In Fig. 2, H_{c2}(*theta*) data are shown for
two low-T_{c} C_{4}KHg samples, one a gold
T_{c} = 0.95 K specimen prepared at MIT, and one a
T_{c} = 0.73 K whose critical fields were reported by
Iye and Tanuma.[50] The
dotted lines are fits to the formula:

where *epsilon* is the critical field anisotropy
parameter of Morris, Coleman and Bhandari[40] defined by:

*epsilon* = H_{c2,par}/H_{c2,perp}

and H_{c2}(0°) is . The fits were chosen
to minimize the residual parameter :[6]

where the errors *sigma*_{i} are estimated as:
sigma_{i} = 0.1 H^{exp}_{i} (1 + sin
*theta*)

and *nu* is the number of free parameters. This form
for the error is used to account for the fact that a small
error in reading *theta* produces a much larger error
in H_{c2} when *theta* is near 90° than
when *theta* is near 0°. Equation 1 describes the
angular dependence of the critical field of anistropic
3D-coupled superconductors with uniaxial symmetry.[40,33] As Fig. 2 shows, this formula
gives a good description of the
H_{c2}(*theta*) data for low-T_{c}
gold C_{4}KHg samples.

H_{c2}(*theta*) data for two T_{c} =
1.5 K samples is shown in Fig. 3 along with two curves
produced by Eq. 1. The curve marked by () is the
residual-minimizing curve according to the definition in Eq.
2. Using other reasonable definitions of the errors
*sigma*_{i} in Eq. 2 (such as assuming an
angle-independent error *sigma*_{i} =
*sigma*) did not produce a fit that goes through the
peak of the data. If the fit is forced through the data at
*theta* = 90°, the solid curve in Fig. 3 is the
result. Extensive experience in trying to fit the
H_{c2}(*theta*) data of T_{c} = 1.5 K
C_{4}KHg samples shows that Eq. 1 is simply
inadequate as a detailed description of the experimental
results.

There are several possibilities that come to mind as an
explanation of the deviations from Eq. 1 that are displayed
in Fig. 3. One possibility is that mosaic spread of the
samples is affecting the data. The 2°-3° mosaic
spread seen in neutron rocking curves can be accounted for by
convolving Eq. 1 with a gaussian. This correction actually
makes the agreement worse since the convolution broadens the
H_{c2}(*theta*) peak. As the solid line in
Fig. 3 shows, the fit that goes through the peak of the data
is already much broader than the data.

Another possible extrinsic factor that could influence the
angular dependence measurements is a possible misalignment of
the sample during mounting. Detailed analysis of the
consequences of improper mounting[10] demonstrates that the only
effect of a tilted sample is to increase the measured value
of . Because the H_{c2}(*theta*)
curves are quite flat near *theta* = 0°, the
effect of improper mounting for reasonable tilt angles (on
the order of 5°) is negligible.

A more interesting explanation for the deviations seen in
Fig. 3 is suggested by the specific heat data of Alexander
*et al.* [4]
Using the linear specific-heat coefficient = 0.95
mJ/(molK^{2}) measured by Alexander, the
zero-temperature thermodynamic critical field H_{c}
can be estimated using the standard formula[55] . No superconducting
transition was measured down to 0.8 K during the specific
heat measurements,[4]
so it is not clear that this linear specific heat coefficient
is appropriate for a T_{c} =1.5 K sample.
Nonetheless, an estimate of H_{c} can be made by
assuming a (2 × 2)R0° structure. This procedure
gives 112 gauss for H_{c} at T = 0 K. Using the usual
quadratic form for the temperature dependence of
H_{c} results in an estimate of 75 gauss for the
thermodynamic critical field at a reduced temperature t ==
T/T_{c} = 0.57. Since, as Fig. 3 shows, 75 gauss is
larger than the measured H_{c2}(*theta*) for
*theta* less than about 70°, this value of
H_{c} implies that superconductivity in T_{c}
= 1.5 K C_{4}KHg samples is type I in character for
most applied field orientations.

When H_{c} is greater than H_{c2},
H_{c} will be measured as the upper critical field.
Since H_{c} is a thermodynamic quantity, it is
expected to be angle-independent. If type I superconductivity
is present for some range of angles, one therefore expects a
modified angular dependence of the form

H_{c2,eff}(*theta*) = H_{c2} where
H_{c2}(*theta*) > H_{c} (type II
region);

and H_{c2,eff}(*theta*) = H_{c} where
H_{c2}(*theta*) < H_{c} (type I
region). (3)

This type of angular dependence has previously been
observed[37,56] in C_{8}K and in TaN.
Using Eq. 1 for H_{c2}(*theta*), the modified
form given by Eq. 3 has been fit to the angular dependence
data for the T_{c} = 1.5 K C_{4}KHg samples.
In the fits to Eq.3, H_{c} was taken as a free
parameter in addition to H_{c2}(0°) and
*epsilon*. The resulting fit is shown in Fig. 4.
Consultation of standard tables on statistics[6] shows that the addition of
the third free parameter H_{c} is justified by the
factor of 1.5 reduction in the residual index. The hypothesis
of type I superconductivity in the higher-T_{c} pink
C_{4}KHg specimens therefore appears to be justified
not only by the specific heat measurements of Alexander and
coworkers,[4] but also
by the improvement in the H_{c2}(*theta*) fits
provided by the use of Eq. 3.