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131I diffusion in charge-transfer complexes
Solid State Ionics 3/4 (1981) 191-195 North-Holland Publishing Company
lSll DIFFUSION IN C H A R G E - T R A N S F E R C O M P L E X E S J.I. F R A N C O , L. P E R I S S I N O T F I Research Commission of the Province of Buenos Aires, Argentina and The Armed Forces Institute for Technological and Scientific Research, 1603 Buenos Aires, Argentina
and N.E. WALStDE D E R E C A The National Council for Scientific and Technological Research and The Armed Forces Institute for Technological and Scientific Research, 1603 Buenos Aires, Argentina
The diffusion coefficients of the active species (12) was evaluated in 212.pyrene, 212-violanthrene and in 312.2phenotiazin which are employed at present as charge-transfer complexes in solid-state ceils. The measurements were performed by the Gruzin-Seibel method in a range of temperatures between 0.5 and 60°C. In all three cases a strong contribution of short-path diffusion was observed. The autoradiographs enabled us to follow the process and to compare our results with those of the Gruzin method and with the structural aspect observed by scanning electron microscopy (SEM).
1. Experimental
1.2. Preparation of samples for the Gruzin-Seibel method
1.1. Autoradiographic sample preparation Cylindrical samples of the complexes of height 0.3-0.7 cm and area 1.29 c m 2 w e r e pressed under 1 ton cm -2. In the same conditions 13q-doped specimens of the complexes were o b t a i n e d . 1311 (A --- 8.04 days) is a 3/ and fl emitter. Both specimens were previously stabilized and then pressed together in a special device and thermostatted in a sealed jar between 0.5 and 60°C, employing a Lauda thermostat (AT = -0.1°C). After diffusion the samples were polished perpendicular to the diffusion flux direction. Autoradiographs were obtained with N U C - A g f a G e v a e r t films with exposure times between 28 and 76 h at - 1 0 to -15°C. Corrections for radioisotope decay as well as lowt e m p e r a t u r e diffusion during exposure were taken into account. SEM m e a s u r e m e n t s were made in a Jeol J M - I I I at accelerating voltages between 5 and 10 kV.
Cylindrical specimens (similar to those employed in autoradiographic experiments) were stabilized and doped with 131I. The radioisotope was deposited on one face of the specimens in the following way: a cellulose p a p e r on the deposit face was wetted with 131Iin CHCI3 solution. After drying, the specimens were thermostatted as described above.
1.3. Gruzin-Seibel method An important condition to apply this method is the exponential absorption of radioisotope radiation ( B e e r - L a m b e r t law). This fact was previously proved. Also, the size of grain boundaries must be large enough (~b > 200 ~t m) in order to avoid contributions of grain-boundary diffusion to the bulk diffusion coefficients. The Gruzin method considers a radioactive infinite thin source diffusing in a semi-infinite solid. I0 is the initial activity corresponding to
0167-2738/81/0000-0000/$02.50 O North-Holland Publishing C o m p a n y
J.L Franco et al. / t311diffusion in charge-transfer complexes
192
the initial surface x0. T h e activity is m e a s u r e d with a Tracerlab counter. Successive abrasions are p e r f o r m e d and the r e m o v e d thickness is d e t e r m i n e d by weight difference (AG = _1 × 10 -6 g).
m =-2~/2(rrDvt) '/~(Dv/Dsp~) '/2.
T h e concentration of radioactive material at the time t(s) is C ( X ) . O n c e polished, the specimen at a distance x, f r o m the original surface, the whole remaining activity (I,) is measured, resulting [1] in I.
C(x) e x p ( - / z x ) dx,
k exp0zxn)
2. Results and discussion
where # is the radiation absorption coefficient (cm-l). By a convenient c h a n g e of variables, we have (2)
H e r e C(x) is given by
C(x) = M(rrDvt) -I/2 e x p ( - x2./4Dvt),
At intermediate temperatures, volume and short-range mechanisms of diffusion coexist. For the specimen layers near the surface a linear distribution results in the plot of In(#/. aI,dax.) versus x~ while for d e e p e r layers ln(~I. - OI,,/Ox.) versus x. is linear. A u t o r a d i o g r a p h s give clear information on radioisotope distribution and the results complement the Gruzin m e t h o d .
