The electrical resistivity for single crystals of molybdenum after various amounts of bending at room temperature and after annealing isothermally at several temperatures was measured and correlated with metallographic and X-ray observations. Resistivity during room-temperature bending is found to increase slightly initially and is followed by a rapid rise coincident with crossing slip bands. Etch-pit density measurements are found to be proportional to the reciprocal of the bend radius, in agreement with the Cottrell relation. &TUDES
DE SOUS-GRAINS ET DE RKSISTIVITB BLECTRIQUE LES MONOCRISTAUX DE MOLYBDKNE
La resistivite Blectrique de monocristaux de molybdene apres divers degres de flexion Q la temperature ordinaire et revenus isothermes a des temperatures differentes a 6te mesuree et mise en relation avec des observations microscopiques et de rayons X. La resistivite pendant la flexion a la temperature ordinaire augmente d’abord legerement puis d’une man&e considerable lors de l’apparition de bandes de “crossslip”. La densite de piqures de corrosion a et& trouvee proportionnelle it l’inverse du rayon de courbure, en accord avec la relation de Cottrell. UNTERSUCHUNGEN
SUBKORNER UND ELEKTRISCHEN MOLYBDAN-EINKRISTALLEN
An Molybdan-Einkristallen wurde der elektrische Widerstand gemessen, nachdem die Kristalle bei Zimmertemperatur verschieden stark gebogen und danach bei verschiedenen Temperaturen isotherm angelassen worden waren. Die Ergebnisse wurden mit metallographischen und mit Riintgen-Beobachtungen verglichen. Es zeigt sich, dass der Widerstand mit dem Biegen bei Raumtemperatur zunitchst langsam anwachst; sein darauf folgender starker Anstieg fallt mit dem Auftreten sich durchschneidender Gleitbiinder zusammen. Das Auszahlen van Atzgrtibchen ergibt, dass ihre Dichte umgekehrt proportional sum Biegeradius ist, was mit der Cottrellschen Beziehung in Einklang steht.
It is possible to obtain in deformed of
which leads to discontinuous X-ray
crystals a type polygonization,
Cahno) has observed
in the Laue
in bent single crystals of zinc, magnesium,
of the asterism
have shown that’
is effected i.e.
to dislocations. of dislocations
Since out of
by a decrease in the electrical resistivity initially
It has not, as yet, been possible to calculate the resistivity due to groups of piled-up dislocations
* Received July 21, 1955; revised version March 6, 1956. t The Johns Hopkins Universitv. Now at the General Electric Research -Laboratory, Schenectady, New York. z The Johns Hopkins University. Now at The University of Pennsylvania, Philadelphia 4, Pa. 4, NOVEMBER
This process involves the migration
to or from the edges of the half-planes
their slip planes involves
of the dislocations. Mottc3) and Seegarc5) have also suggested that the process of recovery, as well as
on a dislocation
to the edges of the half planes, it should be expected
process in polygonization is the movement or climbing of edge dislocations out of their slip planes in order to change their grouping from a “horizontal” one to a “vertical”
are annihilated by diffusing the process of the climbing
walls was confirmed
by Cahno) and by Dunn and Daniels.t2) Mottt3)
can act as sinks for vacancies.
spots is believed to be due to the alignment of the edge dislocations introduced by bending into the walls, perpendicular
may be dependent
climb process. Calculations,
has also been suggested by Nabarro”)
and sodium chloride, after annealing near the meltingpoint.
which are considered to be present in cold-worked metals.(s) If groups of piled-up dislocations contribute substantially to the resistivity, as is quite likely, it is to be expected that a decrease in resistivity may be accompanying an alteration of the piled-up arrays into configurations containing less strain-energy. The present investigation was initiated to determine under what conditions polygonization or subgrain
in order to obtain a quantitative
ment of the changes polygonization.
treatments. a bent
in an identical
between the potential leads was constant.
A correction was made to take account of the increase in specimen length between the potential leads due to the bending.
