The determination of the stoichiometry of graphite intercalation compounds is an important aspect of their characterization. The reason is that intercalation is a slow chemical process, particularly for higher-stage and ternary compounds. Even if an intercalation reaction proceeds for several weeks at an elevated temperature, the final product (a GIC) may not have reached its equilibrium state. The hypothetical metastable final state of the GIC might be a mixed-stage compound, which wouldn't be so bad, since mixed-stage samples are easily detectable with (00l) x-rays. Mixed-stage samples can be separated out from the well-staged ones and discarded.
A much more insidious situation arises if the compound is well-staged but is off the equilibrium stoichiometry. For one thing, there is the question of what the equilibrium stoichiometry is, a longstanding problem with acceptor GIC's.[74] In principle, stoichiometries can be determined from the x-ray diffraction pattern, as was done with the neutron scattering data. However, to have real confidence in the stoichiometries found from fits to (00l) integrated intensities, one needs either a large number of peaks, or extensive knowledge of the structure of the material in question. Especially in the case of multiphase systems like the KHg- and CsBi-GIC's, an independent check of the stoichiometries determined from diffraction data is highly desirable.
One type of non-destructive chemical analysis that has been used with great success on GIC's is Rutherford backscattering spectrometry (RBS). RBS provides information on composition only in about the top one micron of a specimen,[212] but it has the advantage of doing so in a structure-independent way. Also, since RBS gives depth resolution as well as species identification, any alloy adsorbed on the surface can readily be differentiated from the bulk. RBS measurements were performed on KHg-GIC's by Salamanca-Riba et al., who found stoichiometries of C3.0 ± 1.5KHg0.77 ± 0.08 for stage 1, C7 ± 1.4KHg0.72 ± 0.07 for stage 2, and C13 ± 1.3KHg0.62 ± 0.06 for stage 3. The low ratio of carbon atoms to potassium atoms found in this study is somewhat surprising, but the margin of error is so large that no definite conclusions can be drawn. However, the tentative C/K ratio of 3.0 supports the existence of the ( sqrt3 × sqrt3)R30° phase, for which 3.0 is the stoichiometric C/K ratio. For the (2 × 2)R0° and (sqrt3 × 2)R(30°, 0°) phases, a ratio of four is anticipated. Once again, the ( sqrt3 × sqrt3)R30° phase seems to be turning up in a surface-sensitive experiment; this phase had previously been seen only in Raman scattering and TEM studies.[247] Because of the nature of the measurements in which the ( sqrt3 × sqrt3)R30° phase has been seen, one might wonder if its appearance is related to deintercalation due to sample heating.
The better-bracketed parameter found by RBS is the Hg/K ratio,
which appears to be about 0.7. The stoichiometries found for the KHg-GIC's
in several different experiments are summarized in Table .
As is evident from the Table, a Hg/K ratio of 0.7 is less than any of the
values established from the x-ray or neutron diffraction experiments. This
Hg/K ratio was only determined on one GIC of each stage,[212] so its
magnitude may be affected by sample dependence. However, the agreement for
all three samples of different stage is impressive. In fact, one might
wonder if the constant Hg/K ratio with such a widely varying C/K ratio is
not a sign that another property of the surface rather than the bulk is
being measured. This possibility was put forward by the authors of
Ref. [212], who noted that surface depletion of mercury from C4KHg under heating had been observed using x-rays.[82] The
explanation of the tendency toward surface depletion of mercury is that
since it intercalates after the potassium does,[82,70] it
must also deintercalate first. This idea is believable also because
mercury has a high vapor pressure and is rather chemically inert, with the
result that its gradual surface depletion is a common phenomenon in many
types of materials. For example, surface mercury depletion is a problem in
HgCdTe wafers used in infrared detectors.[143]
RBS measurements have also been performed on the CsBi-GIC's in
collaboration with Dr. J. Steinbeck.[36] The experimental conditions
were similar to those of Ref. [212], except that the GIC's were
cleaved before measurement to remove the alloy adhered on the surface. For
an alpha-phase stage 1 CsBi-GIC sample, the result of this experiment
was a stoichiometry C(2.5 ± 0.65)CsBi0.59 ± 0.03, in
excellent agreement with the previously reported Bi/Cs ratio of C4CsBi0.55.[145,271] The accord between the Cs/Bi ratio
found here and that determined by x-rays[145,271] increases
one's confidence in the Hg/K ratio found from RBS, although there is not a
problem with volatility in the CsBi-GIC's the way that there is in
mercury-containing materials. The problem in synthesizing the CsBi-GIC's
is signalled by the unexpectedly low C/Cs ratio, which is an indication of
the tendency to have macroscopic alloy inclusions in the samples, even when
the surfaces are cleaned of any adhered metal. These inclusions are
discussed further in Section .
