- Email: [email protected]
Measurement of electrical conductivity of graphite intercalation compounds by a contactless Wien bridge method
Synthetic Metals, 3 (1981) 247 - 254
247
© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
M E A S U R E M E N T OF ELECTRICAL CONDUCTIVITY OF GRAPHITE I N T E R C A L A T I O N COMPOUNDS BY A CONTACTLESS WIEN BRIDGE METHOD
S. C. SINGHAL and A. KERNICK Westinghouse Research and Development Center, Pittsburgh, PA 15235 (U.S.A.) (Received May 19, 1980)
Summary The classic 4-point bridge method is impractical and leads to serious errors when applied to measure electrical conductivity of graphite intercalation c o m p o u n d s because of their high anisotropy and problems in making electrical contacts. In order to overcome such difficulties, a new, contactless technique utilizing an all-copper Wien inductance bridge oscillator has been developed to accurately measure electrical conductivity of graphite intercalation compounds. This technique offers such advantages as: (1) more sensitivity to sample resistivity while operating at 1000 Hz rather than at radio frequency, (2) accurate principle of operation based upon a self-balancing precision bridge circuit, (3) greater temperature range of testing while eliminating the need for separate temperature recording equipment, (4) provision for convenient BCD data o u t p u t for both frequency and temperature. The technique has been applied to measure the room temperature basal plane electrical conductivity of AsFs-graphite intercalation compounds. A maximum conductivity of about 68 percent, of that of pure OFHC copper has been measured for a second stage AsFs-graphite intercalation compound.
1. Introduction
The most c o m m o n technique used for conductivity measurement in isotropic materials is t h e 4-point Kelvin bridge method. However, this method results in localized surface and edge damage due to the necessity to bake on contact paste or wrap around contact wires, and it is difficult to interpret results due to the problems of current distribution at each current contact. Furthermore, graphite intercalation compounds generally require hermetic sealing to prevent any reaction with air, which complicates making electrical contacts to the sample. Even the ingenious eight point techniques
248 of Montgomery [1 ] have proven inadequate in determining basal plane conductivity in AsF5-graphite and other acceptor intercalation compounds which are highly anisotropic with respect to resistivity [2]. Various contactless techniques for the measurement of electrical conductivity have been proposed to overcome the limitations of the 4-point probe method. These methods generally involve the interaction of the sample being measured with high frequency excitations. Miller e t al. [3] proposed a technique which is essentially an adaptation of the Boonton "Q" meter, and Zeller e t al. [2] used a technique at radio frequency (100 kHz) based upon the slight upward frequency shift which results when the sample to be measured introduces minuscule resistance increase and inductance decrease into an RLC resonant circuit. McRae and H~rold [4] used a tuned circuit with an integral FET oscillator wherein the sample is subjected to eddy currents, induced by the electromagnetic field in the air gap of a ferrite inductor core; the resulting perturbation in oscillator frequency becomes a measure of the electrical conductivity of the sample. These methods, however, require the operator to perform balancing adjustments and to take independent temperature data of the test. Also, a ferrite magnetic material is used so that a temperature range of interest, say, --75 to +125 °C, affects the stability of the sensing inductor. This paper discusses a new, contactless approach using an all-copper Wien inductance bridge oscillator (WIBO) which circumvents these obstacles to convenient, reliable conductivity measurement. Additionally, this technique offers the following advantages over other contactless methods: (a) The principle of operation is based upon a self-balancing precision bridge circuit, described exactly by electronic equations for the Wien bridge and the standard data on air core inductors. (b) The frequency range of operation is feasible from about 400 Hz (below skin-effect significance) to radio frequencies. (c) Frequency data are obtained automatically to 10 parts per million where sensitivity is high because only R and L (and not C) parameters are involved. (d) The temperature range of testing is wide (say, " 7 5 to +125 °C), since it does not employ ferrite materials which would require various compensations in order to coordinate the test equipment. (e) Temperature data are integral with frequency data; this keeps them inseparable and eliminates the need for separate temperature recording equipment. (f) The BCD (binary coded decimal} cycle count per one second interval is available for frequency and temperature automatic data processing, thus eliminating human reading error. 2. Circuit and test instrument description
Figure 1 shows the Wien inductance bridge with its two governing equations which must be satisfied simultaneously in the perfectly balanced
249
RL ~ - ~
14
