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Structure of C_{8}K, a typical
stage 1 intercalation compound. Stage n means that n layers
of graphite are present between each pair of intercalant
layers.[67] a) The layer
structure. The lattice constant along the direction
perpendicular to the planes is called I_{c} in
GIC's. b) Three common inplane structures. C_{8}K
has the (2 × 2)R0° structure.

Evidence for dimensionality crossover in a
Nb/Ge superlattice.[208] Solid lines are fits to
the KLB theory.[131] The
direction marked ``'' means __ ^c in the vernacular of
GIC's and the direction marked ``__'' is  ^c in GIC
terms. The H_{c2} data marked __ is almost
unaffected by the dimensionality crossover. The
H_{c2} data marked  covers the range from the
fully 3D regime (45 Å/ 7 Å specimen) to the
fully 2D regime (45 Å/ 50 Å specimen). The
intermediate 65 Å/35 Å specimen shows a
crossover from 3D to 2D character as the temperature is
lowered.

H_{c2}(t) data on Nb/Ta
superlattices showing two lowtemperature critical field
discontinuities. From Ref. [30]. The discontinuity in
slope at t 0.80.9 is the 3D2D coupling change. The
identity of the lower transition at t = 0.49 has not been
definitely determined.

H_{c2}(theta) data on Nb/Ta
superlattices from Ref. [29]. The data is for three
samples at a reduced temperature t = 0.9. Lambda is
the bilayer period, which corresponds to I_{c} in
the GIC case. Data in the trace marked 3D are fit with Eqn.
, while data in the
traces marked 2D are fit with Eqn.
.

T_{c} vs layer thickness in Nb/Cu
superlattices. From Ref. [14]. The decrease of
T_{c} with decreasing thickness of the
superconducting component is predicted by proximityeffect
theories.[49,54] The predictions of the
standard proximityeffect theories is indicated by the
solid line. The proximity effect calculation modified to
allow a thicknessdependent T_{c} for the Nb layers
is indicated by the dashed line.

H_{c2}(theta) for a high
T_{c} superconductor. From Ref. [118]. Each set of symbols
corresponds to a different definition of H_{c2}.
For example, the curve labeled 0.7 R _{N} was
obtained by plotting versus theta the values of H
that satisfy R(H,theta) = 0.7 R_{N}. Each
curve is also labeled in parentheses with the magnitude of
the anisotropy parameter 1/epsilon that was used for
the fit to Eqn. .

Phase diagrams of the KHg and CsBi
binary alloys.[103]

Range of compositions of the starting
alloy which will produce a given stage GIC in the KHg and
CsBi binary systems. From Ref. [145]. Upper, KHg system. In
region (1), C_{8}K is produced; in region (2),
C_{4}KHg; in region (3), C_{8}KHg; in
region (4), C_{12}KHg; in region (5), higherstage
binary compounds, or no reaction. Lower, CsBi system. In
region (1), C_{8}Cs is produced; in (2),
C_{4}CsBi; in region (3), no reaction.

(00l) xray scans for pink and
gold C_{4}KHg. The large peak near 22° in each
scan is from the copper sample holder. The broad hump from
about 6° to 14° is due to the glass tube that the
sample holder is in. a) I_{c} = (10.22 ±
0.03) Å pink sample. T_{c} = 1.53 K. b)
I_{c} = (10.18 ± 0.03) Å gold sample.
T_{c} = 0.95 K.

(00l) xray scans before and after
hydrogenation for a gold C_{4}KHg sample. The broad
hump from about 6° to 14° is due to the glass tube
that the sample is in. Before: T_{c} = 0.84 K gold
C_{4}KHg sample. I_{c} = (10.24 ±
0.03) Å. After: Same sample as in ``Before'' picture,
only after exposure to 200 torr hydrogen gas. T_{c}
= 1.535 K. I_{c} = (10.24 ± 0.03)
Å.

(00l) xray scans for
alphaphase stage 1 CsBiGIC's. The broad hump from
about 6° to 14° is due to the glass tube that the
sample holder is in. a) I_{c} = (10.61 ±
0.03) Å alphaphase sample. b) Similar
(00l) scan taken by BendrissRerhrhaye.[17] In b), theta is
increasing from right to left, whereas in a) 2theta
is increasing from left to right.

