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High-temperature dislocation rearrangement in lightly cold-deformed niobium
JOURNAL OF THE LESS-COMMON Elsevicr Sequoia S.A., LausannePrinted
METALS in The Netherlands
HIGH-TEMPERATURE DISLOCATION COLD-DEFORMED NIOBIUM
H. CARVALHINHOS, MONTEIRO*
L. LYNCE
DE FARIA.
REARRANGEMENT
JOSe
Lahorardrio de Fisica e Engenharia Nucleares. Sacakm (Received
October
ALMEIDA
SEQUEIRA
IN LIGHTLY
AND
J. CUNHA
I Portugal)
5th. 1971)
SUMMARY
The etch-pit technique has been used to evaluate the kinetics of the dislocation density decrease in lightly deformed niobium as a function of‘time and temperatures between 1000” and 1200°C. The results show that the initial large drops in dislocation density are simultaneous with dislocation rearrangement during the formation of two dimensional networks. It is believed that after this mechanism is exhausted, the dislocation density reduction is increasingly controlled by the mutual annihilation of three dimensional network dislocations, according to a model developed by Friedel.
INTRODUCTION
Steady state creep at temperatures of about half the melting point and low stresses have been thought ’ - 3 to be due to the recovery of the three dimensional dislocation network which develops during the transient stage. In this model, the rate at which dislocations are torn away from the network determines the creep rate and, hence, information must be obtained on the kinetics of the network mesh size increase. Friede14 deduced an equation which describes the change in the size of the Frank network when the only driving force present is the tendency for the total line energy to decrease and the mechanism available is climb of edge dislocations. The average mesh size, r, is then found to increase parabolically with time, t. according to the expression : rz
_
W3q
- --@--
(t+const).
(1)
In this equation, D is the diffusion coefficient at temperature T,p is the shear modulus, b is the Burgers vector, cj is the jog concentration and k is the Boltzmann constant. The introduction of this equation in any creep theory can only be justified after checking its applicability to the kind of network structures and creep conditions * J. Cunha
Monteiro.
who initiated
this work. was killed in a car accident
in January
1969
J. Less-Common Metuls, 27 (1972)
H. CARVALHINHOS
2
et a/.
commonly encountered in practice. This paper describes work carried out on the recovery of the dislocation structures of lightly deformed niobium. The etch-pit technique was used for determining the number of dislocations because the dislocation densities reported after steady state creep at high temperatures and low stresses are normally low and of the order of 107-lo8 cm-‘. EXPERIMENTAL
The niobium used in this work was supplied in rod form with a diameter of 7 mm and a total interstitial content of 764 ppm. The composition according to the supplier is given in Table I. The rod was swaged down to 3 mm diam. and then recrystallised. TABLE IMPURITY
I CONTENT
(ppm)
OF THE
NIOBIUM
USED
538
N 98
C 128
Fe 240
Ni 60
Cr 47
Si 78
Ca 12
Cu
Ti
V <3
MO < 10
0
IN THE
Mg 83 Zr < 10
INVESTIGATION
Mn < 1
1
W < 30
Ta 151
AS SUPPLIED
BY THE+ PRODUCER
AI
Previous reports5-7 and preliminary tests showed that the formation of etch pits is strongly dependent on the orientation of the grains. Grains with the {111) crystallographic planes parallel to the external surface are easily etched. In order to increase the number of grains with a suitable orientation for etch-pit formation, a compression texture was produced with the compression axis normal to the 3 mm diam. rod axis. An intermediate anneal was needed and, after a final reduction of 4 %, the thickness of the sheet obtained was 1.6 mm. Recrystallization of this material yielded a grain size of 0.061 mm. All recrystallizations were performed under a vacuum better than 2 x 10m6 Torr. The sheets produced were then deformed 2.4 % in tension in order to introduce a certain amount of cold work. Sections were cut from the