A current of 5 amp was passed through the specimen for a period of less than 10 sec. All resistance measurements were made at atmospheric temperature (21”
The specimens were about 3 mm in diameter and 18 cm long, with single crystals approximately 2 cm
to 5 cm in length occupying
of each specimen.
the entire center sections
The specimens were electrolytically
polished and then bent at room temperature, the
argon atmosphere temperatures X-ray
300°C to approximately Laue
in an 1600°C.
obtained from the crystals in the grown and bent conditions and after the various annealing treatments. The
the initially unstrained crystals are shown in Fig. 1 in a unit stereographic triangle. Microscopic examination was conducted after etching the crystals in a sodium hydroxide
and potassium ferricyanide
and also after electroetching
in 5% oxalic acid at 4 V.
The electroetch method was found to be more sensitive for
at an elevated
molybdenum examined temperature
1OW ohms and the accuracy was fl
for periods of 1 hour to 25 hours at
x 10e6 ohms.
radius of bend of the crystals was varied from 8 cm to 1.5 cm.
were made with
a Leeds and Northrup Kelvin double bridge, after increasing amounts of bend and after the various
the split-up of Laue reflections in molybdenum crystals
to a slight external
high-temperature annealing. Typical examples are shown in Figs. 2a and 2b, which were obtained from a crystal
1 o/o in tension
2OOO”C, and from another crystal (M-2) deformed by bending to a l&cm radius at the same temperature. The average size of the subgrains depicted is about 10 microns.
in Fig. 2a
Etch pits which are spaced in a
nearly regular manner are visible at the sub-boundaries. It is also evident,
in the lower part of
Fig. 270,that the density of etch pits changes markedly when
The etch pits are believed
sub-boundary to occur
which are found at regularly spaced distances aligned in the sub-boundary. The average spacing of the etch pits in the sub-boundaries was 1 x lo-* cm to 2 x lo-* where
From the dislocation
8 = orientation
and h = etch pit spacing,
0, of 0.01” to 0.02” were calculated deformed
0 = A/h,
;1 = interatomic misorientations, for the crystals
slightly at 2000°C.
Microscopic examination at x 1300 of the singlecrystal section adjacent to a polycrystalline end revealed boundary
no apparent where
change of direction meets
of a grain
indicates that the “pull” of a sub-boundary at the junction is very much smaller than that of a grain boundary. Back-reflection Laue photograms revealed
FIG. 1. Initial orientations of molybdenum crystals investigated.
a breakup of each Laue reflection into discrete spots, similar to that observed by Chen and Maddin for a single crystal of molybdenum bent at about 2400°C. The orientation-spread between the individual spots of a Laue reflection
was less than 0.1’.
that it is unlikely
by an athermal
on plastic deformation. Another
at room temperature at temperatures
which was bent to 2.3 cm
and then annealed for one hour
from 300°C to lOOO”C, also showed
no structural changes. This same crystal was then bent from 2.3 cm to 1.8 cm during an anneal at’ 1200°C. Microscopic
shown in Fig. 3a, similar to those observed in an early stage of formation
by Dunn and Danielsc2) in bent
FIG. 2. Sub-boundaries in molybdenum single crystalselectrolytically polished and electroetched 15 see in 5% oxalic acid solution. (a) Top: Crystal M-l deformed in tension at 2000°C; x 400. (b) Bottom: Crystal M-2 deformed in bending at 2000°C; x 500.