Raman spectra on gold and pink
C_{4}KHg. a) Spectrum of a T_{c} = 0.719 K
gold sample with a single I_{c} value = 10.14
Å. The peak frequency is 1597.1 cm^{1} and
the HWHM is 13.2 cm^{1}. b) Spectrum of a
T_{c} = 1.53 K pink sample with a single
I_{c} value = 10.22 Å. The peak frequency is
1593.9 cm^{1} and the HWHM is 15.5
cm^{1}.

Xray and neutron diffraction
(00l) spectra of a gold C_{4}KHg specimen.
The betaphase peaks are marked with
downarrow. a) Only the I_{c} = 10.24 Å
alpha phase is clearly visible using xrays. The
small bump to the left of the (002) may be the
betaphase (002) peak. b) With neutrons, both the
I_{c} = 10.24 Å alpha phase and the
I_{c} = 10.83 Å beta phase show
welldefined peaks.

Neutron diffraction spectra of a gold
C_{4}KHg specimen with hydrogen and a pink specimen
without hydrogen. Note the lack of beta phase in
either sample. a) Spectrum of a gold sample whose
T_{c} was 0.84 K before hydrogenation and 1.54 K
afterward. b) Spectrum of a pink C_{4}KHg
sample.

Definition of the distances z_{i}
used in the fits to the neutron diffraction data (from Ref.
[272]). The distances
are measured from the center of the sandwich, halfway
between the mercury layers. Deltaz, the Hg layer
splitting, is twice the distance of the Hg layers from z =
0.

Realspace structure of the majority
phase of C_{4}KHg along the caxis as calculated
from the Fourier transform of the extended neutron
diffraction data. All plots were scaled to a carbon peak
height of 1.0. a) Plot of nuclear scattering intensity
versus distance along the graphite caxis for a pink sample
(*) and a gold sample (circ). b) A similar plot
comparing the structure of the MIT pink sample (*) to a
structure (circ) calculated from fit parameters
reported by Yang et al.[272]

Experimental definition of
T_{c}.

a) dc magnetization versus field for
ideal type I and type II superconductors. H_{c1} is
the lower critical field, H_{c} is the
thermodynamic critical field, and H_{c2} is the
upper critical field. kappa <
1/sqrt2 indicates type I superconductivity;
kappa 0.8 indicates weak type II behavior;
kappa 2 indicates strongly type II behavior. b) ac
susceptibility versus field for ideal type II
superconductor with kappa 0.8. Adapted from Ref.
[252].

A sketch of the sample holder used in
the critical field measurements. The dimension d of
the metal piece was chosen to be the inner diameter of the
sample tube so that the holder would be centered and fixed
inside the tube. A careful effort was made to orient the
carbon (graphene) planes parallel to the holder's surface.
The GIC's were affixed to the metal pieces with Apiezon N
grease.

A schematic drawing of the inductance
bridge. The sample capsule was placed inside the primary
coil. The windings were made from 38 gauge magnet wire.
There were 20 complete layers of winding in the secondary
coils and 2 complete layers of winding in the primary.

A schematic of the data acquisition
system. For zerofield temperature sweeps, the thermometer
voltage was attached to the xinput of the flatbed plotter.
For fixedtemperature magnetic field sweeps, the dc output
of a stepping motor on the magnet power supply was attached
to the xinput of the plotter.

Illustration of how a sample which is
only partially superconducting can mimic full
superconductivity in an inductive transition.

a) Definition of the angle theta,
the angle between the applied magnetic field and the
graphite caxis. This angle is the complement to that
usually used in the thinfilm superconductivity literature,
but corresponds to customary usage in the GIC literature.
b) A sketch showing how H_{c2} is determined
graphically from raw susceptibility versus magnetic field
data. Note the similarity of this trace to Figure b).

a) Superconducting transitions with the
magnetic field applied parallel and perpendicular to the
graphite caxis for a typical C_{4}KHg sample.
Notice how much broader the transition is in the
vecH__ ^c case. b) Similar data from Iye and
Tanuma, Ref.[120],
Figure 2.