deformed sheets and the recovery treatments were conducted at SOO”,1000”, 1100” and 1200°C for times ranging from 15 min to 6 h. Again, all treatments were done under a vacuum better than 2 x lop6 Torr. Mechanical, followed by electrolytic polishing was used. Electrolytic polishing was conducted in a solution of 9 parts of H,S04 and one part of 48% HF7 at 7 V supplied by a potentiometric circuit, 5 min being sufficient for the removal of any marks from the mechanical polishing and to obtain a well-polished surface. This polishing was immediately followed by etching in the same solution after decreasing the voltage to 1.5. Etching time was observed not to influence the number of etch pits obtained. This time was adequately adjusted in order that etch-pit counting could be comfortably made. Decoration of the dislocations by interstitials proved to be necessary for complete development of the etch-pit structure and this was achieved by treatment for 3 h at 350°-4OO’C under vacuum. In all specimens, decoration was obtained through the natural cooling speed of the vacuum furnace. J. Less-Common
Metals,
27 (1972)
HIGH-TEMPERATURE
DISLOCATION
REARRANGEMENT
IN DEFORMED
Nb
3
RESULTS
Subgrain boundary formation was observed in all heat-treated specimens except those treated at 800°C and at 1000°C for 1 h. In Fig. 1 a typical example is given of the kind of substructures obtained and the plot of Fig. 2 shows how the average distance between subgrain boundary walls changes with temperature and time. There is a marked tendency for the average distance between walls to decrease with time, which should be interpreted as due to the formation of more and more welldefined, two-dimensional dislocation networks as the duration of the treatment increases. It is also apparent that at 1200°C the formation of these walls occurs faster than at 1100°C.
Fig. 1. Etch-pit structure for 4 h. ( x 3650)
of a niobium
specimen
deformed
2.4% in tension
and heat treated
at 1200°C
5
4
s, 2
I
Fig.
k Average
distance
between
etch-pit
walls as a function
of time (0
1200°C;
a,
11003C).
J.Less-CommonMauls,27 (1972)
4
Fig. 3. Grain
H. CARVALHINHOS
boundary
Fig. 4. Etch-pit J. Less-Common
structure Metals,
migration
in niobium 27 (1972)
in niobium
after 1 h at 12OO’C.
near a grain boundary
(x 1800)
after 4 h at 1200°C. ( x 3650)
et Ui.
HIGH-TEMPERATURE DISLOCATION REARRANGEMENT IN DEFORMED
Nb
5
Migration of the grain boundaries during heat treatment was a factor to consider in the evaluation of the etch-pit density. Migration was more pronounced at 1200°C (Fig. 3). The moving grain boundary leaves behind a rearranged dislocation distribution characterized by the formation of subgrain boundaries nearly perpendicular to the grain boundary and a considerable decrease in the overall dislocation density (Fig. 4). Taking this into consideration, etch-pit counting was done only in areas sufficiently far from the grain boundaries to insure that free rearrangement of dislocations was the only phenomenon to be evaluated. On determining the etch pit densities, the following two different criteria were applied : (i) counting all of the etch pits ; ii counting only those etch pits not included in well-defined, two dimensional disloca!i!n networks.
0
2
1
3
401 t (hour)
2
3
4
Fig. 5. Etch pit density as a function of time. (a) Total density. (b) Density of etch pits which do not belong to well-formed walls.
The average values obtained for each one of the sample surfaces observed are plotted in Fig. 5 as a function of time. The total number of etch pits counted for each pair of time-temperature values ranged from about 600 to 2600. Etch-pit counting was not possible on all the specimens treated at SOO”C,nor on the specimens treated at 1000” C, for times of less than one hour because the densities were too high to allow the resolution of the individual etch pits. DISCUSSION
Friedel’s equation (1) can be rearranged and written in the following form: 1
1
_-=-+_ P PO
t (1)
B J. ~~s-Co~~on
Metals, 27 (1972)
6
H. CARVALHINHOS
et al.