2. Bending at Room Temperature followed by Annealing In a previous investigation,(lO) of molybdenum ture revealed
X-ray Laue patterns
single crystals bent at room temperaa breakup
intensity regions connected by diffuse areas. This phenomenon was interpreted in terms of crystallite fragmentation
where the individual
connected by high-strain regions. In the present study, four single crystals (M-3, M-4, M-5, M-6) were bent from 8 cm to 1.5 cm at room temperature and annealed in an argon atmosphere
for periods up to ten hours
at temperatures from 300°C to 1400°C. No significant change was noted either in orientation or in the appearance
of the Laue reflections
after the above
treatments. Microscopic examination after chemical and electroetching showed no evidence of subgrain formation or polygonization. It is possible, of course, that subgrains were present, but still too small in size and misorientation to be detected by conventional However, the failure to detect any techniques. structural
even after ten hours at 14OO”C,
* ., Fm. 3. (a) top: Sub-boundaries in molybdenum single crystal (M-7) after 1-hr anneal at 1500°C. Crystal was previously bent to 2.3 cm at room temperature, and then bent to 1.8 cm at 1200°C. Electrolytically polished and electroetched 15 set in 5% oxalic acid solution. x 300. (b) Centre: Enlarged Lam spot of M-7 after bending to 2.3 cm at room temperature. (c) Bottom: Enlarged Laue spot of M-7 after an additional bending to 1.8 cm at 1200°C and annealed 1 hr at 1500°C.
annealed and examination at boundary
silicon-iron x 1000
su~eession of etch pits similar to the walls of edge dislocations revealed in aluminum crystals by Cahn.o) crystal
of the etch
was 0.5 x lo-* cm, which
to a misorientation the dislocation
t3 of 0.04O when calculated
8 = A/h. From the relation-
w x 57.3
3. Etch-pit Densities Microscopic
were conducted on several crystals after eleetroetching in 5% oxalic acid solution. The excess density of edge dislocations of the same sign to produoe a certain’ amount of strain in bending was calculated from
where p is the number
p = I/&,
per unit area
parallel to the bend axis, r is the bend-radius
b is the
where W is the average width %eos (6) of the subgrains, i is the radius of bend, and # the
dislocation. For molybdenum, b is the interatomic distance in the (111) direction. The results are
0 is calculated
in Table 1.
to be 0.08”. The latter value of misorientation is in reasonable agreement with the 0.04” value derived
The reasonable agreement between the measured etch-pit density and the dislocation density calculated
from the etch-pit spacing. Enlarged Laue reflections
in a preferential
order to the formation
to 1.8 cm
The X-ray photo~ams
suggesting of the sub-
from crystal M-7 also
revealed partial Debye rings of a textured after bending
regions of Fig. 3e appear
to be arranged grains.
3b and 3c, after room-temperature
and after the additional
at 1200°C and after further
anneals at 1400°C and 1500%. The Debye arcs consisted of very small spots, reminiscent of polygonization, which became better developed and increased from
in size as the temperature
1200°C to 1500%
observed in bent silicon-iron crystals when annealed from 950°C to 1300”C.(2) The orientation difference between
spots in the X-ray
of crystal M-7 was less than O.l”, which is consistent with
observations. Crystal M-7
a slight additional
amount at room temperature in order to reveal slip traces. It was observed on microscopic examination
the etch pits locations
with the surface.
also found and
are locations calculated
found in crystal M-7 (Fig. 3a) from the irregular network
described as polygonization. However, as the structure coarsens, it loses t,he characteristics of a polygonized one, not because the lamellar structure disappears, but possibly because larger units no longer have simple orientation relationships.(2)
and Machlin(i2) for bent
crystals such that (112)-edge
were measured after electroetching. 4. Increase of Electrical Resistivity due to Bending. The electrical resistivity at 21°C (p 21’) of molybdenum single crystals in the “as-grown” condition cm.
was found to be 5.95 (*0.05)
X [email protected]
The effect of amount of bending at room tempera-
ture on the electrical resistivity crystals was measured.