L3 _ RI(RL+R3) L4 R2R3-RIR4
(1)
J L3L4= R4(RL+ R3I- RLR3~I (2)
Fig. 1. Wien inductance bridge. state. The sensing inductor for contactless conductivity measurement is L4 with its resistance R4. Equation (2) defines the frequency sensitivity of the Wien inductance bridge to variations in L4 and R4. When inductances L3 and L4 remain constant, it is to be observed from eqn. (2) that, if R1, R2, R3, R4 and RL all respond alike to temperature, frequency tracks the change precisely to form an accurate resistance wire thermometer. Such a desired condition for "machine temperature" is achieved if the resistor R3 is wound bi-filar non-inductively with, say, copper to match the temperature coefficient of copper in inductors L3 and L4. Since meaningful conductivity measurements must always have temperature controlled and recorded simultaneously, the frequency at bridge balance becomes doubly significant. The intended conductivity apparatus appears in Fig. 2 in its most rudimentary operational form. Sensing inductor L4 is wound in two equal sections in order to provide the thin sample with a slit entry into the central portion of an air-core solenoid. The self-tuning characteristic of the Wien inductance bridge oscillator (WIBO) to the exact frequency of the bridge balance is well known. The use of the non-linear characteristic of the miniature lamp to stabilize output voltage is equally well known [5]. For conductivity measurement, arms three and four of the WIBO are mounted in close proximity on a test fixture which bears the sample being measured inside an environmental chamber. All components of arms three and four are wound with the same material, copper, in order to translate the temperature sensitivity into an integral, precision thermometer outputting frequency. The base frequency, indicating "machine temperature", is recorded prior to insertion of the sample being measured. When the sample is inserted into the sensing inductor, there are two concomitant effects which cooperate to shift the WIBO frequency upwards: (a) the sample couples inductively as if in parallel to reduce L4, and (b) the sample resistance transfers to the L4 primary winding in an apparent series effect which increases R4. The shift from base frequency varies directly with sample conductivity where all samples are of exactly the same geometry.
250
Rl
Gl
#380 I-&-r? Lamp
1-
R 133 R
"
O"o cc
Test Fixture
Fig. 2. Wien inductance
Fig. 3. Block diagram
-.
bridge oscillator
of the conductivity
(WIBO).
instrument.
Sample insertion, however, does change the sensing inductor coil current even when the #380 miniature lamp maintains essentially constant WIBO output voltage. The coil current elevates “machine temperature” above ambient temperature. If the coil current is permitted to change (perhaps +lO%) after sample insertion, the new frequency reading will not settle until the “machine temperature” rise above ambient readjusts. This disturbing drift could persist for, say, one minute, in which time the environmental control for test temperature would also drift at least a small amount. To circumvent this drift, the test instrument was refined by avoiding use of the miniature lamp and emnlovine: the “given coil current at the given
251 copper temperature" control scheme shown in Fig. 3. In this scheme, another copper resistor, R ca, is m o u n t e d within the test fixture at "machine t e m p e r a t u r e " to burden properly a small current transformer that senses coil current. At each base frequency, the concomitant temperature determines a unique coil current; however, the voltage on RcB, despite resistance change, is kept constant (at 0.9 V) by the control scheme shown in Fig. 3. Performance data on this servo loop are presented in Table 1 given within Fig. 4 over a temperature range. The voltage follower prevents parallel loading of RcB b y non-copper resistance, which may also be at other than the "machine temperature" of the test fixture. When current in arms three and four is controlled to the unique current value either before or after sample insertion, the frequency drift then must be due to either ambient temperature change or sample heating from eddy currents. A typical electronic counter requires 100 s, a most inconveniently long time, to resolve frequency to 0.01 Hz. For convenience, as well as to avoid temperature drift during each observation, it is desirable that frequency be resolved to 0.01 Hz in just 1 s. In order to achieve this, a phase-locked-loop (PLL) and a 100:1 divider are used together to step-up WIBO o u t p u t frequency 100 times for presentation to the electronic counter. A convenient way to operate the counter is to adjust to 50% d u t y cycle such that the display persists 1 s while accumulating readings on alternate seconds. Also, where temperature control is sufficient, an optional integration over 10 s can resolve frequency data to 0.001 Hz. Electronic counters are available, having digital BCD o u t p u t capability to various processing circuits, which can provide any degree of automated testing and recording desired. A properly programmed read-only m e m o r y (ROM) storing the copper-wire 0oC 14~
14~
1200
1100
I100
:
:
y ~ o
-
oc
Vo vi_ v,
g
i 700
/
• / , .