where p0 is the dislocation density at t = 0, t is the time for which the dislocation density has decreased top, and p N l/r2. Parameter B is a function of temperature according to :
(2) where Qsr, is the activation energy for self diffusion and D, is the diffusion constant. A plot of l/p against t was attempted but no linearity was obtained. Putting b=2.86 x lo-* cm, ~=3.75 x 10” dyne/cme2, Do= 1.94 cm2 see-’ and Qs,, = 98 kcal mole- i, it is easy to check that Friedel’s equation gives very small dislocation density variations for the durations and temperatures used in this work. In fact at the end of 4 h of treatment at 12OO”C,t/B is only 3.9 x lo- l1 cm2. Assuming that p,, > lo9 cm -2, the results of this research show that the decrease in dislocation density cannot be explained by this model. On the other hand, the two plots, p VS.t, at 1000°C suggest that, between one and two hours of treatment, the appreciable reduction in the number of dislocations which do not belong to two-dimensional networks is due to the formation of these same networks. Obviously, these two-dimensional networks form and grow at the expense of the available dislocations which belong to tangles or to the three-dimensional network. An illustration of this effect is shown in the micrographs of Figs. 6 and 7 which compare the structures obtained at the end of 1 h and 14 h, respectively, for a temperature of 1000°C.
Fig. 6. Etch-pit 1 h. (x 4150) J. Less-Common
structure
of a niobium
Metals, 27 (1972)
specimen
deformed
2.4% in tension
and heat treated
at 1000°C for
HIGH-TEMPERATURE
DISLOCATION
Fig. 7. Etch-pit structure 1.5 h. ( x 3700)
of a niobium
REARRANGEMENT
specimen
deformed
IN DEFORMED
2.4% in tension
Nb
and heat treated
at 1000°C for
It is, then, concluded that the formation of two-dimensional walls of dislocations is a faster mechanism for the reduction of dislocations from the bulk than mutual annihilation, as required in Friedel’s model. This model will possibly apply only when the former mechanism is exhausted. At 1100” and 1200°C this seems to take place after approximately 3 and a h, respectively. Well-formed subgrain substructures are already apparent at the end of these periods, and therefore the largest dislocation rearrangements taking place since the beginning of the heat treatment are practically over. The decrease of the dislocation density becomes progressively much slower and, for longer periods, will probably finish by reaching the low rates predicted by Friedel’s equation. The non-linearity of the l/p us. t plot can also be verified for the results of Keh’ on iron at 550°C. The derivative, d(l/p)/dt, continuously decreases and after 16 h its value is approaching l/Br6.5 x 10-i’ cm2 set-’ as calculated from eqn. (2). CONCLUSIONS
It has been observed that, at temperatures between 1000” and 12OO”C, a tangled dislocation structure, typical of cold-deformed niobium, initially recovers by an extensive rearrangement of the dislocations into two-dimensional walls accompanied by simultaneous mutual annihilation. This period is not described by Friedel’s Equation (1) which predicts much lower rates for the annihilation. However, the rate of change of the dislocation density continuously decreases with time. Previous work J. Less-Common Metals, 27 (1972)
8
H. CARVALHINHOS et U/.
on iron also suggests that Friedel’s model will be obeyed after longer times than those used in the present investigation; this will probably happen when the mechanism of dislocation rearrangement in two-dimensional networks is exhausted. ACKNOWLEDGEMENTS
This paper is published by permission of Laboratorio Nucleares, Sacavem, Portugal.
de Fisica e Engenharia
REFERENCES The creep of molybdenum and molybdenum-niobium alloys, Ph. D. Thesis, University of Sheffield, Nov. 1966. R. JACKSON,H. C~VA~INH~ ANDB. B. ARGENT,J. Inst. Mefuls, 96 (1968) 210. B. B. ARGENT,M. N. VANNIECKERKANDG. A. REDFERN,J. iron Steel ht., 208 (1970) 830. J. FRIEDBL,Dislocations, Pergamon Press, Oxford, 1964. E. ZEDLFX,J. Appl. Phys., 38 (1967) 1070. R. G. VARDIMANANDM. R. ACHTER,Trans. AIME, 242 (1968) 196-205. J. PELLEG,J. Less-Common Metals, 17 (1969) 130. A. S. KEH, Direct observation of imperfections in crystals, Proc. St. Louis Tech. Conf., A.Z.M.E., 1961, Interscience, New York, 1962, p. 213.