(1)
xn
lzl. - aI./ax. = kC(x).
(3)
where M is the initial a m o u n t of deposited radioisotope and Dv is the bulk diffusion coefficient (cm 2 s-l). The aI./ax, are o b t a i n e d f r o m the penetration curve I. versus x.. F r o m the slope p = -1/4Dvt of the plot of l n ( / z I . - aI./ax.) versus x2. the diffusion coefficients are obtained. At very low t e m p e r a t u r e s ( T < T / 2 ) shortrange diffusion b e c o m e s important. T h e specific activity I ( x . ) c o r r e s p o n d i n g to a concentration C(x) varies exponentially with in(/zI~ - aI./Ox.).
Fig. 1 is a typical penetration curve I. versus x. c o r r e s p o n d i n g to 131I diffusion in 212-pyrene during ! h at 26°C. T h r e e zones are easily observed: (I) which c o r r e s p o n d s to the volume or bulk diffusion region, where the Dv are evaluated; (II) c o r r e s p o n d i n g to simultaneous volume and short-path diffusion processes; an a p p a r e n t diffusion coefficient Da is calculated in this case; and (III) which c o r r e s p o n d s to a strong-path diffusion contribution and where Dsp6 values are obtained. T h e plot of ln(~I. - aI./Ox.) versus x~ corresponding to the same specimen shows a curvature of the function which implies a strong contribution to Da due to short-path diffusion. Table 1 summarizes the Dv, Da and Ospt~ values o b t a i n e d for 131I diffusion in the different CTC. Because of the low t e m p e r a t u r e s of the
If
C(x.) = k,{l - exp[(x. - ½6)/2(D~t)'/2]},
(4)
where 6 is the m e a n value of short-path diameter and the corresponding specific activity is: I (x.) = k ' e x p [ - 7r-]/4(Dvt)-m[3-]/2x. ],
II in.lO~(e.s ~) I 10(}
(5)
with
fl : [6/2( Dvt )I/2]D~p/D~ .
(7)
50
(6)
D~p is the short path diffusion coefficient. T h e plot of ln(/zI. - aI./ax.) versus x. is a straight line whose slope m enables us to calculate Dsp8 if Fisher conditions are accomplished [2]
Fig. 1. I. versus X..
J.L Franco et al. / t~ll diffusion in charge-transfer complexes
Table
193
1 T(K)
D~ ( c m 2 s -I)
212.violanthrene (Tdesc
=
Da (cm I s -l)
Dwt5 (cm 2 s i)
220°C)
309
(1.31 -+0.14)× 10 6
298 298 288 Da = 2.20 × 10 3 exp(-4563/RT)
(9.95 -+ 1.09) × 10 7 (9.58-+ 1.(15)× 10 7 (7.62-+ 0.83) × 10 7
212.pyrene (Tt = 319 309
120°C) (4.25-+0.46) × 10 s (2.98 -+ 0.32) × 10 -s
303
( 1 . 9 6 - + 0 . 2 1 ) × 10 8
299 298
( 1 . 6 5 - + 0 . 1 7 ) × I0 ~ (1.56 -+ 0.17) × 10 8
292.5 288
(1.23 -+ 0.13) × 10 -8 (9.40 -+ 1.05) × 10 '~