~ ~ 4 . 9 ~
~
los2A +4_o,_o~.16~ o;9o~ n~.2 +00.o~s.z4 3.OlO.~1
~
!
I :
5011
I
-65
I
-45
. I
-25
3.3~~o:~o~
12ss.z +100.oIs.~ Z.T30.~
~L i I
-5
700
:.. i~.z I
+15
I
+35
+~2s.o I ~.45 2.~ i
I
+55
+/5
I
+95
o.~o~ I
500
+115
Temperature. DegreesCentigrade
Fig. 4. Copper-wize thermometer characteristic v/a the WIBO.
252 temperature characteristic of Fig. 4 can output directly in a degrees Centigrade display corresponding to the base frequency with the sample withdrawn. If the samples to be measured are thin, quasi-infinite sheets, the fringing flux does not affect the conductivity data, and calibration with a single sheet of known thickness made from an isotropic non-ferromagnetic metal conductor is sufficient for conductivity determinations. In such cases, conductivity is linear with sample thickness in all geometries. However, graphite intercalation compounds synthesized using highly oriented pyrolytic graphite (HOPG) are usually in the form of small rectangular pieces which cannot be considered quasi-infinite sheets. Furthermore, it is desirable to measure their conductivity while still contained inside the reaction tube because of their instability in air. To facilitate such in situ conductivity measurements, the reaction tube is usually a glass rectangular tube of ~ 5 mm outer dimension which can be directly inserted into the sensing inductor halves. Because of this tube dimension, the spacing of the sensing inductor halves also precludes treating small samples of graphite intercalation compounds as quasi-infinite sheets, and, here, fringing flux around the sample will have a significant effect on the conductivity data. To circumvent this problem, the test instrument is accurately calibrated using an exact geometrical replica of the sample fabricated precisely from a non-ferromagnetic material (e.g., copper) whose conductivity has been determined by the standard 4-point probe method. Between the graphite intercalation compound sample and the calibration sample, conductivity being the differentiating parameter, the shift from the base frequency becomes a linear comparison between the calibration sample and the sample under test. The following empirical rules were found to apply from extensive calibration experiments using a variety of materials of known conductivity: (a) The frequency shift is proportional to thickness of the sample. (b) The frequency shift is directly proportional to conductivity when samples of identical geometry and thickness are compared. (c) The frequency shift responds to the 3.24th power of the oscillator base frequency (i.e., a 1000 Hz oscillator produces nearly 20 times the frequency shift as a 400 Hz oscillator upon the same sample). (d) The frequency shift responds to the 3.77th power of the sample diameter for circular samples. This emphasizes the importance of sample replication to exact outline and the greater sensitivity to conductivity contributed by sample portions at the periphery.