1 I-I. CARVALHINHOS,
2 3 4 5 6 7 8
J. Less-Common Metals, 27 (1972)
METALS in The Netherlands
HIGH-TEMPERATURE DISLOCATION COLD-DEFORMED NIOBIUM
H. CARVALHINHOS, MONTEIRO*
L. LYNCE
DE FARIA.
REARRANGEMENT
JOSe
Lahorardrio de Fisica e Engenharia Nucleares. Sacakm (Received
October
ALMEIDA
SEQUEIRA
IN LIGHTLY
AND
J. CUNHA
I Portugal)
5th. 1971)
SUMMARY
The etch-pit technique has been used to evaluate the kinetics of the dislocation density decrease in lightly deformed niobium as a function of‘time and temperatures between 1000” and 1200°C. The results show that the initial large drops in dislocation density are simultaneous with dislocation rearrangement during the formation of two dimensional networks. It is believed that after this mechanism is exhausted, the dislocation density reduction is increasingly controlled by the mutual annihilation of three dimensional network dislocations, according to a model developed by Friedel.
INTRODUCTION
Steady state creep at temperatures of about half the melting point and low stresses have been thought ’ - 3 to be due to the recovery of the three dimensional dislocation network which develops during the transient stage. In this model, the rate at which dislocations are torn away from the network determines the creep rate and, hence, information must be obtained on the kinetics of the network mesh size increase. Friede14 deduced an equation which describes the change in the size of the Frank network when the only driving force present is the tendency for the total line energy to decrease and the mechanism available is climb of edge dislocations. The average mesh size, r, is then found to increase parabolically with time, t. according to the expression : rz
_
W3q
- --@--
(t+const).
(1)
In this equation, D is the diffusion coefficient at temperature T,p is the shear modulus, b is the Burgers vector, cj is the jog concentration and k is the Boltzmann constant. The introduction of this equation in any creep theory can only be justified after checking its applicability to the kind of network structures and creep conditions * J. Cunha
Monteiro.
who initiated
this work. was killed in a car accident
in January
1969
J. Less-Common Metuls, 27 (1972)
H. CARVALHINHOS
2
et a/.
commonly encountered in practice. This paper describes work carried out on the recovery of the dislocation structures of lightly deformed niobium. The etch-pit technique was used for determining the number of dislocations because the dislocation densities reported after steady state creep at high temperatures and low stresses are normally low and of the order of 107-lo8 cm-‘. EXPERIMENTAL
The niobium used in this work was supplied in rod form with a diameter of 7 mm and a total interstitial content of 764 ppm. The composition according to the supplier is given in Table I. The rod was swaged down to 3 mm diam. and then recrystallised. TABLE IMPURITY
I CONTENT
(ppm)
OF THE
NIOBIUM
USED
538
N 98
C 128
Fe 240
Ni 60
Cr 47
Si 78
Ca 12
Cu
Ti
V <3
MO < 10
0
IN THE
Mg 83 Zr < 10
INVESTIGATION
Mn < 1
1
W < 30
Ta 151
AS SUPPLIED
BY THE+ PRODUCER
AI
Previous reports5-7 and preliminary tests showed that the formation of etch pits is strongly dependent on the orientation of the grains. Grains with the {111) crystallographic planes parallel to the external surface are easily etched. In order to increase the number of grains with a suitable orientation for etch-pit formation, a compression texture was produced with the compression axis normal to the 3 mm diam. rod axis. An intermediate anneal was needed and, after a final reduction of 4 %, the thickness of the sheet obtained was 1.6 mm. Recrystallization of this material yielded a grain size of 0.061 mm. All recrystallizations were performed under a vacuum better than 2 x 10m6 Torr. The sheets produced were then deformed 2.4 % in tension in order to introduce a certain amount of cold work. Sections were cut from the deformed sheets and the recovery treatments were conducted at