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Fluctuation-induced conductivity above the superconducting transition temperature in polysulfur nitride, (SN)x
Solid State Communications, Vol. 18, PP. 1205—1208, 1976.
Pergamon Press.
Printed in Great Britain
FLUCTUATION-INDUCED CONDUCTIVITY ABOVE THE SUPERCONDUCTING TRANSITION TEMPERATURE IN POLYSULFUR NITRIDE, (SN)x* R.L. Civiak, C. Elbaum, W. Junker and C. Gought Department of Physics and Metals Research Laboratory, Brown University, Providence, RI 02912, U.S.A. and H.!. Kao, L.F. Nichols and M.M. Labes Department of Chemistry, Temple University, Philadelphia, PA 19122, U.S.A. (Received 24November 1975 by J. Tauc) Measured excess conductivity above the superconducting transition temperature in polymeric (SN)~is found to be consistent with fluctuation conductivity of the one-dimensional Aslamasov—Larkin type. The dominant “wire diameter” deduced from these measurements is several hundred angstroms. IT HAS RECENTLY been shown that the highly anisotropic conducting polymer, polysulfur nitride, (SN)~, which has metal like properties to low temperatures,”2 becomes superconducting near 0.3 K.3 It is unclear however, to what extent the anisotropic properties of (SN)~ may be attributed to electron localization onto individual polymer chains, or within the transverse dimensions of fibers consisting of a number of chains. In fact, (SN),, specimens always display a fibrous structure and 4fiber We diameters as small 1500 to A have have examined the asextent whichbeen this observed. material behaves in a “one-dimensional” manner with respect to the superconducting transition. In particular, we have analyzed the temperature dependence of the fluctuation conductivity near the transition temperature to determine if it is characterisitic of a material of transverse dimensions smaller than the coherence length. Having found so, we determine whether the dominant transverse dimension is that of individual polymer chains, or fibers. There are two contributions to the fluctuationinduced conductivity of a superconductor above its transition temperature. They are the contribution due to superconducting pairs, first discussed by Aslamazov and Larkin5(AL), and that due to the interaction of pairs with normal electrons, whose importance was revealed by Maid.6 However, in the presence of large pair *
Research supported by the Advance Research Projects Agency and the National Science Foundation (through the Materials Research Laboratory at Brown Uni~ ~ 24202.
~ Permanent address: Department of Physics, University of Birmingham, Birmingham B15, England.
breaking effects the AL term dominates.7 It is given by ~ 0ALI UN
/ \(4~D)I2
—
(
—
~Eci~
i
where 0N is the normal state conductivity, D is the number of dimensions in which the superconductor is larger than the temperature dependent coherence length, ~(t); e~is a constant dependent upon the dimensionality and e = (T— T~)/T~o; where T~, 0and T~,are the transition temperatures in the absence andexponent presence of ofequation pair breakmg effects. By determining the (I), (if indeed the enhanced conductivity follows such a power law) the dimensionality of a system with respect to ~ can be determined. The preparation of the samples is described elsewhere.1 We have studied samples with the current both parallel and perpendicular to the high conducting direction. The longitudinal sample is rod shaped with dimensions 0.2 x 0.2 x 2.0 mm. It is laid across four 0.001 in. gold wires and wrap around contacts are painted on with silver paint to produce a standard 4 probe electrical conductivity measurement configuration. Its conductivity at 4.2 K is approximately 450 (~2-cm)~. Samples with conductivities greater than iO~(f2-cm)’ at 4.2 were available; however, the voltage signals across them at low currents were too small for a reliable measurement of the excess conductivity. The transverse sample is an irregularly shaped piece resembling a cube of approximately 1.5 mm on each side. The (SN)~fibers are, however, all parallel to one another. Four gold wires are attached with silver paint in a row on one “edge” of the cube such that the current, between the outer contacts, is predominantly in the transverse direction. This results in a low normal state conductivity which enables us to measure conductivity changes as small as 0.1%. At room
1205
1206
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN)~ I I
I I
10
lOG
~/
fs~om~s 250
300
90
240
350
290
400
Vol. 18, Nos. 9/10
I
00
I
I
I
I I I
-
450
500
T (rnKI
Fig. 1. Voltage nieasured on the transverse sample of (SN)~,as a function of temperature, above the superconducting transition temperature, with a nominal current of 10 pA. The uppermost straight line is the determined normal-state reference (see text). The inset shows the normalized resistance over the entire transition region for two values of current, as shown. The current dependence is attributed to self-heating, on the basis of the observation that the shift in the transition curve is proportional to the square of the current. All three curves are drawn “free-hand” through the experimental points.