3. Measurement of conductivity of AsFs-graphite intercalation compounds The conductivity measurement technique discussed above was applied to determine the basal plane electrical conductivity of several AsFs-graphite intercalation compounds. For these measurements, highly oriented pyrolytic graphite (HOPG), obtained from the Union Carbide Corporation, was inter-
253
calated with AsF5 vapors at room temperature and 0.5 atm pressure, for different time periods, to obtain different stage compounds. The progress of intercalation was monitored by in situ measurement of the sample thickness using a telescopic micrometer. The intercalated samples were characterized b y their X-ray 001 reflections. After extensive experimentation, it was found that the stage 1 AsFs-graphite c o m p o u n d could be prepared in pure form, and the stage 2 c o m p o u n d in essentially pure form with occasional traces of the stage 3 c o m p o u n d . However, all other intercalated samples were found to be mixtures of several different stage compounds. The X-ray analysis of five representative intercalated samples, designated A through E, is summarized in Table 2. Sample A was pure stage 1 compound, whereas sample B was essentially pure stage 2 compound. Samples C, D and E were mixtures of several different stages and some unreacted graphite. The d-spacing of different stage (n) c o m p o u n d s was found to be related b y the expression: d = 8.0 + 3.35 (n -- 1) A. The room temperature basal plane electrical conductivity data on the various intercalated samples at 1000 Hz, obtained using the contactless WIBO technique, are summarized in Table 2. The conductivity is expressed as a percentage of IACS copper conductivity. It is clear from these data that the conductivity peaks at stage 2 in AsFs-graphite intercalation compounds. This trend in conductivity as a function of stage is consistent with other TABLE 2 Basal plane conductivity of various AsF5-graphite intercalation compounds Sample designation
Compounds present
Temperature (°C)
Frequency shift at 1 mm thickness A f (Hz)
HOPG Intercalated sample A Intercalated sample B Intercalated sample C
Graphite Stage 1
23.1 23.1
0.16 0.63
4.4 17.4
Stage 2
23.1
2.48
68.3
23.1
1.84
50.7
23.1
0.41
11.2
23.1
0.28
7.8
22.9
3.66
101.0
Stage 3 (major) Stage 4 (minor) Stage 2 (trace) Intercalated Stage 3 (major) sample D Stages 4 and 5 (minor) Stage 6 and graphite (trace) Intercalated Stage 4 (major) sample E Stages 3 and 5 (minor) Graphite (trace) OFHC copper Copper
Conductivity as a percentage of IACS copper conductivity
254
investigations on AsF5-graphite intercalation compounds [6 - 81. The maximum conductivity measured was about 68 percent. of that of pure copper; this value is lower than that reported by Vogel et al. [6, 71 but in substantial agreement with the conductivity results obtained by McKee et al. [8] on AsF,-graphite compounds synthesized using HOPG crystals.
4. Conclusions A new, contactless technique based on an all-copper Wien inductance bridge oscillator offers a convenient and reliable method for measuring, in situ, the basal plane electrical conductivity of highly anisotropic graphite intercalation compounds. The technique has the added advantages of integrating the temperature data with the frequency data and its operation can be made automatic without any balancing adjustments. The technique has been applied to measure the room temperature basal plane conductivity of several AsF5-graphite intercalation compounds. The conductivity in these compounds has been found to peak at the second stage with a value of about 68 percent. of that of pure copper.
Acknowledgments The authors gratefully acknowledge the contributions of J. Schreurs and R. C. Kuznicki to the X-ray diffraction analysis of the intercalation compounds, and the technical assistance of J. A. Fraino in conducting the intercalation experiments.
References 1 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 2 C. Zeller, G. M. T. Foley, E. R. Falardeau and F. L. Vogel, Mater. Sci. Eng., 31 (1977) 255. 3 G. L. Miller, D. A. H. Robinson and J. D. Wiley, U. 5’. Patent No. 4,000,458 (1976). 4 E. McRae and A. Hbrold,Mater. Sci. Eng., 31 (1977) 249. 5 A. J. Diefenderfer, Basic Techniques in Electronic Instrumentation, W. B. Saunders Co., Philadelphia, 1972, p. 245. 6 F. L. Vogel, G. M. T. Foley, C. Zeller, E. R. Falardeau and J. Gan, Mater. Sk. Eng., 31 (1977) 261. 7 G. M. T. Foley, C. Zeller, E. R. Falardeau and F. L. Vogel, Solid State Commun., 24 (1977) 371. 8 D. W. McKee, L. V. Interrante and R. S. Markiewicz, Extended Abstract of the paper presented at the 14th Biennial Conf. on Carbon, Pennsylvania State University, 1979.