SOO”,1000”, 1100” and 1200°C for times ranging from 15 min to 6 h. Again, all treatments were done under a vacuum better than 2 x lop6 Torr. Mechanical, followed by electrolytic polishing was used. Electrolytic polishing was conducted in a solution of 9 parts of H,S04 and one part of 48% HF7 at 7 V supplied by a potentiometric circuit, 5 min being sufficient for the removal of any marks from the mechanical polishing and to obtain a well-polished surface. This polishing was immediately followed by etching in the same solution after decreasing the voltage to 1.5. Etching time was observed not to influence the number of etch pits obtained. This time was adequately adjusted in order that etch-pit counting could be comfortably made. Decoration of the dislocations by interstitials proved to be necessary for complete development of the etch-pit structure and this was achieved by treatment for 3 h at 350°-4OO’C under vacuum. In all specimens, decoration was obtained through the natural cooling speed of the vacuum furnace. J. Less-Common
Metals,
27 (1972)
HIGH-TEMPERATURE
DISLOCATION
REARRANGEMENT
IN DEFORMED
Nb
3
RESULTS
Subgrain boundary formation was observed in all heat-treated specimens except those treated at 800°C and at 1000°C for 1 h. In Fig. 1 a typical example is given of the kind of substructures obtained and the plot of Fig. 2 shows how the average distance between subgrain boundary walls changes with temperature and time. There is a marked tendency for the average distance between walls to decrease with time, which should be interpreted as due to the formation of more and more welldefined, two-dimensional dislocation networks as the duration of the treatment increases. It is also apparent that at 1200°C the formation of these walls occurs faster than at 1100°C.
Fig. 1. Etch-pit structure for 4 h. ( x 3650)
of a niobium
specimen
deformed
2.4% in tension
and heat treated
at 1200°C
5
4
s, 2
I
Fig.
k Average
distance
between
etch-pit
walls as a function
of time (0
1200°C;
a,
11003C).
J.Less-CommonMauls,27 (1972)
4
Fig. 3. Grain
H. CARVALHINHOS
boundary
Fig. 4. Etch-pit J. Less-Common
structure Metals,
migration
in niobium 27 (1972)
in niobium
after 1 h at 12OO’C.
near a grain boundary
(x 1800)
after 4 h at 1200°C. ( x 3650)
et Ui.
HIGH-TEMPERATURE DISLOCATION REARRANGEMENT IN DEFORMED
Nb
5
Migration of the grain boundaries during heat treatment was a factor to consider in the evaluation of the etch-pit density. Migration was more pronounced at 1200°C (Fig. 3). The moving grain boundary leaves behind a rearranged dislocation distribution characterized by the formation of subgrain boundaries nearly perpendicular to the grain boundary and a considerable decrease in the overall dislocation density (Fig. 4). Taking this into consideration, etch-pit counting was done only in areas sufficiently far from the grain boundaries to insure that free rearrangement of dislocations was the only phenomenon to be evaluated. On determining the etch pit densities, the following two different criteria were applied : (i) counting all of the etch pits ; ii counting only those etch pits not included in well-defined, two dimensional disloca!i!n networks.
0
2
1
3
401 t (hour)
2
3
4
Fig. 5. Etch pit density as a function of time. (a) Total density. (b) Density of etch pits which do not belong to well-formed walls.
The average values obtained for each one of the sample surfaces observed are plotted in Fig. 5 as a function of time. The total number of etch pits counted for each pair of time-temperature values ranged from about 600 to 2600. Etch-pit counting was not possible on all the specimens treated at SOO”C,nor on the specimens treated at 1000” C, for times of less than one hour because the densities were too high to allow the resolution of the individual etch pits. DISCUSSION
Friedel’s equation (1) can be rearranged and written in the following form: 1
1
_-=-+_ P PO
t (1)
B J. ~~s-Co~~on
Metals, 27 (1972)
6
H. CARVALHINHOS
et al.