283.5 283 274.5 273.5 D~ = 0.222 e x p ( - 9 7 1 1 / R T ) Da = 46.52 exp(-8879/RT) Q(l~lI short-path diffusion) = 4495 3I~-2phenotiazin (Tf = 171.5°C) 319 ( 3 . 9 9 - + 0 . 4 3 ) x I0 9 311 ( 2 . 6 8 - + 0 . 2 9 ) x 10 9 305 ( 2 . 1 5 - + 0 . 2 3 ) x 10 9 303 ( 1 . 8 5 - + 0 . 2 0 ) x 10 o 298 ( 1 . 5 0 + 0 . 1 6 ) x 10 -9 298 (1.61 - + 0 . 1 7 ) x 10 -9 292.5 286 279.5 273.5 Ov = 5.30 × 10 -4 exp(-7528/RT) D . = 0.523 e x p ( - 7604/RT) Q(13Jl short-path diffusion) = 4193
(4.28 -+ 0.47) × 10 ~ (2.63-+0.28) x 10 -5 (1.66-+ 0.18) x 1(1-s ( 1 . 3 8 - + 0 . 1 4 ) × 10 5 ( 1 . 3 2 - + 0 . 1 4 ) x 10 5 (1.04-+0.11) x 10 5 (7.83 -+ (I.86) x 10 -6 ( 6 . 8 6 - + 0 . 7 5 ) × 10 6 (6.56-+(1.72)× 10 ~' (4.11 -+0.45)× 10 -6 (3.89-+0.42) x 10 6
cal mole
experiments the Dv values for 131I diffusion in 212-Vi were not calculated. Otherwise the Dsp• values corresponding to lower temperatures of diffusion (in 212"Py and in 313-2Phe) were obtained employing Dv values which were extrapolated from experiments at higher temperatures. Fig. 2 shows an autoradiograph (M -- 320×) of a 131I diffused 212"Py specimen, taken at a depth corresponding to z o n e III of fig. 1. Fig. 3 is a SEM micrography of the same specimen ( M = 320x) showing the short-paths
(1.79-+0.34)× (1.52-+0.28)× (1.42-+0.26)× (1.411-+0.26)× (1.23-+0.23)× (1.06-+0.20) x
10 10 10 10 10 I0
" N H ii H 11
(8.56-+3.43)× (8.32 -+ 3.32) x (6.01-+2.41)× (5.96 -+ 2.38) x
10 1() 10 10
12 12 12 12
(1.72-+0.33)x (1.27-+0.24)x (1.08-+0.20)x (9.53 + 1 . 8 1 ) x ( 8 . 2 0 +- 1.56) x (7.83-+ 1 . 4 9 ) x (7.52 -+ 3.01) x (6.33-+2.52)x (3.83 -+ 1.53) x (2.81 -+ 1.13) × (2.22 -+ 0.99) ×
10 ii i0 ii 10 H 10 -12 10 -12 10 J2 10 -12 10 12 10 -12 10 12 10 -12
1
(3.46-+0.38) x (2.35-+l).25) x (1.86-+0.20)x (1.62_+0.14) x (1.31 -+0.15) x (1.41 -+0.15) x (1.22 -+ 0.13) x (1.11 - + 0 . 1 2 ) x (8.08 -+ 0.88) × (4.98 -+ 0.55) × (4.21 -+ 0.46) ×
cal mole
( 2 . 2 7 - + 0 . 4 3 ) × 10 N
10 6 10 6 10 -6 10 -6 10 6 10 6 10 -6 10 ~ 10 -7 10 -7 10 -7
i
and pores through which the diffusion is accelerated. Fig. 4 ( M = 80×) shows an autoradiograph of a t31I diffused 312.2Phe specimen taken in the z o n e II; it is possible to observe the volume and short-path diffusions. Fig. 5 corresponds to t3~I diffusion in 212"Vi in z o n e (III) ( M = 80x). In Dv versus 1/T, In DR versus 1/T and In Dw8 versus 1/T follow an Arrhenius function from which the frequency factor Do (cm s -1) and the activation energy Q (cal mole -~) can be evaluated. These values are reported in table 1.
J.L Franco et al, / 131I diffusion in charge-transfer complexes
194
at ,
"
A4,
• -"
.
~.3t~.