Critical field H_{c2} as a
function of the angle theta for 4 C_{4}KHg
GIC's at T 0.4 K. Fits (dotted lines) were calculated using
Equation . a) Data for an MIT
C_{4}KHg sample with T_{c} = 0.95 K
(circ) and also for a T_{c} = 0.73 K sample
(bullet) from Ref. [240]. For T_{c} = 0.95 K
sample, 1/epsilon = 10.0 and H_{c2}(0°)
= 24 Oe with a residual cal R = 0.29. For data of
Ref. [240],
1/epsilon = 11.3, H_{c2}(0°) = 26 Oe,
and cal R = 0.090. b) Data for two C_{4}KHg
samples with T_{c} 1.5 K. (circ),
T_{c} = 1.53 K with 1/epsilon = 10.2,
H_{c2}(0°) = 46 Oe, and cal R = 0.73;
bullet, T_{c} = 1.54 K with 1/epsilon
= 9.5, H_{c2}(0°) = 47 Oe, and cal R =
1.18.

Why a tilted sample affects the shape of
H_{c2}(theta). The notation ( vecH
cdot ^x)^x signifies the projection of vecH
along ^x. a) The aligned case. Rotations of the sample
around the vertical ^z allow theta to be varied all
the way from ( vecH^c) to ( vecH__^c) (
vecH__^c = vecH ^a). b) The misaligned
case. H_{c2,__^c} can still be measured correctly,
but instead of the true value of H_{c2^c} one
will get
H_{c2,^c}/sqrtcos^{2}ø
+
epsilon^{2}sin^{2}ø.

The effect of sample tilt on
H_{c2}(theta). The three curves in this
picture were calculated using the parameters H_{c2,
^c} = 42 Oe, anisotropy == 1/epsilon = 15 and
the following values for the tilt angle: (circ)
ø = 0°; (bullet) ø = 10°;
(diamond) ø = 40°. The ø = 0°
curve corresponds to one of the fits shown in Figure b). Note that the
curves for ø = 10° and for ø = 0° are
almost indistinguishable.

The effect of mosaic spread on
H_{c2}(theta), calculated using Equation
. The same parameters
were used as in Figure
, except that here the mosaic spread, Delta, is
varied: (circ) Delta = 0°;
(bullet) Delta = 3°; (diamond)
Delta = 10°.

Comparison of the effect of the two
definitions of H_{c2} on
H_{c2}(theta). circ, tangent
definition; diamond, 90% definition. Data are for a
T_{c} = 1.53 K sample at T/T _{c} = 0.29.
The 90% method tends to produce slightly higher critical
fields, but there is only a small difference between the
shapes of the curves for the two analysis methods. Use of
the 90% definition does not improve agreement with Eqn.
.

H_{c2}(theta) for
C_{8}K, from Ref. [141]. The fields are labeled
H_{c2} in the type II region and H_{c3} and
H_{c} in the type I region.

H_{c2}(theta) curves for
TaN showing a transition from type I to type II character
as a function of field direction. From Ref. [259]. TaN is the only bulk
superconductor besides C_{8}K (and possibly
C_{4}KHg) known to display this variability. The
temperatures at which the curves were taken and the
thermodynamic critical fields are indicated. Note that at
1.65 K, the sample is entirely type II, but that at 2.4 K
it is entirely type I.

Anisotropic GinzburgLandau model fits
(dotted curves) to H_{c2}(theta) data as a
function of temperature. All fits were produced with the
parameters tilt = 0° and mosaic spread = 0°. a) t =
0.29, H_{c2,^c} = 47 Oe, anisotropy
(1/epsilon) = 9.5, and residual parameter cal
R = 1.18. b) t = 0.57, H_{c2, ^c} = 33 Oe,
anisotropy (1/epsilon) = 5.5, and cal R =
1.25. c) t = 0.78, H_{c2,^c} = 23.1 Oe,
anisotropy (1/epsilon) = 4.5, and cal R =
1.43.

Anisotropic GinzburgLandau model fits
(dotted curves) to H_{c2}(theta) data as a
function of temperature, taking into account the
possibility of type I behavior. All fits were produced with
the parameters tilt = 0° and mosaic spread = 0°. a)
t = 0.29, H_{c2,^c} = 35 Oe, anisotropy
(1/epsilon) = 14, H_{c} = 65 Oe, and
residual parameter cal R = 0.39. b) t = 0.57,
H_{c2, ^c} = 19 Oe, anisotropy (1/epsilon)
= 15.5, H_{c} = 43 Oe, and cal R = 0.84. c)
t = 0.78, H_{c2,^c} = 14.5 Oe, anisotropy (1/
epsilon) = 12.5, H_{c} = 24.5 Oe, and
cal R = 1.11.