where p0 is the dislocation density at t = 0, t is the time for which the dislocation density has decreased top, and p N l/r2. Parameter B is a function of temperature according to :
(2) where Qsr, is the activation energy for self diffusion and D, is the diffusion constant. A plot of l/p against t was attempted but no linearity was obtained. Putting b=2.86 x lo-* cm, ~=3.75 x 10” dyne/cme2, Do= 1.94 cm2 see-’ and Qs,, = 98 kcal mole- i, it is easy to check that Friedel’s equation gives very small dislocation density variations for the durations and temperatures used in this work. In fact at the end of 4 h of treatment at 12OO”C,t/B is only 3.9 x lo- l1 cm2. Assuming that p,, > lo9 cm -2, the results of this research show that the decrease in dislocation density cannot be explained by this model. On the other hand, the two plots, p VS.t, at 1000°C suggest that, between one and two hours of treatment, the appreciable reduction in the number of dislocations which do not belong to two-dimensional networks is due to the formation of these same networks. Obviously, these two-dimensional networks form and grow at the expense of the available dislocations which belong to tangles or to the three-dimensional network. An illustration of this effect is shown in the micrographs of Figs. 6 and 7 which compare the structures obtained at the end of 1 h and 14 h, respectively, for a temperature of 1000°C.
Fig. 6. Etch-pit 1 h. (x 4150) J. Less-Common
structure
of a niobium
Metals, 27 (1972)
specimen
deformed
2.4% in tension
and heat treated
at 1000°C for
HIGH-TEMPERATURE
DISLOCATION
Fig. 7. Etch-pit structure 1.5 h. ( x 3700)
of a niobium
REARRANGEMENT
specimen
deformed
IN DEFORMED
2.4% in tension
Nb
and heat treated
at 1000°C for
It is, then, concluded that the formation of two-dimensional walls of dislocations is a faster mechanism for the reduction of dislocations from the bulk than mutual annihilation, as required in Friedel’s model. This model will possibly apply only when the former mechanism is exhausted. At 1100” and 1200°C this seems to take place after approximately 3 and a h, respectively. Well-formed subgrain substructures are already apparent at the end of these periods, and therefore the largest dislocation rearrangements taking place since the beginning of the heat treatment are practically over. The decrease of the dislocation density becomes progressively much slower and, for longer periods, will probably finish by reaching the low rates predicted by Friedel’s equation. The non-linearity of the l/p us. t plot can also be verified for the results of Keh’ on iron at 550°C. The derivative, d(l/p)/dt, continuously decreases and after 16 h its value is approaching l/Br6.5 x 10-i’ cm2 set-’ as calculated from eqn. (2). CONCLUSIONS
It has been observed that, at temperatures between 1000” and 12OO”C, a tangled dislocation structure, typical of cold-deformed niobium, initially recovers by an extensive rearrangement of the dislocations into two-dimensional walls accompanied by simultaneous mutual annihilation. This period is not described by Friedel’s Equation (1) which predicts much lower rates for the annihilation. However, the rate of change of the dislocation density continuously decreases with time. Previous work J. Less-Common Metals, 27 (1972)
8
H. CARVALHINHOS et U/.
on iron also suggests that Friedel’s model will be obeyed after longer times than those used in the present investigation; this will probably happen when the mechanism of dislocation rearrangement in two-dimensional networks is exhausted. ACKNOWLEDGEMENTS
This paper is published by permission of Laboratorio Nucleares, Sacavem, Portugal.
de Fisica e Engenharia
REFERENCES The creep of molybdenum and molybdenum-niobium alloys, Ph. D. Thesis, University of Sheffield, Nov. 1966. R. JACKSON,H. C~VA~INH~ ANDB. B. ARGENT,J. Inst. Mefuls, 96 (1968) 210. B. B. ARGENT,M. N. VANNIECKERKANDG. A. REDFERN,J. iron Steel ht., 208 (1970) 830. J. FRIEDBL,Dislocations, Pergamon Press, Oxford, 1964. E. ZEDLFX,J. Appl. Phys., 38 (1967) 1070. R. G. VARDIMANANDM. R. ACHTER,Trans. AIME, 242 (1968) 196-205. J. PELLEG,J. Less-Common Metals, 17 (1969) 130. A. S. KEH, Direct observation of imperfections in crystals, Proc. St. Louis Tech. Conf., A.Z.M.E., 1961, Interscience, New York, 1962, p. 213.
1 I-I. CARVALHINHOS,
2 3 4 5 6 7 8
J. Less-Common Metals, 27 (1972)