247
© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
M E A S U R E M E N T OF ELECTRICAL CONDUCTIVITY OF GRAPHITE I N T E R C A L A T I O N COMPOUNDS BY A CONTACTLESS WIEN BRIDGE METHOD
S. C. SINGHAL and A. KERNICK Westinghouse Research and Development Center, Pittsburgh, PA 15235 (U.S.A.) (Received May 19, 1980)
Summary The classic 4-point bridge method is impractical and leads to serious errors when applied to measure electrical conductivity of graphite intercalation c o m p o u n d s because of their high anisotropy and problems in making electrical contacts. In order to overcome such difficulties, a new, contactless technique utilizing an all-copper Wien inductance bridge oscillator has been developed to accurately measure electrical conductivity of graphite intercalation compounds. This technique offers such advantages as: (1) more sensitivity to sample resistivity while operating at 1000 Hz rather than at radio frequency, (2) accurate principle of operation based upon a self-balancing precision bridge circuit, (3) greater temperature range of testing while eliminating the need for separate temperature recording equipment, (4) provision for convenient BCD data o u t p u t for both frequency and temperature. The technique has been applied to measure the room temperature basal plane electrical conductivity of AsFs-graphite intercalation compounds. A maximum conductivity of about 68 percent, of that of pure OFHC copper has been measured for a second stage AsFs-graphite intercalation compound.
1. Introduction
The most c o m m o n technique used for conductivity measurement in isotropic materials is t h e 4-point Kelvin bridge method. However, this method results in localized surface and edge damage due to the necessity to bake on contact paste or wrap around contact wires, and it is difficult to interpret results due to the problems of current distribution at each current contact. Furthermore, graphite intercalation compounds generally require hermetic sealing to prevent any reaction with air, which complicates making electrical contacts to the sample. Even the ingenious eight point techniques
248 of Montgomery [1 ] have proven inadequate in determining basal plane conductivity in AsF5-graphite and other acceptor intercalation compounds which are highly anisotropic with respect to resistivity [2]. Various contactless techniques for the measurement of electrical conductivity have been proposed to overcome the limitations of the 4-point probe method. These methods generally involve the interaction of the sample being measured with high frequency excitations. Miller e t al. [3] proposed a technique which is essentially an adaptation of the Boonton "Q" meter, and Zeller e t al. [2] used a technique at radio frequency (100 kHz) based upon the slight upward frequency shift which results when the sample to be measured introduces minuscule resistance increase and inductance decrease into an RLC resonant circuit. McRae and H~rold [4] used a tuned circuit with an integral FET oscillator wherein the sample is subjected to eddy currents, induced by the electromagnetic field in the air gap of a ferrite inductor core; the resulting perturbation in oscillator frequency becomes a measure of the electrical conductivity of the sample. These methods, however, require the operator to perform balancing adjustments and to take independent temperature data of the test. Also, a ferrite magnetic material is used so that a temperature range of interest, say, --75 to +125 °C, affects the stability of the sensing inductor. This paper discusses a new, contactless approach using an all-copper Wien inductance bridge oscillator (WIBO) which circumvents these obstacles to convenient, reliable conductivity measurement. Additionally, this technique offers the following advantages over other contactless methods: (a) The principle of operation is based upon a self-balancing precision bridge circuit, described exactly by electronic equations for the Wien bridge and the standard data on air core inductors. (b) The frequency range of operation is feasible from about 400 Hz (below skin-effect significance) to radio frequencies. (c) Frequency data are obtained automatically to 10 parts per million where sensitivity is high because only R and L (and not C) parameters are involved. (d) The temperature range of testing is wide (say, " 7 5 to +125 °C), since it does not employ ferrite materials which would require various compensations in order to coordinate the test equipment. (e) Temperature data are integral with frequency data; this keeps them inseparable and eliminates the need for separate temperature recording equipment. (f) The BCD (binary coded decimal} cycle count per one second interval is available for frequency and temperature automatic data processing, thus eliminating human reading error. 2. Circuit and test instrument description
Figure 1 shows the Wien inductance bridge with its two governing equations which must be satisfied simultaneously in the perfectly balanced
249
RL ~ - ~
14
L3 _ RI(RL+R3) L4 R2R3-RIR4
(1)
J L3L4= R4(RL+ R3I- RLR3~I (2)
