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Diffusion in uranium carbide by the mass transfer method
JOURNAL
OF NUCLEAR
DIFFUSION
MATERIALS
34 (1970) 111-l 13. 0 NORTH-HOLLAND
IN URANIUM
CARBIDE
BY THE
PUBLISHING
MASS TRANSFER
CO., AMSTERDAM
METHOD
*
P. S. XA1Y.A and J. L. ROUTBORT Argomne National Laboratory, Argonne, Illinois 60439, USA Received 10 July 1969
fusion coefficient, y is the surface free energy, 9 is the atomic volume, and kT has its usual meaning. If surface diffusion controls the kinetics of formation of groove profiles, then the dependence of the width, W8, on annealing time is given by Ws = 4.6 (Bt)i/4, (2)
The theoretical analysis 192) of the development of grain-boundary grooves on the surface of an annealed polycrystalline material established it as a useful tool for the measurement of surface-effusion coefficients and relative interfacial energies in metals. The growth of grain-boundary grooves has been successfully related to diffusion in oxides such as UOz 394) and MgO 4~5), but few results have been reported on refractory or actinide carbides. Hodkin et at. a) calculated the ratio of grainboundary energy to surface energy in UC from the grain-boundary groove angles produced over a range of temperatures. However, diffusional kinetics in UC using this technique have not been reported. The high thermal conductivity and melting point and large fissile atom density make uranium-plutonium carbides an attractive fuel material for fast breeder reactors. The purpose of this note is to report preliminary results of grain-boundary grooving experiments, at 197O2185 “C, on polycrystalline UC and to show the feasibility of a systematic study of diffusional processes using this method. Mullins has given rigorous mathematical solutions for the growth of lain-boundary grooves in crystals for various operating mechanisms. In particular, for the growth of grooves by a volume diffusion mechanism, the dependence of groove width, W,, on annealing time, t, is given by 2) W,= 5.0 (c%)l/3, (1) where *
c=(D,yQ/kT),
D,
is the volume
dif-
where B= ~D~y~2~l~T),
Ds is the surface dif-
fusion ~oe~cient, and N is the surface atom density. Therefore, the influence of time and temperature on the grain-boundary groove width will yield information on the grooving mechanisms as well as the values of the diffusion coe~cients. The material used in this study was arc-cast polycrystalline UC prepared at Atomics International. The concentrations 0.05 wt%,
respectively.
carbon, in the
oxygen, material
and nitrogen were 4.94 i
138 ppm,
and 320 ppm by weight, The UC sample (9.5 mm in dia-
meter by 9.5 mm high) was contained in a tungsten crucible and annealed at 1600 “C for 8 h in a vacuum of 10-G Torr to degas the specimen, to enlarge the grains, and to stabilize the boundaries. The specimen was ground on silicon carbide paper and then polished on alumina using a mixture of ethylene glycol and methanol as a lubricant. Finally, the flatness of ,the polished surface was checked by observing the in~~erence pattern obtained with a Zeiss interference microscope. No grainboundary grooves were visible within the 300 A limit of vertical resolution of the microscope.
This work was performed under the auspices of the United States Atomic Energy Commission. 111
112
P,
S.
MAIYA
AND
J.
L.
ROUTBORT
Anneals were made at 1970, 2050, and 2185 “C in continuously
flowing
helium for 9, 8, and
0
5 h, respectively. The temperature was eontrolled within i 5 “C and was measured with a calibrated
optical pyrometer
SURFACE
6. VOLUME
DIFFUSION DlFFUSlON
under blackbody
conditions. Since UC oxidized rapidly after removal from the vacuum,
it was necessary
sample in ethylene glycol examined.
to immerse t,he
until the sample was
The surface was cleaned with meth-
anol prior to photographing the profile of the grairl-boundary groove. This procedure allowed at least two grain-boundary profiles to be photographed before oxidation affected the interference pattern. Therefore, before each aIrmeal, it was necessary to polish the specimen surface on alumina to remove the oxide film. Typical grain-boundary grooves formed at the three temperatures are shown in fig. 1. The
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
104/T,“K-’
Fig. 2.