0
:
-
-
o~ I
~
600
T-T~(mK)
Fig. 2. Logarithmic plot of normalized conductivity as a function of T T~for two samples, as indicated. The solid lines are drawn with a slope of— (3/2) and the dashed line with a slope of— 2. Note different temperature scales for upper and lower sets of experimental points. —
temperature the conductivity of this sample is of the order of 10 (~.cmi and at 4.2 K it is 1.6 times the room temperature value, The conductivity measurements were made by a low frequency (300—600 Hz) a.c. technique. Figure 1 shows the voltage measured on the transverse sample, with a nominal current of 10 pA, throughout most of the ternperature region covered. In the inset, the entire transition is shown for 10 and 2 pA through the sample. In the low current limit, the transition temperature (taken as the temperature at which the resistance is 1/2 of its normal state value) of this sample is about 255 mK. In order to determine AG/UN accurately, one needs to know the normal state conductivity very well. We have determined ~N as a function of temperature by using a magnetic field to quench the residual super-0N5° conductivity. The straight line of Fig. 1 represents obtained. As an added precaution we checked whether there was any measurable magnetoresistance in the normal state at 4.2 K, and found none, In Fig. 2 the normalized conductivity, L~U/UN, for both samples is plotted vs T— T~,on a log—log scale. The uncertainty in the transition temperature due to non.uniform heating of the sample by the currrent is represented by the horizontal error bars of 3 mK. The vertical error bars are 0.1 %/-.,,/N, where N is the number of measurements taken at a given temperature. The conductivity measurements on the longitudinal sample extend over a smaller temperature range and have larger
error bars due to the higher normal state conductivity for this sample. A straight line with a slope of— 3/2, indicative of fluctuation conductivity in a I -D system, gives a good fit to the data for the longitudinal sample over the entire temperature range studied and the transverse sample in the temperature region where the error bars are smallest. The data for the transverse sample may deviate towards a slope of 2, indicative of 0-D behavior, close to T1,. Within about 10 mK of the transition —
temperature, deviations may arise due to sample inhomogeneities and to the fact that the AL theory is no longer valid eta!.3 when &i/UN Greene reported 1.that they were unable to fit their conductivity measurements to any of the theories of fluctuation-induced conductivity in one, two or three dimensions. It is possible that this is because the UN they used was too large (i.e., a at 1 K). Our measurements showed a decrease in conductivity in the normal state by nearly 2% between 1 and 0.3 K. Taking the normalized conductivity from Fig. I of reference 3 and readjusting it by 1.8%, we were able to get a good fit to a (T T~)~2 power law between 15 and 60 mK above the transition temperature. In addition, the magnitude of the fluctuation conductivity determined in this manner was similar to that of our samples. The fitted values of -~
—
Vol. 18, Nos. 9/10
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN)~
e~were in the ratio of 1:2.8:3.6 for our transverse sample, the (longitudinal) sample reported in Fig. 1 of reference 3, and our longitudinal sample. Since the extra conductivity of three samples of widely differing normal state conductivities have the same temperature dependence and roughly the same magnitude, and at least one of our samples follows this simple power law to twice the transition temperature, there appears to be no doubt that the effect is substantially due to fluctuation conductivity rather than sample inhomogeneities. The close agreement between the fluctuation conductivity of both of our samples and of the adjusted data from reference 3, with the e3/2 prediction of the Aslamazov—Larkin theory for 1 -D is convincing evidence that the samples are behaving as bundles of at most weakly connected superconducting filaments which are larger than the coherence length in only one dimension. It remains to be seen whether this filament diameter is consistent with individual