Fig. 1. Wien inductance bridge. state. The sensing inductor for contactless conductivity measurement is L4 with its resistance R4. Equation (2) defines the frequency sensitivity of the Wien inductance bridge to variations in L4 and R4. When inductances L3 and L4 remain constant, it is to be observed from eqn. (2) that, if R1, R2, R3, R4 and RL all respond alike to temperature, frequency tracks the change precisely to form an accurate resistance wire thermometer. Such a desired condition for "machine temperature" is achieved if the resistor R3 is wound bi-filar non-inductively with, say, copper to match the temperature coefficient of copper in inductors L3 and L4. Since meaningful conductivity measurements must always have temperature controlled and recorded simultaneously, the frequency at bridge balance becomes doubly significant. The intended conductivity apparatus appears in Fig. 2 in its most rudimentary operational form. Sensing inductor L4 is wound in two equal sections in order to provide the thin sample with a slit entry into the central portion of an air-core solenoid. The self-tuning characteristic of the Wien inductance bridge oscillator (WIBO) to the exact frequency of the bridge balance is well known. The use of the non-linear characteristic of the miniature lamp to stabilize output voltage is equally well known [5]. For conductivity measurement, arms three and four of the WIBO are mounted in close proximity on a test fixture which bears the sample being measured inside an environmental chamber. All components of arms three and four are wound with the same material, copper, in order to translate the temperature sensitivity into an integral, precision thermometer outputting frequency. The base frequency, indicating "machine temperature", is recorded prior to insertion of the sample being measured. When the sample is inserted into the sensing inductor, there are two concomitant effects which cooperate to shift the WIBO frequency upwards: (a) the sample couples inductively as if in parallel to reduce L4, and (b) the sample resistance transfers to the L4 primary winding in an apparent series effect which increases R4. The shift from base frequency varies directly with sample conductivity where all samples are of exactly the same geometry.
250
Rl
Gl
#380 I-&-r? Lamp
1-
R 133 R
"
O"o cc
Test Fixture
Fig. 2. Wien inductance
Fig. 3. Block diagram
-.
bridge oscillator
of the conductivity
(WIBO).
instrument.
Sample insertion, however, does change the sensing inductor coil current even when the #380 miniature lamp maintains essentially constant WIBO output voltage. The coil current elevates “machine temperature” above ambient temperature. If the coil current is permitted to change (perhaps +lO%) after sample insertion, the new frequency reading will not settle until the “machine temperature” rise above ambient readjusts. This disturbing drift could persist for, say, one minute, in which time the environmental control for test temperature would also drift at least a small amount. To circumvent this drift, the test instrument was refined by avoiding use of the miniature lamp and emnlovine: the “given coil current at the given
251 copper temperature" control scheme shown in Fig. 3. In this scheme, another copper resistor, R ca, is m o u n t e d within the test fixture at "machine t e m p e r a t u r e " to burden properly a small current transformer that senses coil current. At each base frequency, the concomitant temperature determines a unique coil current; however, the voltage on RcB, despite resistance change, is kept constant (at 0.9 V) by the control scheme shown in Fig. 3. Performance data on this servo loop are presented in Table 1 given within Fig. 4 over a temperature range. The voltage follower prevents parallel loading of RcB b y non-copper resistance, which may also be at other than the "machine temperature" of the test fixture. When current in arms three and four is controlled to the unique current value either before or after sample insertion, the frequency drift then must be due to either ambient temperature change or sample heating from eddy currents. A typical electronic counter requires 100 s, a most inconveniently long time, to resolve frequency to 0.01 Hz. For convenience, as well as to avoid temperature drift during each observation, it is desirable that frequency be resolved to 0.01 Hz in just 1 s. In order to achieve this, a phase-locked-loop (PLL) and a 100:1 divider are used together to step-up WIBO o u t p u t frequency 100 times for presentation to the electronic counter. A convenient way to operate the counter is to adjust to 50% d u t y cycle such that the display persists 1 s while accumulating readings on alternate seconds. Also, where temperature control is sufficient, an optional integration over 10 s can resolve frequency data to 0.001 Hz. Electronic counters are available, having digital BCD o u t p u t capability to various processing circuits, which can provide any degree of automated testing and recording desired. A properly programmed read-only m e m o r y (ROM) storing the copper-wire 0oC 14~
14~
1200
1100
I100
:
:
y ~ o
-
oc
Vo vi_ v,
g
i 700
/
• / , .