Table: Stoichiometries of the KHg-GIC's as determined from various
experiments. ND = not determined by this experiment; NR = not reported by
the authors of the cited reference.
Another non-destructive measurement that can be performed on
air-stable samples is weight uptake. If the mass of the host graphite is
determined before intercalation, and the stoichiometric ratio of the two
intercalant metals is known from another measurement, such as RBS, then
after intercalation the extent to which the reaction was completed can be
estimated. For C4CsBi0.55, a simple calculation shows that the
expected weight uptake is 5.2 times the graphite mass. Measured weight
uptakes were usually on the order of 5.5 to 5.6 times the graphite mass,
even after careful cleaning of the surface. This excess weight is another
indication of the inclusions indicated by the RBS and TEM studies. (TEM
observations of the inclusions are discussed in Section .)
While it would be highly desirable to perform weight-uptake
measurements on the KHg-GIC's, this has not been done because of the
compounds' high reactivity in air. An ideal set-up would be to have a
microbalance inside a dry-box for routine weight-uptake measurements after
intercalation, a practice carried out at the University of
Kentucky.[63] Weight uptake data on C4KHg would be
particularly interesting to compare to measurements of the areal fraction
of superconductivity from inductive studies of the zero-field transition.
(See Section for an explanation of how the areal
fraction of superconductivity is determined.)
The next-best-thing to weight uptake and RBS for the determination
of stoichiometry is wet chemical analysis. Wet chemical analysis was
performed on C4KHg GIC's by Dr. W. Correia of the Center for
Materials Science Chemical Analysis Facility. The basic procedure is to
dissolve the specimen in a solution and precipitate out the various
constituents separately for weighing. The contribution of each of the
elements in the sample can be determined this way. While these
measurements can be fairly accurate, and have the advantage of giving
information about the bulk of the specimen, they also have the distinct
disadvantage of destroying the sample. Therefore, while wet chemical
analysis is useful, it has been performed on only a few specimens. The
results are included in Table .
Drawing conclusions from the data in the Table is difficult. There does not seem to be a strong connection between Hg content and Tc, contrary to much speculation that Hg-deficient samples have lower transition temperatures.[207] The lowest Tc sample actually has the highest Hg/K ratio of 1.2. The observation that gold lower- Tc specimens have more beta phase than higher- Tc specimens is therefore consistent with the work of Yang et al.,[272,270] who found the beta phase of C4KHg has a higher Hg content (of 1.3). The Tc = 1.3 K sample has a composition that agrees well with the RBS measurements, while the Tc = 1.54 K sample agrees in composition with the neutron scattering measurements. All the specimens appear to be close to the expected C/Hg ratio of 4. A systematic study of any possible relation between stoichiometry and superconductivity still needs to be performed on fully characterized samples. The available evidence does not make a strong case for the importance of variable stoichiometry since most of the samples have chemical formulae close to that originally reported by El Makrini.[70]
Of course the most important characterization that needs to be done on superconducting materials is the measurement of the zero-field superconducting transition temperature, called Tc here. Zero-field Tc experiments are discussed in the next section.