Comparison of field sweeps between type
II and possible type I transitions. The vertical direction
is the inductive voltage, while the horizontal direction is
field. All traces taken at about 0.4 K. a) Transitions with
vecH __ ^c and vecH  ^c for a
T_{c} = 0.95 K sample. For both orientations the
transitions appear smooth. b) Transitions with vecH
__ ^c and vecH  ^c for a T_{c} = 1.5 K
sample. For vecH __ ^c, the transition looks
smooth, consistent with its expected type II character. For
vecH  ^c, on the other hand, there is a small
discontinuity in the susceptibility near the upper critical
field which is indicated by an arrow. This feature was seen
consistently in T_{c} = 1.5 K samples.

Thermodynamic critical fields obtained
from H_{c2}(theta) fits versus temperature
for T_{c} = 1.5 K C_{4}KHg specimens. The
numbers plotted here are the same as in Table .
(bigtriangleup), data for a T_{c} = 1.53 K
sample; (circ), data for a T_{c} = 1.54 K
sample; (diamond), a linear fit to the data with
H_{c}(0) = 85.2 g; (circ), a quadratic fit
to the data with H_{c}(0) = 66.5 g; (×),
H_{c}(t) calculated using the specific heat data of
Alexander et al.,[8] which gives
H_{c}(0) = 112 Oe.

Comparison of the Tinkham formula and
AGL theory fits to H_{c2}(theta) data on a
T_{c} = 1.5 K C_{4}KHgGIC. bullet,
data at t = 0.55. circ, AGL fit with
H_{c2}(0°) = 19 Oe, 1/epsilon = 15.5,
and a residual cal R = 0.84. diamond, TF fit
with H_{c2}(0°) = 23 Oe, 1/epsilon = 13,
H_{c} = 41 Oe, and cal R = 0.47. Below, a
plot of the errors of each fit versus theta. The
same symbols are used.

Critical field H_{c2} as a
function of reduced temperature for C_{4}KHg.
Dotted curves are leastsquares line fits to the data. Fit
parameters are given in Table . a) Data for a
C_{4}KHg with T_{c} = 0.95 K:
(circ), vecH __ ^c. (bullet),
vecH  ^c Data for a T_{c} = 0.73 K sample
from Ref. [240]:
(diamond), vecH __ ^c. (×),
vecH  ^c. b) Data for two C_{4}KHgGIC's
with T_{c} 1.5 K. T_{c} = 1.53 K sample:
(circ), vecH __ ^c. (bullet),
vecH  ^c. T_{c} = 1.54 K sample:
diamond, vecH __ ^c. ×, vecH 
^c.

Critical fields with vecH  ^c
for T_{c} 1.5 K C_{4}KHg samples.
Uparrow marks the value of T_{c} found using
a zerofield temperature sweep. a) (bullet), data
for a T_{c} = 1.53 K sample; (diamond), a
linear fit to the data with H_{c2}(0) = 89.7 Oe,
T_{c} = 1.65 K and cal R = 6.25e3; (.), a
quadratic fit to the data with H_{c2}(0) = 64.0 Oe,
T_{c} = 1.55 K and cal R = 1.2e2. b)
(bullet), data for a T_{c} = 1.54 K sample;
(diamond), a linear fit to the data with
H_{c2}(0) = 85.8 Oe, T_{c} = 1.62 K and
cal R = 1.62e3; (.), a quadratic fit to the data
with H_{c2}(0) = 62.8 Oe, T_{c} = 1.51 K
and cal R = 4.7e2.

Comparison of WHH and linear fits to
H_{c2}(T) data taken on a T_{c} = 1.54 K
sample. a) (bullet), data for vecH __ ^c.
(.), linear fit with H_{c2}(0) = 748 Oe,
T_{c} = 1.52 K, and cal R = 6.9e3.
(circ), WHH fit with H_{c2}(0) = 518 Oe,
T_{c} = 1.53 K, and cal R = 1.6e2. b)
(bullet), data with vecH  ^c. (.), linear
fit with H_{c2}(0) = 85.8 Oe, T_{c} = 1.62
K, and cal R = 1.6e3. (circ), WHH fit with
H_{c2}(0) = 59.76 Oe, T_{c} = 1.63 K, and
cal R = 1.2e2.