(p 21°) of molybdenum
Increases of resistivity
15% were observed after bending to a radius of 2 cm. Fig. 4 shows the relationship increase
the per cent bend
1.25-cm length for two molybdenum crystals (M-9 and M-10). A very rapid increase of resistivity is evident
of the slip traces as a result of bending
revealed one system of fairly straight slip bands after
, / I
Measured etch-pit density
bending or tension at 2000°C (Figs. 2a and 2b). The nearly parallel or lamellar sub-boundaries may be
Good agreement ~slo~ation
that the sub-boundaries were approximately at right angles to the slip traces, as predicted by the dislocation mechanism of polygonization.(*J The nearly straight, parallel sub-boundaries differ in appearance
bentfrom 2.3cmt,o 1.8 cm 1.4 at 1200°C and annealed 1 1hr at 1500% j bent to 2.1cm at room, 1.5 temperature and annealed 12 hr at 1550°C I bent to 18cm at 2OOO”Ci 1.8
/ Cdzyd // I
’ location density (em-e)
107 j 1.7 x 10’
12.0 x 107 / /
2.1 x lo6
M - 9
BEPiT ATi ROOM TEUPERATURE
Recovery data for moly~denuul single crystals bent at room temperature.
FIG. 4. Per cent increase in resistivity as a function of amount of bending at room temperature.
a 5” bend, and a slight forked nature of the bands after about 12”. After a 15” bend over 1.25 cm,
of 1.5 cm to 5 cm with resulting increases of resistivity of 15 to 7%. These crystals were given various annea-
the slip bands
and the electrical resistivity measured
at room temperature
and similar to the slip bands previously observed in bent molybdenum crystals (Fig. 10 of reference IO).
at room temperature
curves obtained for bent molybdenum
crystalsoO) also gave some indication of a behavior similar to that shown in the resistivity-angle of bend-curves of Fig. 4. It is interesting to note, Masima
of single crystals of alpha brass increased
was found after 90 hours
and after annealing for periods
up to 10 hours at 1400°C.
Also, no structural changes
were evident after mioroscopic Isothermal
in this ~ol~ne~tion, that
after each anneal.
and X-my examination.
at 1550 -j: 30°C resulted
partial recovery of the total increase of resi&ivity due to bending, as shown for crystals H-6 and B-10 in Fig. 5.
M-10 received no prior anneals (M-10 was bent to a smaller radius of curvature than M-6). This might
increase in resistivity
as a second-slip
to one system.
by only about 1% as slip began and then remained constant during almost the whole period when slip
300 to 14OO”C, prior to the 1550°C treatment;
explain the differences observed in the curves of Fig. 5.
system became operative in alpha brass crystals. The rapid increase in resistivity coincident with
Microscopic and X-ray back-reflection
that the recovery of resistivity could not be attributed
of slip bands
denum crystals may
in bent molyb-
here, and in alpha-brass
affected by the presence of vacancies and piled-up groups of dislocations formed by crossing dislocations. Mott,(*)
given diagrammatic stress-strain curves which are very similar to the resistivity-strain curves found for polycryst~lline
to a reduction in dislocation tion.
section,(l6) may be the result of a high concentration of frozen-in vacancies as well as piled-up groups of dislocations which can remain in the lattice when the deformation
is carried out at room temperature.
5. Recovery of Electrical Resistivity Several
bending and after 1 hour, 8 hours, and 20 hours annealing at 1550°C. A gradual alignment, of the high-intensity regions in crystallographic manner is
enum and tungsten
photo~~~~phs did reveal
distinct structural changes occurring during recovery of resistivity. The Laue reflections of Fig. 6 were
density, i.e. recrystalliza-
high per cent increase in resistivity for bent molybdenum crystals (Fig. 4) and poIycrystalline molybafter
a partial alignment
of etch pits into sub-boundaries, which is depicted in Pig. 7. A calculation of the activation energy for recovery of electrical resistivity from the data at 14OO’C and at 1550°C during the first 5 hours yields a value of between 3.5 and 7 eV. This can be compared with the activation
2.6 eV for
energy for the partial recovery
of electrical resistivity
3.5 and 7 eV.