Variation of the calculated
surface
volume diffusion coefficients with temperature. values are based on alternative
interpretations
and These (see
text).
formation of humps on either side of the boundary, following Mullins’ theory, indicates that groove formation is controlled by diffusion rather than by an evaporation-condensation process. In order to determine whether surface or volume diffusion (or a combination of the two) cont,rols the groove width, the time dependence of the groove dimensions must be studied at a constant temperature. Because of the difficult,y in preventing the oxide film formation, the time dependence was not studied in this ~reIiminary work. However, if either a volume- or surface-diffusion process is assumed, the results can be analyzed on the basis of eqs. (1) and (2) by using a value 7) of y = 1000 erg/cm2 and Q= 3.052 ems/atom. The volume and surface diffusion coefficients calculated by means of these assumptions are shown in fig. 2. The temperature dependence of these coefficients is given by II,= Fig. 1.
Interferograms
of
grain-boundary
formed in UC after annealing in helium temperatures.
Thallium
grooves
at different
light was used.
(a) 1970 “C, 9 h; (b) 205O”C, 8 h; (c) 2185 “C, 5 h.
(0.18 -i: 0.19) x 10-3 exp - (62000 i_ ~OOO~~T~
(3)
and I&=(4.9
rtr 7.3) exp - (70 000 & aOOO/BT),
(4)
DIFFUSION
IN
URANIUM
CARBIDE
BY
Species
I
Carbon
diffusing
:
(wt%)
diffusion data for carbon and uranium
!
!
1266-1684 1266-1684
2.95x
1266-1684
2.76 x 10-3
1200-1940
2 x 10-Z
j
4.82 5.0
113
METHOD
uranium
carbide
4.83
i j
4.83
’
1.75 10-2
Technique
1 I
t
5.1 5.0 Uranium
in arc-cast
& (kcal/mole)
/
4.82 5.6
TRANSFER
/ /
Carbon
MASS
1
TABLE
Volume
THE
Ref.
63 Jr 1
Tracer sectioning
8)
54 & 15
Tracer sectioning
8)
43 f
6
Tracer sectioning
8)
50 & 2
Tracer sectioning
Q)
104 & 7
Tracer sectioning
/
1505-1863
8.47
1600-2120
1.3 x 10-3
1400-2000
1.85 x 10-4
90 + 6
Alpha, energy
100~1400
1.21 x 10-12
28 & 4
Alpha
64 f
9 g, lo)
Tracer sectioning
20
degradation energy
loI
degradation
Not
4.96
1970-2185
1.8x10-4
j
’
62 + 4
identified *
The diffusion parameters
Grain-boundary
j This *
grooving are valid only if volume
where the errors are the standard errors of the least-squares fit. Since we are unaware of any published values for US in UC, it is not possible to compare or comment, on t,he results in eq. (4). However, published values of the volume cation and anion self-diffusivity exist and are tabulated in table 1, along with the results of this work. A meaningful comparison of our activation energy, &, and preexponential factor, DO, with the published data is not possible because of the variation in self-diffusion results. Our values seem t‘o agree with the values for cation diffusion in UC for similar stoichiometry. These preliminary results demonstra~ that the measurement of gra,i~-boundary grooves is useful for studying diffusion in UC. Experiments are now planned to investigate diffusion in carbides by means of surface relaxation techniques.
work
diffusion is responsible for the grooving.
References
1) 9 3,
W.
W.
W.
W. Mullins, Trans. AIME
Mullins, 3. Appl.
I. Am&o,
R.
Phys.
L. Colombo
Solid State Commun.
28 (1957)
333
218 (1960) 354
and G. C. Gsxppiolo,
4 (1966)
237
4) J. Henney and J. W. S. Jones, J. Mater. Soi. 3 (1968)
5) W.
158
M.
Robertson,
phenomena, and Breach,
9
in
Sintering
ed. G. C. Kuczynski
and
related
et al. (Gordon
1967)
E. N. Hodkin,
M. G. Nicholas and D. M. Poole,
J. Nucl.
25 (1968)
Mat.
284
7)
D. T. Livey and P. Murray, Plansee Proc. (1955)
8)
H. M. Lee and L. R. Barrett,
375 (1968)
9)
W.
Chubb,
J. Nucl.
9
J. Nucl.
Mat. 27
275 R.
Mat.
W.