polymer chains or with fibers. ~(t), and hence the upper limit on the diameter of the fibers, d, responsible for the fluctuation conductivitycritical can befield estimated from criticalanisotropic.3 field measurements. The of (SN),, is highly If this is interpreted in terms of an anisotropic effective mass model9 the result is distinct values of ~ for the directions parallel and perpendicular to the chains. This determination has been carried out by Azevedo eta!.4 who estimate that ~~(0) 135 A and ~~~(0) 3500 A. Critical field measurements on our longitudinal sample are close to those reported by Azevedo et a!. on their samples which had conductivities at 4.2 K in the range of 1 o~ (~2-cm)~. This indicates that the coherence lengths are not dependent upon the measured resistivity of the material. The perpendicular coherence length is the quantity of interest here since it sets the upper limit on d. The fluctuation conductivity of our longitudinal sample follows the 1 -D, e3~~2,dependence to at least T = 1 .3T~,hence d < ~~(l.3T~)= ~ 1(0)/~J0.3 250 A. This value should only be considered an order of magnitude estimate. If d <~ as our analysis indicates then the critical fields will be enhanced due to size effects. Since this was not considered in the determination of the s’s, the actual coherence lengths may be larger than the values quoted. Hence this analysis does not rule out the possibility that the filaments that determine the fluctuation conductivity can be identified with the observed fibrous nature of (SN),,. A comparison between the magnitude of the measured fluctuation conductivity and the prediction of
AL, that in 1-D
1207
2 ~~~(0)( r~o\3/2
=
ire i~ ~~‘~i’— r)
(2)
C
can also be used to determine d. There are problems here however, because there is reason to believe that the magnitudes of measured d.c. conductivities of (SN),, are not intrinsic to the material. Calculations of the room ternperature zero frequency conductivity based on the earliest optical measurements1°were in agreement with directly measured values. However, later optical studies’1’~indicated that the zero frequency conductivity was more than 10 times higher than that derived from d.c. measurements, which were likely limited by interruptions of the chains. Further evidence in support of this is the small differences in critical fields and hence in ~ (which in the dirty limit is proportional to I i~2)in samples with widely differing conductivities as deduced from d.c. measurements (see above). With this in mind, it is not surprising that substituting our directly measured ~u into equation (2) yields d 2500 A, which is apparently inconsistent with the upper limit set by ~ 1(t). If 0N~however, both sides of equation are divided by side of the and our measured ~U/UN(2)used on the left equation and on the right UN = 1 x l0~(!7-cm)~(the highest conductivity of any of our samples) the resulting value of d 260 A. This may still be an overestimate of d, as the intrinsic conductivity of (SN),, may be higher still. It is also possible that this value is too small since ~ may be underestimated due to size effects in the critical field measurements as previously mentioned. In conclusion, the excess electrical conductivity above the superconducting transition temperature in (SN),, can be attributed to thermodynamic fluctuations into the superconducting state. The temperature dependence of the fluctuation conductivity is that of a onedimensional superconductor, with respect to the ternperature dependent coherence length. It is difficult to further specify the transverse dimension because of uncertainties in the coherence length and in the magnitude of the electrical conductivity of (SN),,. However, the intrinsic conductivity of our longitudinal sample would have to be at least 2500 times greater than the highest conductivity of (SN),, measured to date in order for our estimate of the filament diameter to be as small as one individual chain. We conclude, therefore, that the superconducting transition in (SN),, takes place in a medium consisting of fibers with cross-sectional dimensions of several hundred angstrom; these fibers may be of the same nature as the ones previously observed.