Summary of all H_{c2} data, both
__ and  to the caxis. The dimensionless quantities
plotted are reduced field ( h^{*}) versus reduced
temperature (t). (bullet), 143 data points taken on
5 different GIC's. (circ), best 2parameter WHH fit
to the data with cal R = 1.7e2. (.), best linear
fit to the data with cal R = 1.3e2. Both fits have
fracdh^{*}dt = 1 at t = 1.

Demonstration of the temperature
dependence of the anisotropy parameter epsilon in
C_{4}KHg, where 1/epsilon ==
H_{c2}(90°)/H_{c2}(0°). Data are
for a T_{c} = 1.54 K C_{4}KHg sample.
(circ), t = 0.29. (bullet), t = 0.55.
(×), t = 0.76. All H_{c2}(0°) values were
determined from the data, not the fits, so that this plot
is modelindependent. Fits to this data are shown in
Figure .

Temperaturedependent anisotropy in
C_{8}KHg is demonstrated by a plot of
H_{c2}(theta)/H_{c2}(0°) versus
theta, just as in Figure
. All data from Iye and Tanuma, Ref. [240] on a T_{c} = 1.94 K
sample. (×), data at t = 0.23. Fit, (diamond),
with 1/epsilon = 17.6 and cal R = 6.8e3.
(bullet), data at t = 0.81. (circ), fit with
1/epsilon = 21.6 and cal R = 5.3e3.

Positive curvature of H_{c2}(T)
in C_{8}RbHg. Data are taken from Iye and Tanuma,
Ref. [120].
(circ), H_{c2, __ ^c}. (bullet),
H_{c2,  ^c}. Parameters for the line fits: for
vecH __ ^c, H_{c2}(0) = 3078 Oe,
T_{c} = 1.36 K, and cal R = 0.56; for
vecH  ^c, H_{c2}(0) = 89.0 Oe,
T_{c} = 1.37 K, and cal R = 3.02e2.
Zerofield T_{c} for this sample was 1.4 K.[120]

Theoretical demonstration of dimensional
crossover in Josephsoncoupled superlattices from the work
of Klemm, Luther and Beasley.[131]. r is the parameter which
characterizes the dimensionality of coupling. alpha,
tau_{SO}, and H _{P} == 4
k_{B} T_{c}/ pi mu are
parameters which characterize the degree of Paulilimiting
(Paulilimiting is discussed in Section
). The inset shows a plot of T^{*}/ T_{c}
(where T^{*} is the dimensionality crossover
temperature) versus r.

T_{c} versus normallayer
thickness for S/N bilayers. Figure taken from Ref. [261] Here D _{N}
and D _{S} are the thicknesses of the normal and
superconducting layers, and T _{cS} is the bulk
T_{c} of the superconducting component.
Approximately T/ T_{cS} = (1  t(D_{N}
> infty))(1 
exp2D_{N}/xi), where xi is
the dirtylimit Pippard coherence length.

Extended critical field linearity due to
smallscale sample inhomogeneity. From a calculation by
Carter and colleagues.[34] The plots are of reduced
field versus reduced temperature for several different
normalized diffusivity distribution functions Q(y). Q(y) ==
D_{ave}P(D), where P(D) is the distribution
function for diffusivity, D_{ave} is the average
diffusivity, and y == D/D _{ave}. In the lower
plot, a P(D) skewed to lower diffusivities produces an even
greater critical field enhancement at low temperatures. The
index n refers to the power of the linear factor used to
skew the symmetric distribution.

Illustration of how v_{__
vecH} (vecq) changes as a function of
wavevector vecq for an ellipsoidal Fermi surface.
vecq is the coordinate of a point on the Fermi
surface. B is Dalrymple's anisotropy parameter, which is
equivalent to epsilon in the AGL model.[50]

Enhanced linearity of h^{*}(t)
calculated from Butler's equations[33] using an ellipsoidal FS
model. Taken from Ref. [50]. Dalrymple's parameter B
is equivalent to 1/epsilon in the AGL model. The B =
1.0 curve is for a spherical Fermi Surface, and so is
equivalent to the WHH theory.

Butlermodel[33] fit of NbSe_{2}
H_{c2}(t) data. Figures taken from Dalrymple's
thesis.[50] a)
H_{c2, __} = H_{c2,  ^c}. An excellent
fit is obtained by using the WexlerWoolley Fermi Surface
model[263] plus an
additional ellipsoid. b) H_{c2, } = H_{c2, __
^c}. The WexlerWoolleyplusellipsoid model produces
the correct shape, but needs to be multiplied by an
additional factor of 2.1 to account for meanfreepath
anisotropy.