~ ~ 4 . 9 ~
~
los2A +4_o,_o~.16~ o;9o~ n~.2 +00.o~s.z4 3.OlO.~1
~
!
I :
5011
I
-65
I
-45
. I
-25
3.3~~o:~o~
12ss.z +100.oIs.~ Z.T30.~
~L i I
-5
700
:.. i~.z I
+15
I
+35
+~2s.o I ~.45 2.~ i
I
+55
+/5
I
+95
o.~o~ I
500
+115
Temperature. DegreesCentigrade
Fig. 4. Copper-wize thermometer characteristic v/a the WIBO.
252 temperature characteristic of Fig. 4 can output directly in a degrees Centigrade display corresponding to the base frequency with the sample withdrawn. If the samples to be measured are thin, quasi-infinite sheets, the fringing flux does not affect the conductivity data, and calibration with a single sheet of known thickness made from an isotropic non-ferromagnetic metal conductor is sufficient for conductivity determinations. In such cases, conductivity is linear with sample thickness in all geometries. However, graphite intercalation compounds synthesized using highly oriented pyrolytic graphite (HOPG) are usually in the form of small rectangular pieces which cannot be considered quasi-infinite sheets. Furthermore, it is desirable to measure their conductivity while still contained inside the reaction tube because of their instability in air. To facilitate such in situ conductivity measurements, the reaction tube is usually a glass rectangular tube of ~ 5 mm outer dimension which can be directly inserted into the sensing inductor halves. Because of this tube dimension, the spacing of the sensing inductor halves also precludes treating small samples of graphite intercalation compounds as quasi-infinite sheets, and, here, fringing flux around the sample will have a significant effect on the conductivity data. To circumvent this problem, the test instrument is accurately calibrated using an exact geometrical replica of the sample fabricated precisely from a non-ferromagnetic material (e.g., copper) whose conductivity has been determined by the standard 4-point probe method. Between the graphite intercalation compound sample and the calibration sample, conductivity being the differentiating parameter, the shift from the base frequency becomes a linear comparison between the calibration sample and the sample under test. The following empirical rules were found to apply from extensive calibration experiments using a variety of materials of known conductivity: (a) The frequency shift is proportional to thickness of the sample. (b) The frequency shift is directly proportional to conductivity when samples of identical geometry and thickness are compared. (c) The frequency shift responds to the 3.24th power of the oscillator base frequency (i.e., a 1000 Hz oscillator produces nearly 20 times the frequency shift as a 400 Hz oscillator upon the same sample). (d) The frequency shift responds to the 3.77th power of the sample diameter for circular samples. This emphasizes the importance of sample replication to exact outline and the greater sensitivity to conductivity contributed by sample portions at the periphery.