1208
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN),,
Vol. 18, Nos. 9/10
REFERENCES 1.
WALATKA V.V., Jr., LABES M.M. & PERLSTEIN J.H., Phys. Rev. Lett. 31, 1139 (1973); HSU C. & LABES M.M.,J. Chem. Phys. 61,4640(1974).
2.
GREENE R.L., GRANT P.M. & STREET G.B.,Phys. Rev. Lett. 34,89(1975).
3. 4.
GREENE R.L., STREET G.B. & SUTER L.J.,Phys. Rev. Lert. 34, 577 (1975). AZEVEDO L.J., CLARK W.G., GREENE R.L., STREET G.B. & SUTER L.J. (to be published).
5.
ASLAMAZOV L.G. & LARKIN A.I., Fiz., Tverd. Tela 10, 1104 (l968)[translated in Soy. Phys. Solid State 10, 875 (1968)];Phys. Lett. 26A, 238 (1968). MAKI K., Progr. Theor. Phys. (Kyoto) 39, 897 (1968); 40, 193 (1968).
6. 7. 8. 9. 10. II
-
12.
For a sunmiary of the experimental evidence relating to the regions of validity of the various theories of fluctuation-conductivity, see CRAVEN R.A., THOMAS G.A. & PARKS R.D.,Phys. Rev. B7, 157 (1973). Although the geometry and the fibrous nature of the material limit the absolute measurement of the conductivity, conductivity ratios can be accurately measured. See TILLEY D.R.,F~oc.Phys. Soc. (London) 86, 289 (1965) and references cited therein. BRIGHT A.A., COHEN J.J., GARITO A.F., HEEGER A.J., MIKULSKI C.M., RUSSO P.J. & MACDIARMID A.G.,Phys. Rev. Lett. 34,206(1975). KAMIMURA H., GRANT A.J., LEVY F., YOFFE A.D. & PITT G.D., Solid State Commun. 17,49(1975). PINTSCHOVIUS L., GESERICH H.P. & MOLLER W., Solid State Commun. 17,477 (1975).
Pergamon Press.
Printed in Great Britain
FLUCTUATION-INDUCED CONDUCTIVITY ABOVE THE SUPERCONDUCTING TRANSITION TEMPERATURE IN POLYSULFUR NITRIDE, (SN)x* R.L. Civiak, C. Elbaum, W. Junker and C. Gought Department of Physics and Metals Research Laboratory, Brown University, Providence, RI 02912, U.S.A. and H.!. Kao, L.F. Nichols and M.M. Labes Department of Chemistry, Temple University, Philadelphia, PA 19122, U.S.A. (Received 24November 1975 by J. Tauc) Measured excess conductivity above the superconducting transition temperature in polymeric (SN)~is found to be consistent with fluctuation conductivity of the one-dimensional Aslamasov—Larkin type. The dominant “wire diameter” deduced from these measurements is several hundred angstroms. IT HAS RECENTLY been shown that the highly anisotropic conducting polymer, polysulfur nitride, (SN)~, which has metal like properties to low temperatures,”2 becomes superconducting near 0.3 K.3 It is unclear however, to what extent the anisotropic properties of (SN)~ may be attributed to electron localization onto individual polymer chains, or within the transverse dimensions of fibers consisting of a number of chains. In fact, (SN),, specimens always display a fibrous structure and 4fiber We diameters as small 1500 to A have have examined the asextent whichbeen this observed. material behaves in a “one-dimensional” manner with respect to the superconducting transition. In particular, we have analyzed the temperature dependence of the fluctuation conductivity near the transition temperature to determine if it is characterisitic of a material of transverse dimensions smaller than the coherence length. Having found so, we determine whether the dominant transverse dimension is that of individual polymer chains, or fibers. There are two contributions to the fluctuationinduced conductivity of a superconductor above its transition temperature. They are the contribution due to superconducting pairs, first discussed by Aslamazov and Larkin5(AL), and that due to the interaction of pairs with normal electrons, whose importance was revealed by Maid.6 However, in the presence of large pair *
Research supported by the Advance Research Projects Agency and the National Science Foundation (through the Materials Research Laboratory at Brown Uni~ ~ 24202.