Twoband model fit to anomalous
H_{c2}(t) of
Cs_{0.1}WO_{2.9}F_{0.1} from Ref.
[81]. The plot is of
h^{*} versus t. The curve labeled (4) is the
HelfandWerthamer isotropic theory. The crosses, circles
and squares are experimental data for three different
crystallographic orientations (the orientations are not
specified). Curve (1) is the twoband model with no
interbandscattering, whereas (2) and (3) correspond to
increasing interbandscattering. The parameters of these
fits are too numerous to list here, but may be found in
Ref. [81].

Fermi surface computed for
C_{4}KHg by Holzwarth and colleagues.[112] The basic structure of
the Fermi surface is similar to that of NbSe_{2}[51] in that both have
pieces of nearly cylindrical symmetry at the corner of a
hexagonal Brillouin zone, and both have higher masses for
transport along k_{z} than in the layer planes. The
hexagonal solid line is the Brillouin zone; the roughly
triangular pieces drawn with a solid line at the corners of
the BZ are the graphitic pi bands. The pieces drawn
with a dotted line are due to mercury bands. The small
circular zonecenter part is from Hg 6s holes; the
hexagonal portion is from Hg 6ppi electron carriers;
and the trigonal pieces at the zone corner are derived from
H 6psigma bands.

Comparison of H_{c2}(T) in
C_{8}K and C_{6}K, one of its highpressure
phases. a) Data on a T_{c} = 134 mK C_{8}K
sample taken by Koike and Tanuma.[141] Note the marked positive
curvature of the critical fields. H_{sc} is a
supercooling field. b) Data on a T_{c} = 1.5 K
sample of C_{6}K from Ref. [13]. (circ), H_{c2,
__ ^c}; (bigtriangleup), H_{c2, 
^c}. Note the enhanced linearity of the critical
fields.

Hydrogen stoichiometry dependence of the
superconducting transition temperature T_{c}, Debye
temperature theta_{D}, the Einstein
temperature T_{E}, and the linear specific heat
coefficient Gamma in C_{8}KH_{x} and
C_{8}RbH_{x}. From Ref. [78]. The label F(x)/F(0)
indicates that each of the quantities is plotted normalized
to 1.0 at x = 0.

Schematic densityofstates for a)
C_{8}K and b) C_{8}KH_{0.55}. From
Ref. [171]. Note
the very small hole band near E_{F} in b).

T_{c} increase in
TaS_{2} induced by a) hydrogenation and b)
pressure. a) From Ref. [179]. The error bars represent
the transition width, while the circles are the volume %
superconducting. This experiment was performed on a powder
sample. At a hydrogen concentration ofu.87, T_{c}
;SPM_{l}t; 0.5 K (not shown). b) From Ref. [90]. T_{CDW} is the
CDW onset temperature, while T_{c} is the usual
superconducting transition temperature. 4H _{b} and
2H are TaS_{2} polytypes with different crystal
structures.

Inplane resistivity discontinuities in
TaSe_{2} associated with CDW formation. From Ref.
[264]. 1T and 2H
refer to different polytypes (crystal structures). The CDW
transitions occur at 473 K in 1TTaSe_{2} and at
117 K in 2HTaSe_{2}, respectively. Notice that
1TTaSe_{2} has a higher resistivity below its
transition, whereas the resistivity of 2HTaSe_{2}
decreases at its transition.

Superconducting transitions before and
after hydrogenation in three types of C_{4}KHg
samples. a) A gold sample. T_{c} increases from
0.88 K to 1.54 K, and Delta T_{c}/
T_{c} decreases from 7.3× 10^{2} to
7.8× 10^{2}. b) A pink sample. T_{c}
is almost constant; Delta T_{c}/
T_{c} decreases from 4.7× 10^{2} to
2.2× 10^{2}. c) A coppercolored sample.
T_{c} increase from 1.32 K to 1.50 K; Delta
T_{c}/ T_{c} decreases from 0.138 to
6.47× 10^{2}.