" Z
.--. Fig. 2, A u t o r a d i o g r a p h of a 13~I diffused 212"Py specimen, taken at a depth corresponding to zone III of fig. 1 ( M = 320 x ).
•
-'
"
* "4,
°.
:
~
'
7,(
,-
r
-5
°°"
-"
~lb
*
.
•
0.
-'
Q "
Fig. 4. A u t o r a d i o g r a p h of a ]~lI diffused 312.2Phe specimen taken in zone II ( M = 80×).
Fig. 3. SEM micrograph corresponding to the same area of fig. 2 (M = 320×).
Fig. 5. A u t o r a d i o g r a p h y of a ]3~I diffused 212.Vi taken in the zone IIl ( M = 80×).
3. Conclusions
(2) By the same method the bulk diffusion coefficients (Dv) were determined when temperature was higher enough and D~p6 values at lower temperatures (employing extrapolated Dv values). (3) The Dr, D, and D~p(5 variation with temperature follows an Arrhenius distribution and enabled us to calculate the activation energy and frequency factor of the process.
(1) The apparent diffusion coefficients (Da) in three C T C (212"Py, 212"Vi and 312.2Phe) were calculated with the G r u z i n Seibel method in the range of temperatures from 0.5 to 60°C (working t e m p e r a t u r e range of solid-state cells), showing an important shortpath diffusion contribution. f o r ~31I diffusion
J.L Franco et al. / 13ti diffusion in charge-transfer complexes
(4) The autoradiographs enabled us to follow the processes and to corroborate the above reported results. (5) The correlation between structural aspect and autoradiographic results was performed by SEM. The porous structure of complexes justifies the high observed diffusivities.
Acknowledgement JIF and NEWdR gratefully acknowledge grants from CONICET, CIC and the "Alberto
195
J. Roemmers" Foundation. We thank V. Frank for his valuable help in the computer processing.
References [1] Y. Adda and J. Philibert, La diffusion dans les solides (Presses Universitaires de France, Paris, 1966) pp. 264, 716. [2] P. Guiraldenq, Metaux, corrosion et industries, Vol. 39 (1964) p. 374.
lSll DIFFUSION IN C H A R G E - T R A N S F E R C O M P L E X E S J.I. F R A N C O , L. P E R I S S I N O T F I Research Commission of the Province of Buenos Aires, Argentina and The Armed Forces Institute for Technological and Scientific Research, 1603 Buenos Aires, Argentina
and N.E. WALStDE D E R E C A The National Council for Scientific and Technological Research and The Armed Forces Institute for Technological and Scientific Research, 1603 Buenos Aires, Argentina
The diffusion coefficients of the active species (12) was evaluated in 212.pyrene, 212-violanthrene and in 312.2phenotiazin which are employed at present as charge-transfer complexes in solid-state ceils. The measurements were performed by the Gruzin-Seibel method in a range of temperatures between 0.5 and 60°C. In all three cases a strong contribution of short-path diffusion was observed. The autoradiographs enabled us to follow the process and to compare our results with those of the Gruzin method and with the structural aspect observed by scanning electron microscopy (SEM).
1. Experimental
1.2. Preparation of samples for the Gruzin-Seibel method
1.1. Autoradiographic sample preparation Cylindrical samples of the complexes of height 0.3-0.7 cm and area 1.29 c m 2 w e r e pressed under 1 ton cm -2. In the same conditions 13q-doped specimens of the complexes were o b t a i n e d . 1311 (A --- 8.04 days) is a 3/ and fl emitter. Both specimens were previously stabilized and then pressed together in a special device and thermostatted in a sealed jar between 0.5 and 60°C, employing a Lauda thermostat (AT = -0.1°C). After diffusion the samples were polished perpendicular to the diffusion flux direction. Autoradiographs were obtained with N U C - A g f a G e v a e r t films with exposure times between 28 and 76 h at - 1 0 to -15°C. Corrections for radioisotope decay as well as lowt e m p e r a t u r e diffusion during exposure were taken into account. SEM m e a s u r e m e n t s were made in a Jeol J M - I I I at accelerating voltages between 5 and 10 kV.