~ Permanent address: Department of Physics, University of Birmingham, Birmingham B15, England.
breaking effects the AL term dominates.7 It is given by ~ 0ALI UN
/ \(4~D)I2
—
(
—
~Eci~
i
where 0N is the normal state conductivity, D is the number of dimensions in which the superconductor is larger than the temperature dependent coherence length, ~(t); e~is a constant dependent upon the dimensionality and e = (T— T~)/T~o; where T~, 0and T~,are the transition temperatures in the absence andexponent presence of ofequation pair breakmg effects. By determining the (I), (if indeed the enhanced conductivity follows such a power law) the dimensionality of a system with respect to ~ can be determined. The preparation of the samples is described elsewhere.1 We have studied samples with the current both parallel and perpendicular to the high conducting direction. The longitudinal sample is rod shaped with dimensions 0.2 x 0.2 x 2.0 mm. It is laid across four 0.001 in. gold wires and wrap around contacts are painted on with silver paint to produce a standard 4 probe electrical conductivity measurement configuration. Its conductivity at 4.2 K is approximately 450 (~2-cm)~. Samples with conductivities greater than iO~(f2-cm)’ at 4.2 were available; however, the voltage signals across them at low currents were too small for a reliable measurement of the excess conductivity. The transverse sample is an irregularly shaped piece resembling a cube of approximately 1.5 mm on each side. The (SN)~fibers are, however, all parallel to one another. Four gold wires are attached with silver paint in a row on one “edge” of the cube such that the current, between the outer contacts, is predominantly in the transverse direction. This results in a low normal state conductivity which enables us to measure conductivity changes as small as 0.1%. At room
1205
1206
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN)~ I I
I I
10
lOG
~/
fs~om~s 250
300
90
240
350
290
400
Vol. 18, Nos. 9/10
I
00
I
I
I
I I I
-
450
500
T (rnKI
Fig. 1. Voltage nieasured on the transverse sample of (SN)~,as a function of temperature, above the superconducting transition temperature, with a nominal current of 10 pA. The uppermost straight line is the determined normal-state reference (see text). The inset shows the normalized resistance over the entire transition region for two values of current, as shown. The current dependence is attributed to self-heating, on the basis of the observation that the shift in the transition curve is proportional to the square of the current. All three curves are drawn “free-hand” through the experimental points.
0
:
-
-
o~ I
~
600
T-T~(mK)
Fig. 2. Logarithmic plot of normalized conductivity as a function of T T~for two samples, as indicated. The solid lines are drawn with a slope of— (3/2) and the dashed line with a slope of— 2. Note different temperature scales for upper and lower sets of experimental points. —
temperature the conductivity of this sample is of the order of 10 (~.cmi and at 4.2 K it is 1.6 times the room temperature value, The conductivity measurements were made by a low frequency (300—600 Hz) a.c. technique. Figure 1 shows the voltage measured on the transverse sample, with a nominal current of 10 pA, throughout most of the ternperature region covered. In the inset, the entire transition is shown for 10 and 2 pA through the sample. In the low current limit, the transition temperature (taken as the temperature at which the resistance is 1/2 of its normal state value) of this sample is about 255 mK. In order to determine AG/UN accurately, one needs to know the normal state conductivity very well. We have determined ~N as a function of temperature by using a magnetic field to quench the residual super-0N5° conductivity. The straight line of Fig. 1 represents obtained. As an added precaution we checked whether there was any measurable magnetoresistance in the normal state at 4.2 K, and found none, In Fig. 2 the normalized conductivity, L~U/UN, for both samples is plotted vs T— T~,on a log—log scale. The uncertainty in the transition temperature due to non.uniform heating of the sample by the currrent is represented by the horizontal error bars of 3 mK. The vertical error bars are 0.1 %/-.,,/N, where N is the number of measurements taken at a given temperature. The conductivity measurements on the longitudinal sample extend over a smaller temperature range and have larger