3. Measurement of conductivity of AsFs-graphite intercalation compounds The conductivity measurement technique discussed above was applied to determine the basal plane electrical conductivity of several AsFs-graphite intercalation compounds. For these measurements, highly oriented pyrolytic graphite (HOPG), obtained from the Union Carbide Corporation, was inter-
253
calated with AsF5 vapors at room temperature and 0.5 atm pressure, for different time periods, to obtain different stage compounds. The progress of intercalation was monitored by in situ measurement of the sample thickness using a telescopic micrometer. The intercalated samples were characterized b y their X-ray 001 reflections. After extensive experimentation, it was found that the stage 1 AsFs-graphite c o m p o u n d could be prepared in pure form, and the stage 2 c o m p o u n d in essentially pure form with occasional traces of the stage 3 c o m p o u n d . However, all other intercalated samples were found to be mixtures of several different stage compounds. The X-ray analysis of five representative intercalated samples, designated A through E, is summarized in Table 2. Sample A was pure stage 1 compound, whereas sample B was essentially pure stage 2 compound. Samples C, D and E were mixtures of several different stages and some unreacted graphite. The d-spacing of different stage (n) c o m p o u n d s was found to be related b y the expression: d = 8.0 + 3.35 (n -- 1) A. The room temperature basal plane electrical conductivity data on the various intercalated samples at 1000 Hz, obtained using the contactless WIBO technique, are summarized in Table 2. The conductivity is expressed as a percentage of IACS copper conductivity. It is clear from these data that the conductivity peaks at stage 2 in AsFs-graphite intercalation compounds. This trend in conductivity as a function of stage is consistent with other TABLE 2 Basal plane conductivity of various AsF5-graphite intercalation compounds Sample designation
Compounds present
Temperature (°C)
Frequency shift at 1 mm thickness A f (Hz)
HOPG Intercalated sample A Intercalated sample B Intercalated sample C
Graphite Stage 1
23.1 23.1
0.16 0.63
4.4 17.4
Stage 2
23.1
2.48
68.3
23.1
1.84
50.7
23.1
0.41
11.2
23.1
0.28
7.8
22.9
3.66
101.0
Stage 3 (major) Stage 4 (minor) Stage 2 (trace) Intercalated Stage 3 (major) sample D Stages 4 and 5 (minor) Stage 6 and graphite (trace) Intercalated Stage 4 (major) sample E Stages 3 and 5 (minor) Graphite (trace) OFHC copper Copper
Conductivity as a percentage of IACS copper conductivity
254
investigations on AsF5-graphite intercalation compounds [6 - 81. The maximum conductivity measured was about 68 percent. of that of pure copper; this value is lower than that reported by Vogel et al. [6, 71 but in substantial agreement with the conductivity results obtained by McKee et al. [8] on AsF,-graphite compounds synthesized using HOPG crystals.
4. Conclusions A new, contactless technique based on an all-copper Wien inductance bridge oscillator offers a convenient and reliable method for measuring, in situ, the basal plane electrical conductivity of highly anisotropic graphite intercalation compounds. The technique has the added advantages of integrating the temperature data with the frequency data and its operation can be made automatic without any balancing adjustments. The technique has been applied to measure the room temperature basal plane conductivity of several AsF5-graphite intercalation compounds. The conductivity in these compounds has been found to peak at the second stage with a value of about 68 percent. of that of pure copper.
Acknowledgments The authors gratefully acknowledge the contributions of J. Schreurs and R. C. Kuznicki to the X-ray diffraction analysis of the intercalation compounds, and the technical assistance of J. A. Fraino in conducting the intercalation experiments.
References 1 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 2 C. Zeller, G. M. T. Foley, E. R. Falardeau and F. L. Vogel, Mater. Sci. Eng., 31 (1977) 255. 3 G. L. Miller, D. A. H. Robinson and J. D. Wiley, U. 5’. Patent No. 4,000,458 (1976). 4 E. McRae and A. Hbrold,Mater. Sci. Eng., 31 (1977) 249. 5 A. J. Diefenderfer, Basic Techniques in Electronic Instrumentation, W. B. Saunders Co., Philadelphia, 1972, p. 245. 6 F. L. Vogel, G. M. T. Foley, C. Zeller, E. R. Falardeau and J. Gan, Mater. Sk. Eng., 31 (1977) 261. 7 G. M. T. Foley, C. Zeller, E. R. Falardeau and F. L. Vogel, Solid State Commun., 24 (1977) 371. 8 D. W. McKee, L. V. Interrante and R. S. Markiewicz, Extended Abstract of the paper presented at the 14th Biennial Conf. on Carbon, Pennsylvania State University, 1979.