Cylindrical specimens (similar to those employed in autoradiographic experiments) were stabilized and doped with 131I. The radioisotope was deposited on one face of the specimens in the following way: a cellulose p a p e r on the deposit face was wetted with 131Iin CHCI3 solution. After drying, the specimens were thermostatted as described above.
1.3. Gruzin-Seibel method An important condition to apply this method is the exponential absorption of radioisotope radiation ( B e e r - L a m b e r t law). This fact was previously proved. Also, the size of grain boundaries must be large enough (~b > 200 ~t m) in order to avoid contributions of grain-boundary diffusion to the bulk diffusion coefficients. The Gruzin method considers a radioactive infinite thin source diffusing in a semi-infinite solid. I0 is the initial activity corresponding to
0167-2738/81/0000-0000/$02.50 O North-Holland Publishing C o m p a n y
J.L Franco et al. / t311diffusion in charge-transfer complexes
192
the initial surface x0. T h e activity is m e a s u r e d with a Tracerlab counter. Successive abrasions are p e r f o r m e d and the r e m o v e d thickness is d e t e r m i n e d by weight difference (AG = _1 × 10 -6 g).
m =-2~/2(rrDvt) '/~(Dv/Dsp~) '/2.
T h e concentration of radioactive material at the time t(s) is C ( X ) . O n c e polished, the specimen at a distance x, f r o m the original surface, the whole remaining activity (I,) is measured, resulting [1] in I.
C(x) e x p ( - / z x ) dx,
k exp0zxn)
2. Results and discussion
where # is the radiation absorption coefficient (cm-l). By a convenient c h a n g e of variables, we have (2)
H e r e C(x) is given by
C(x) = M(rrDvt) -I/2 e x p ( - x2./4Dvt),
At intermediate temperatures, volume and short-range mechanisms of diffusion coexist. For the specimen layers near the surface a linear distribution results in the plot of In(#/. aI,dax.) versus x~ while for d e e p e r layers ln(~I. - OI,,/Ox.) versus x. is linear. A u t o r a d i o g r a p h s give clear information on radioisotope distribution and the results complement the Gruzin m e t h o d .
(1)
xn
lzl. - aI./ax. = kC(x).
(3)
where M is the initial a m o u n t of deposited radioisotope and Dv is the bulk diffusion coefficient (cm 2 s-l). The aI./ax, are o b t a i n e d f r o m the penetration curve I. versus x.. F r o m the slope p = -1/4Dvt of the plot of l n ( / z I . - aI./ax.) versus x2. the diffusion coefficients are obtained. At very low t e m p e r a t u r e s ( T < T / 2 ) shortrange diffusion b e c o m e s important. T h e specific activity I ( x . ) c o r r e s p o n d i n g to a concentration C(x) varies exponentially with in(/zI~ - aI./Ox.).
Fig. 1 is a typical penetration curve I. versus x. c o r r e s p o n d i n g to 131I diffusion in 212-pyrene during ! h at 26°C. T h r e e zones are easily observed: (I) which c o r r e s p o n d s to the volume or bulk diffusion region, where the Dv are evaluated; (II) c o r r e s p o n d i n g to simultaneous volume and short-path diffusion processes; an a p p a r e n t diffusion coefficient Da is calculated in this case; and (III) which c o r r e s p o n d s to a strong-path diffusion contribution and where Dsp6 values are obtained. T h e plot of ln(~I. - aI./Ox.) versus x~ corresponding to the same specimen shows a curvature of the function which implies a strong contribution to Da due to short-path diffusion. Table 1 summarizes the Dv, Da and Ospt~ values o b t a i n e d for 131I diffusion in the different CTC. Because of the low t e m p e r a t u r e s of the
If
C(x.) = k,{l - exp[(x. - ½6)/2(D~t)'/2]},
(4)
where 6 is the m e a n value of short-path diameter and the corresponding specific activity is: I (x.) = k ' e x p [ - 7r-]/4(Dvt)-m[3-]/2x. ],
II in.lO~(e.s ~) I 10(}
(5)
with
fl : [6/2( Dvt )I/2]D~p/D~ .