error bars due to the higher normal state conductivity for this sample. A straight line with a slope of— 3/2, indicative of fluctuation conductivity in a I -D system, gives a good fit to the data for the longitudinal sample over the entire temperature range studied and the transverse sample in the temperature region where the error bars are smallest. The data for the transverse sample may deviate towards a slope of 2, indicative of 0-D behavior, close to T1,. Within about 10 mK of the transition —
temperature, deviations may arise due to sample inhomogeneities and to the fact that the AL theory is no longer valid eta!.3 when &i/UN Greene reported 1.that they were unable to fit their conductivity measurements to any of the theories of fluctuation-induced conductivity in one, two or three dimensions. It is possible that this is because the UN they used was too large (i.e., a at 1 K). Our measurements showed a decrease in conductivity in the normal state by nearly 2% between 1 and 0.3 K. Taking the normalized conductivity from Fig. I of reference 3 and readjusting it by 1.8%, we were able to get a good fit to a (T T~)~2 power law between 15 and 60 mK above the transition temperature. In addition, the magnitude of the fluctuation conductivity determined in this manner was similar to that of our samples. The fitted values of -~
—
Vol. 18, Nos. 9/10
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN)~
e~were in the ratio of 1:2.8:3.6 for our transverse sample, the (longitudinal) sample reported in Fig. 1 of reference 3, and our longitudinal sample. Since the extra conductivity of three samples of widely differing normal state conductivities have the same temperature dependence and roughly the same magnitude, and at least one of our samples follows this simple power law to twice the transition temperature, there appears to be no doubt that the effect is substantially due to fluctuation conductivity rather than sample inhomogeneities. The close agreement between the fluctuation conductivity of both of our samples and of the adjusted data from reference 3, with the e3/2 prediction of the Aslamazov—Larkin theory for 1 -D is convincing evidence that the samples are behaving as bundles of at most weakly connected superconducting filaments which are larger than the coherence length in only one dimension. It remains to be seen whether this filament diameter is consistent with individual polymer chains or with fibers. ~(t), and hence the upper limit on the diameter of the fibers, d, responsible for the fluctuation conductivitycritical can befield estimated from criticalanisotropic.3 field measurements. The of (SN),, is highly If this is interpreted in terms of an anisotropic effective mass model9 the result is distinct values of ~ for the directions parallel and perpendicular to the chains. This determination has been carried out by Azevedo eta!.4 who estimate that ~~(0) 135 A and ~~~(0) 3500 A. Critical field measurements on our longitudinal sample are close to those reported by Azevedo et a!. on their samples which had conductivities at 4.2 K in the range of 1 o~ (~2-cm)~. This indicates that the coherence lengths are not dependent upon the measured resistivity of the material. The perpendicular coherence length is the quantity of interest here since it sets the upper limit on d. The fluctuation conductivity of our longitudinal sample follows the 1 -D, e3~~2,dependence to at least T = 1 .3T~,hence d < ~~(l.3T~)= ~ 1(0)/~J0.3 250 A. This value should only be considered an order of magnitude estimate. If d <~ as our analysis indicates then the critical fields will be enhanced due to size effects. Since this was not considered in the determination of the s’s, the actual coherence lengths may be larger than the values quoted. Hence this analysis does not rule out the possibility that the filaments that determine the fluctuation conductivity can be identified with the observed fibrous nature of (SN),,. A comparison between the magnitude of the measured fluctuation conductivity and the prediction of