results are interpreted
in terms of the suggestions
Mott and Seegar that the phenomena of recovery of electrical resistivity and polygonization are dependent
on a dislocation
electrical resistivity may also be considered in terms of a realignment of piled-up groups of dislocations into
A relatively room-temperature
FIG. 6. Laue reflections from crystal M-6 after (1) (2) (3) (4)
crystals was observed. The begimring of a rapid increase in resistivity was found to coincide with the
room-temperature bending, 1 hour at 1550°C. 8 hours at 155O”C, 20 hours at 1550°C.
slip bands. of a high
This result may concentration
“frozen-in” vacancies and piled-up groups of dislocaGood agreement tions formed by crossing dislocations. was obtained
area density of dislocations
and that calculated
the Cottrell formula for the excess density as a function of the radius of curvature experimental in
of the bent crystal. of
with the dislocation
model of the structure
and with the dislocation
of polygonization. ACKNOWLEDGMENTS
The authors would like to acknowledge FIG. i. Sub-boundaries revealed by alignment of etch pits in crystal M-10 after 12.hr anneal at 1550°C. Electrolytically x 700. polished and electroetched 15 see in 5% oxalic acid.
silicon-iron A higher
crystals obtained by Dunn and Hibbard.(lT) activation
in view of its much greater temperature
of melting as compared
of 0.01” single
to 0.02” were observed in crystals subjected to slight
by bending or tension at approximately
2000°C. No experimental evidence of polygonization, recovery of electrical resistivity, or recrystallization was found in crystals bent only at room temperature to radii from 8 cm to 1.5 cm and annealed for periods up to 10 hours at 1400°C. However, evidence of polygonization was observed in bent molybdenum crystals after isothermal annealing at approximately 1550% for periods of 1 to 20 hours. A partial recovery of the total increase of resistivity due to bending was also found to occur during the annealing An approximate calculation of the
at 1550%. activation
of Drs. N. K. Chen, R. IV. Cahn, and F. C. Miller. The research was sponsored at The Johns Hopkins University by the Office of Naval Research. REFERENCES
1. R. W. CAHN J. Inst. Metds 76, 121 (1949). 2. C. G. DUNN and F. W. DANIELS l’mns. Amer. Inst. Min. Met. Eng. 191,147 (1951). 3. N. F. MOTT Proc. Phys. 8oc. BS4, 129 (1951); Report of 9th Solvuu Conference (1952). Dislo&tio&s cmtl Plastic Flow in C’rystala 4. A. H. C&R& Oxford, Clarendon Press, 182 (1953). Conference on Defects in Crystal 5. A. SEEGARInternational line SoEids Univ. Bristol, July, 1954. 6. P. JONGENBURGER Phys. Rev. 90, 710 (1953). 7. F. R. N. NABARRO Report of the Co$erence on Strength of Solids (London: Physical Sot.) 75 (1948). 8. N. F. hIOTT Phil. Mag. 43, 1151 (1952). 9. N. K. CHEN, R. MADDIN, and R.B. PONI) Trans. AmeT. Inst. Min. Met. Eng. 191, 461 (1951). 10. K. T. AUST, R. MADDIN, and N. K. CHEN Trans. Amer. Inst. Min. Met. Eng. 197, 1477 (1953). 11. N. K. CHEN and R. MADDIN Tmns Amer. Inst. Min. Met. Eng. 191, 531 (1951). 12. A. A. HENDHICKSON and E. S. MACHLIN Actcc Met. 3, 64 (1955). 13. C. G. DUNN and W. R. HIBBAR~ JR. Amer. Inst. Min. Met. Eng. Research in Progress. Chicago, Feb. 1955. 50, 161 (1928); 14. M. MASID~ and 0. SACHS Zeit. Physik 51, 321. 15. T. B~oo_nl PTOC. Phys. Sot. Bf35, 871 (1952). 16. W. GEISS and J. A. M. VAN LIEMPT Z&t Physik 41, 867 (1927). 17. C. G. DUNN and W. R. HIBB~RD JR. Private Communication.