(7)
50
(6)
D~p is the short path diffusion coefficient. T h e plot of ln(/zI. - aI./ax.) versus x. is a straight line whose slope m enables us to calculate Dsp8 if Fisher conditions are accomplished [2]
Fig. 1. I. versus X..
J.L Franco et al. / t~ll diffusion in charge-transfer complexes
Table
193
1 T(K)
D~ ( c m 2 s -I)
212.violanthrene (Tdesc
=
Da (cm I s -l)
Dwt5 (cm 2 s i)
220°C)
309
(1.31 -+0.14)× 10 6
298 298 288 Da = 2.20 × 10 3 exp(-4563/RT)
(9.95 -+ 1.09) × 10 7 (9.58-+ 1.(15)× 10 7 (7.62-+ 0.83) × 10 7
212.pyrene (Tt = 319 309
120°C) (4.25-+0.46) × 10 s (2.98 -+ 0.32) × 10 -s
303
( 1 . 9 6 - + 0 . 2 1 ) × 10 8
299 298
( 1 . 6 5 - + 0 . 1 7 ) × I0 ~ (1.56 -+ 0.17) × 10 8
292.5 288
(1.23 -+ 0.13) × 10 -8 (9.40 -+ 1.05) × 10 '~
283.5 283 274.5 273.5 D~ = 0.222 e x p ( - 9 7 1 1 / R T ) Da = 46.52 exp(-8879/RT) Q(l~lI short-path diffusion) = 4495 3I~-2phenotiazin (Tf = 171.5°C) 319 ( 3 . 9 9 - + 0 . 4 3 ) x I0 9 311 ( 2 . 6 8 - + 0 . 2 9 ) x 10 9 305 ( 2 . 1 5 - + 0 . 2 3 ) x 10 9 303 ( 1 . 8 5 - + 0 . 2 0 ) x 10 o 298 ( 1 . 5 0 + 0 . 1 6 ) x 10 -9 298 (1.61 - + 0 . 1 7 ) x 10 -9 292.5 286 279.5 273.5 Ov = 5.30 × 10 -4 exp(-7528/RT) D . = 0.523 e x p ( - 7604/RT) Q(13Jl short-path diffusion) = 4193
(4.28 -+ 0.47) × 10 ~ (2.63-+0.28) x 10 -5 (1.66-+ 0.18) x 1(1-s ( 1 . 3 8 - + 0 . 1 4 ) × 10 5 ( 1 . 3 2 - + 0 . 1 4 ) x 10 5 (1.04-+0.11) x 10 5 (7.83 -+ (I.86) x 10 -6 ( 6 . 8 6 - + 0 . 7 5 ) × 10 6 (6.56-+(1.72)× 10 ~' (4.11 -+0.45)× 10 -6 (3.89-+0.42) x 10 6
cal mole
experiments the Dv values for 131I diffusion in 212-Vi were not calculated. Otherwise the Dsp• values corresponding to lower temperatures of diffusion (in 212"Py and in 313-2Phe) were obtained employing Dv values which were extrapolated from experiments at higher temperatures. Fig. 2 shows an autoradiograph (M -- 320×) of a 131I diffused 212"Py specimen, taken at a depth corresponding to z o n e III of fig. 1. Fig. 3 is a SEM micrography of the same specimen ( M = 320x) showing the short-paths
(1.79-+0.34)× (1.52-+0.28)× (1.42-+0.26)× (1.411-+0.26)× (1.23-+0.23)× (1.06-+0.20) x
10 10 10 10 10 I0
" N H ii H 11
(8.56-+3.43)× (8.32 -+ 3.32) x (6.01-+2.41)× (5.96 -+ 2.38) x
10 1() 10 10
12 12 12 12
(1.72-+0.33)x (1.27-+0.24)x (1.08-+0.20)x (9.53 + 1 . 8 1 ) x ( 8 . 2 0 +- 1.56) x (7.83-+ 1 . 4 9 ) x (7.52 -+ 3.01) x (6.33-+2.52)x (3.83 -+ 1.53) x (2.81 -+ 1.13) × (2.22 -+ 0.99) ×
10 ii i0 ii 10 H 10 -12 10 -12 10 J2 10 -12 10 12 10 -12 10 12 10 -12
1
(3.46-+0.38) x (2.35-+l).25) x (1.86-+0.20)x (1.62_+0.14) x (1.31 -+0.15) x (1.41 -+0.15) x (1.22 -+ 0.13) x (1.11 - + 0 . 1 2 ) x (8.08 -+ 0.88) × (4.98 -+ 0.55) × (4.21 -+ 0.46) ×