AL, that in 1-D
1207
2 ~~~(0)( r~o\3/2
=
ire i~ ~~‘~i’— r)
(2)
C
can also be used to determine d. There are problems here however, because there is reason to believe that the magnitudes of measured d.c. conductivities of (SN),, are not intrinsic to the material. Calculations of the room ternperature zero frequency conductivity based on the earliest optical measurements1°were in agreement with directly measured values. However, later optical studies’1’~indicated that the zero frequency conductivity was more than 10 times higher than that derived from d.c. measurements, which were likely limited by interruptions of the chains. Further evidence in support of this is the small differences in critical fields and hence in ~ (which in the dirty limit is proportional to I i~2)in samples with widely differing conductivities as deduced from d.c. measurements (see above). With this in mind, it is not surprising that substituting our directly measured ~u into equation (2) yields d 2500 A, which is apparently inconsistent with the upper limit set by ~ 1(t). If 0N~however, both sides of equation are divided by side of the and our measured ~U/UN(2)used on the left equation and on the right UN = 1 x l0~(!7-cm)~(the highest conductivity of any of our samples) the resulting value of d 260 A. This may still be an overestimate of d, as the intrinsic conductivity of (SN),, may be higher still. It is also possible that this value is too small since ~ may be underestimated due to size effects in the critical field measurements as previously mentioned. In conclusion, the excess electrical conductivity above the superconducting transition temperature in (SN),, can be attributed to thermodynamic fluctuations into the superconducting state. The temperature dependence of the fluctuation conductivity is that of a onedimensional superconductor, with respect to the ternperature dependent coherence length. It is difficult to further specify the transverse dimension because of uncertainties in the coherence length and in the magnitude of the electrical conductivity of (SN),,. However, the intrinsic conductivity of our longitudinal sample would have to be at least 2500 times greater than the highest conductivity of (SN),, measured to date in order for our estimate of the filament diameter to be as small as one individual chain. We conclude, therefore, that the superconducting transition in (SN),, takes place in a medium consisting of fibers with cross-sectional dimensions of several hundred angstrom; these fibers may be of the same nature as the ones previously observed.
1208
CONDUCTIVITY IN POLYSULFUR NITRIDE, (SN),,
Vol. 18, Nos. 9/10
REFERENCES 1.
WALATKA V.V., Jr., LABES M.M. & PERLSTEIN J.H., Phys. Rev. Lett. 31, 1139 (1973); HSU C. & LABES M.M.,J. Chem. Phys. 61,4640(1974).
2.
GREENE R.L., GRANT P.M. & STREET G.B.,Phys. Rev. Lett. 34,89(1975).
3. 4.
GREENE R.L., STREET G.B. & SUTER L.J.,Phys. Rev. Lert. 34, 577 (1975). AZEVEDO L.J., CLARK W.G., GREENE R.L., STREET G.B. & SUTER L.J. (to be published).
5.
ASLAMAZOV L.G. & LARKIN A.I., Fiz., Tverd. Tela 10, 1104 (l968)[translated in Soy. Phys. Solid State 10, 875 (1968)];Phys. Lett. 26A, 238 (1968). MAKI K., Progr. Theor. Phys. (Kyoto) 39, 897 (1968); 40, 193 (1968).
6. 7. 8. 9. 10. II
-
12.
For a sunmiary of the experimental evidence relating to the regions of validity of the various theories of fluctuation-conductivity, see CRAVEN R.A., THOMAS G.A. & PARKS R.D.,Phys. Rev. B7, 157 (1973). Although the geometry and the fibrous nature of the material limit the absolute measurement of the conductivity, conductivity ratios can be accurately measured. See TILLEY D.R.,F~oc.Phys. Soc. (London) 86, 289 (1965) and references cited therein. BRIGHT A.A., COHEN J.J., GARITO A.F., HEEGER A.J., MIKULSKI C.M., RUSSO P.J. & MACDIARMID A.G.,Phys. Rev. Lett. 34,206(1975). KAMIMURA H., GRANT A.J., LEVY F., YOFFE A.D. & PITT G.D., Solid State Commun. 17,49(1975). PINTSCHOVIUS L., GESERICH H.P. & MOLLER W., Solid State Commun. 17,477 (1975).