTA
METALLURGICA,
the same strains, but larger than the energy stored in metals cold worked to the same strains. 6. The results of the tensile tests indicate that up to a stress level corresponding to the maximum of the yield hump, the compound deforms at low strain rates and high homologous temperatures by slip within the grains. On deforming at these strain rates to strains in excess of the yield hump, however, grain boundary sliding appears to be a major mechanism of deformation. Mutual annihilation of dislocations may also occur under these conditions. At low strain rates and at strains in excess of the yield hump, therefore, the compound d&forms with slight work hardening and little change in electrical resistivity. 7. An increase in the strain rate tends to suppress the onset of grain boundary sliding. At high strain rates, therefore, the compound deforms at all strain levels by slip within the grains and work hardens after yielding until fracture occurs after small elongations. Under these conditions, the resistivity continues to increase with increasing strain in torsion. An increase in the grain size of the specimens affects the change in resistivity on deformation in a similar way as an increase in the strain rate, but it affects the yield stress in the opposite way. ACKNOWLEDGMENTS
The authors thank Dr. K. C. Chuang and Mr. Praveen Chaudhari for many helpful discussions. They are indebted to Dr. M. D. Banus of Lincoln Laboratory, Massachusetts Institute of Technology, for providing facilities for extrusion. The assistance of Mr. L. I. Sudenfield with the experimental work is gratefully acknowledged. This work was supported by the U.S. Atomic Energy Commission under Contract ATI30-lj-1002. I I
VOL.
14, 1966 REFERENCES
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