Pressure dependence of T_{c} in
KHgGIC's. From Ref. [55]. a) Pressureinduced
transition narrowing in C_{4}KHg. Notice that the
application of a small pressure, 0.8 kbar, increases
T_{c} to 1.5 K, while application of further
pressure decreases T_{c} at a rate
dT_{c}/dP = 5×10^{5} K/bar. b)
Monotonic decline of T_{c} with pressure in
C_{8}KHg. dT_{c}/dP =
6.5×10^{5} K/bar.

Possible Fermi surface nesting wave
vector in C_{8}K. From Ref. [115]. The horizontal
crosssection of the FS in the GammaKM plane is
shown. The arrow indicates the proposed nesting wave vector
near the M point.

Temperature dependence of the
resistivity and susceptibility in the alkalimetal mercury
GIC's. From Ref. [72]. a) Temperature
dependence of the resisitivity. Curves (1) and (2) are for
C_{4}RbHg; (3) is for C_{4}KHg; (4) is for
C_{8}RbHg; and (5) is for C_{8}KHg. b)
Temperature dependence of the susceptibility. Curves (1)
and (2) are for C_{4}KHg; (3) is for
C_{8}RbHg; (4) is for
C_{4}K_{0.5}Rb_{0.5}Hg; (5) is for
C_{4}RbHg, and (6) is for C_{8}KHg.

An electron micrograph showing
intercalant inclusions (bright regions) in a
C_{4}CsBi_{x} alpha +
betaphase polycrystal grown here at MIT. The
magnification for this micrograph is indicated by the 100
nm scale bar. [Micrograph prepared by J. Speck, MIT.]

A plot of superconducting transition
temperature T_{c} for C_{4}CsBi_{x}
versus starting alloy Bi/Cs ratio. bigotimes, MIT
data from Ref. [36];
bigtriangleup, University of Kentucky data from Ref.
[270]; and bigcirc,
Freie Universität Berlin data from Ref. [223]. The X are alloy (not GIC)
data from the CRC Handbook. The presence of
downarrow means that the nearest point represents an
upper bound on T_{c}. Data from the University of
Nancy is not included because precise starting alloy
compositions are not given for their samples.

The transverse magnetoresistance of a
C_{4}CsBi_{0.6} (stage 1,
alphaphase) sample at 1.2 K with a current of 1 mA.
The current is applied in the graphite planes; the magnetic
field is along the graphite caxis.

a) Fourier transform of the data in
Figure . Most reproducible
frequency is (1120 ± 110) T, although other
frequencies sometimes occur. b) Comparison of the data from
Figure with a simulated trace
calculated using Equation and parameters
obtained from the Fourier transform of the data. The
calculated curve is offset from the data for clarity.

(3root13 X 8)R(15°,0°)
inplane unit cell proposed for
C_{4}CsBi_{0.6} by A.
BendrissRerhrhaye.[17].

a) Softening of the elastic constant
C_{33} as a function of composition in the
C_{8}K_{(1x)}Rb_{x} system. From
Ref. [183]. The
elastic constant was obtained from a fit to the acoustic
branch of the phonon system. The phonons were observed
using inelastic neutron scattering. Similar softening of
the Mpoint optic modes has been seen using Raman
scattering.[219] b)
T_{c} versus x in the
C_{8}K_{(}1x)Rb_{x} system. Only
the endpoint compounds have been characterized.

Coherence lengths of a uniaxial
superconductor. As pointed out by Morris et
al.,[175] the
coherence length of a uniaxial superconductor is the length
of a vector from the center of a biaxial ellipsoid to its
edge. a) The case of an aligned sample, which is described
by Eqn. . (See Figure
a).) The ellipsoid has two radii of length
xi_{a} and one of length epsilon
xi_{a}. b) The case where the sample is
tilted by an angle ø, which is described by Eqn. . Now the ellipsoid is
triaxial, with one of the coherence lengths of size
xi_{a} from a) being replaced by one of size
xi_{a} sqrtcos^{2}
ø + epsilon^{2}
sin^{2} ø.

Crosssection of the flux quantum in a
uniaxial superconductor. In all cases, the magnetic field
is directed out of the paper. a) The aligned case. For
vecH  ^c, the crosssection of the flux quantum
along the field direction is circular. b) The tilted case.
Now that the ellipsoid that determines
xi(theta) is triaxial, the crosssection of
the flux quantum is noncircular for all field
orientations.
alchaiken@gmail.com
(Alison Chaiken)
Wed Oct 11 22:59:57 PDT 1995