Getz
13 (1964)
and
C. W.
Townley,
63
R. Lindner, G. Riemer and H. L. Scherff, J. Nucl. Mot.
23 (1967)
222
OF NUCLEAR
DIFFUSION
MATERIALS
34 (1970) 111-l 13. 0 NORTH-HOLLAND
IN URANIUM
CARBIDE
BY THE
PUBLISHING
MASS TRANSFER
CO., AMSTERDAM
METHOD
*
P. S. XA1Y.A and J. L. ROUTBORT Argomne National Laboratory, Argonne, Illinois 60439, USA Received 10 July 1969
fusion coefficient, y is the surface free energy, 9 is the atomic volume, and kT has its usual meaning. If surface diffusion controls the kinetics of formation of groove profiles, then the dependence of the width, W8, on annealing time is given by Ws = 4.6 (Bt)i/4, (2)
The theoretical analysis 192) of the development of grain-boundary grooves on the surface of an annealed polycrystalline material established it as a useful tool for the measurement of surface-effusion coefficients and relative interfacial energies in metals. The growth of grain-boundary grooves has been successfully related to diffusion in oxides such as UOz 394) and MgO 4~5), but few results have been reported on refractory or actinide carbides. Hodkin et at. a) calculated the ratio of grainboundary energy to surface energy in UC from the grain-boundary groove angles produced over a range of temperatures. However, diffusional kinetics in UC using this technique have not been reported. The high thermal conductivity and melting point and large fissile atom density make uranium-plutonium carbides an attractive fuel material for fast breeder reactors. The purpose of this note is to report preliminary results of grain-boundary grooving experiments, at 197O2185 “C, on polycrystalline UC and to show the feasibility of a systematic study of diffusional processes using this method. Mullins has given rigorous mathematical solutions for the growth of lain-boundary grooves in crystals for various operating mechanisms. In particular, for the growth of grooves by a volume diffusion mechanism, the dependence of groove width, W,, on annealing time, t, is given by 2) W,= 5.0 (c%)l/3, (1) where *
c=(D,yQ/kT),
D,
is the volume
dif-
where B= ~D~y~2~l~T),
Ds is the surface dif-
fusion ~oe~cient, and N is the surface atom density. Therefore, the influence of time and temperature on the grain-boundary groove width will yield information on the grooving mechanisms as well as the values of the diffusion coe~cients. The material used in this study was arc-cast polycrystalline UC prepared at Atomics International. The concentrations 0.05 wt%,
respectively.
carbon, in the
oxygen, material
and nitrogen were 4.94 i
138 ppm,
and 320 ppm by weight, The UC sample (9.5 mm in dia-
meter by 9.5 mm high) was contained in a tungsten crucible and annealed at 1600 “C for 8 h in a vacuum of 10-G Torr to degas the specimen, to enlarge the grains, and to stabilize the boundaries. The specimen was ground on silicon carbide paper and then polished on alumina using a mixture of ethylene glycol and methanol as a lubricant. Finally, the flatness of ,the polished surface was checked by observing the in~~erence pattern obtained with a Zeiss interference microscope. No grainboundary grooves were visible within the 300 A limit of vertical resolution of the microscope.
This work was performed under the auspices of the United States Atomic Energy Commission. 111
112
P,
S.
MAIYA
AND
J.
L.
ROUTBORT
Anneals were made at 1970, 2050, and 2185 “C in continuously
flowing
helium for 9, 8, and
0
5 h, respectively. The temperature was eontrolled within i 5 “C and was measured with a calibrated
optical pyrometer
SURFACE
6. VOLUME
DIFFUSION DlFFUSlON
under blackbody
conditions. Since UC oxidized rapidly after removal from the vacuum,
it was necessary
sample in ethylene glycol examined.
to immerse t,he
until the sample was
The surface was cleaned with meth-
anol prior to photographing the profile of the grairl-boundary groove. This procedure allowed at least two grain-boundary profiles to be photographed before oxidation affected the interference pattern. Therefore, before each aIrmeal, it was necessary to polish the specimen surface on alumina to remove the oxide film. Typical grain-boundary grooves formed at the three temperatures are shown in fig. 1. The
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
104/T,“K-’
Fig. 2.
