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.