cal mole
( 2 . 2 7 - + 0 . 4 3 ) × 10 N
10 6 10 6 10 -6 10 -6 10 6 10 6 10 -6 10 ~ 10 -7 10 -7 10 -7
i
and pores through which the diffusion is accelerated. Fig. 4 ( M = 80×) shows an autoradiograph of a t31I diffused 312.2Phe specimen taken in the z o n e II; it is possible to observe the volume and short-path diffusions. Fig. 5 corresponds to t3~I diffusion in 212"Vi in z o n e (III) ( M = 80x). In Dv versus 1/T, In DR versus 1/T and In Dw8 versus 1/T follow an Arrhenius function from which the frequency factor Do (cm s -1) and the activation energy Q (cal mole -~) can be evaluated. These values are reported in table 1.
J.L Franco et al, / 131I diffusion in charge-transfer complexes
194
at ,
"
A4,
• -"
.
~.3t~.
" Z
.--. Fig. 2, A u t o r a d i o g r a p h of a 13~I diffused 212"Py specimen, taken at a depth corresponding to zone III of fig. 1 ( M = 320 x ).
•
-'
"
* "4,
°.
:
~
'
7,(
,-
r
-5
°°"
-"
~lb
*
.
•
0.
-'
Q "
Fig. 4. A u t o r a d i o g r a p h of a ]~lI diffused 312.2Phe specimen taken in zone II ( M = 80×).
Fig. 3. SEM micrograph corresponding to the same area of fig. 2 (M = 320×).
Fig. 5. A u t o r a d i o g r a p h y of a ]3~I diffused 212.Vi taken in the zone IIl ( M = 80×).
3. Conclusions
(2) By the same method the bulk diffusion coefficients (Dv) were determined when temperature was higher enough and D~p6 values at lower temperatures (employing extrapolated Dv values). (3) The Dr, D, and D~p(5 variation with temperature follows an Arrhenius distribution and enabled us to calculate the activation energy and frequency factor of the process.
(1) The apparent diffusion coefficients (Da) in three C T C (212"Py, 212"Vi and 312.2Phe) were calculated with the G r u z i n Seibel method in the range of temperatures from 0.5 to 60°C (working t e m p e r a t u r e range of solid-state cells), showing an important shortpath diffusion contribution. f o r ~31I diffusion
J.L Franco et al. / 13ti diffusion in charge-transfer complexes
(4) The autoradiographs enabled us to follow the processes and to corroborate the above reported results. (5) The correlation between structural aspect and autoradiographic results was performed by SEM. The porous structure of complexes justifies the high observed diffusivities.
Acknowledgement JIF and NEWdR gratefully acknowledge grants from CONICET, CIC and the "Alberto
195
J. Roemmers" Foundation. We thank V. Frank for his valuable help in the computer processing.
References [1] Y. Adda and J. Philibert, La diffusion dans les solides (Presses Universitaires de France, Paris, 1966) pp. 264, 716. [2] P. Guiraldenq, Metaux, corrosion et industries, Vol. 39 (1964) p. 374.