Variation of the calculated
surface
volume diffusion coefficients with temperature. values are based on alternative
interpretations
and These (see
text).
formation of humps on either side of the boundary, following Mullins’ theory, indicates that groove formation is controlled by diffusion rather than by an evaporation-condensation process. In order to determine whether surface or volume diffusion (or a combination of the two) cont,rols the groove width, the time dependence of the groove dimensions must be studied at a constant temperature. Because of the difficult,y in preventing the oxide film formation, the time dependence was not studied in this ~reIiminary work. However, if either a volume- or surface-diffusion process is assumed, the results can be analyzed on the basis of eqs. (1) and (2) by using a value 7) of y = 1000 erg/cm2 and Q= 3.052 ems/atom. The volume and surface diffusion coefficients calculated by means of these assumptions are shown in fig. 2. The temperature dependence of these coefficients is given by II,= Fig. 1.
Interferograms
of
grain-boundary
formed in UC after annealing in helium temperatures.
Thallium
grooves
at different
light was used.
(a) 1970 “C, 9 h; (b) 205O”C, 8 h; (c) 2185 “C, 5 h.
(0.18 -i: 0.19) x 10-3 exp - (62000 i_ ~OOO~~T~
(3)
and I&=(4.9
rtr 7.3) exp - (70 000 & aOOO/BT),
(4)
DIFFUSION
IN
URANIUM
CARBIDE
BY
Species
I
Carbon
diffusing
:
(wt%)
diffusion data for carbon and uranium
!
!
1266-1684 1266-1684
2.95x
1266-1684
2.76 x 10-3
1200-1940
2 x 10-Z
j
4.82 5.0
113
METHOD
uranium
carbide
4.83
i j
4.83
’
1.75 10-2
Technique
1 I
t
5.1 5.0 Uranium
in arc-cast
& (kcal/mole)
/
4.82 5.6
TRANSFER
/ /
Carbon
MASS
1
TABLE
Volume
THE
Ref.
63 Jr 1
Tracer sectioning
8)
54 & 15
Tracer sectioning
8)
43 f
6
Tracer sectioning
8)
50 & 2
Tracer sectioning
Q)
104 & 7
Tracer sectioning
/
1505-1863
8.47
1600-2120
1.3 x 10-3
1400-2000
1.85 x 10-4
90 + 6
Alpha, energy
100~1400
1.21 x 10-12
28 & 4
Alpha
64 f
9 g, lo)
Tracer sectioning
20
degradation energy
loI
degradation
Not
4.96
1970-2185
1.8x10-4
j
’
62 + 4
identified *
The diffusion parameters
Grain-boundary
j This *
grooving are valid only if volume
where the errors are the standard errors of the least-squares fit. Since we are unaware of any published values for US in UC, it is not possible to compare or comment, on t,he results in eq. (4). However, published values of the volume cation and anion self-diffusivity exist and are tabulated in table 1, along with the results of this work. A meaningful comparison of our activation energy, &, and preexponential factor, DO, with the published data is not possible because of the variation in self-diffusion results. Our values seem t‘o agree with the values for cation diffusion in UC for similar stoichiometry. These preliminary results demonstra~ that the measurement of gra,i~-boundary grooves is useful for studying diffusion in UC. Experiments are now planned to investigate diffusion in carbides by means of surface relaxation techniques.
work
diffusion is responsible for the grooving.
References
1) 9 3,
W.
W.
W.
W. Mullins, Trans. AIME
Mullins, 3. Appl.
I. Am&o,
R.
Phys.
L. Colombo
Solid State Commun.
28 (1957)
333
218 (1960) 354
and G. C. Gsxppiolo,
4 (1966)
237
4) J. Henney and J. W. S. Jones, J. Mater. Soi. 3 (1968)
5) W.
158
M.
Robertson,
phenomena, and Breach,
9
in
Sintering
ed. G. C. Kuczynski
and
related
et al. (Gordon
1967)
E. N. Hodkin,
M. G. Nicholas and D. M. Poole,
J. Nucl.
25 (1968)
Mat.
284
7)
D. T. Livey and P. Murray, Plansee Proc. (1955)
8)
H. M. Lee and L. R. Barrett,
375 (1968)
9)
W.
Chubb,
J. Nucl.
9
J. Nucl.
Mat. 27
275 R.
Mat.
W.
Getz
13 (1964)
and
C. W.
Townley,
63
R. Lindner, G. Riemer and H. L. Scherff, J. Nucl. Mot.
23 (1967)
222