For our final estimate of 
from diffraction studies, we first average our two x-ray results, 
Å
from Fourier analysis and 
Å
from hybrid modeling, with the two results, 
Å
and 
Å
,
obtained from neutron diffraction results in the preceding paragraph. This
gives our final diffraction estimate, 
Å
.
Once the area 
is determined, a number of other quantities follow from simple relations
described by Nagle and Wiener (1988). One of the most illuminating quantities
is the number of water molecules 
per lipid molecule between the bilayers in regular multilamellar vesicles;
this is easily calculated from
where 
Å
and 
Å
at 
in the
phase and
Å
and 
Å
at 
in the
gel phase. In addition to representing the bilayer thickness as 
,
it is also frequently represented as 
which is the volume fraction of the D-spacing that would be occupied by
the lipid bilayer if the interface with water were a plane. 
is given by
and the corresponding water spacing is then 
.
Of course, the bilayer/water interface is not so simple, so a slightly
more complex model (Nagle and Wiener, 1988) assumes that the headgroup
(that includes the acyl chain carbonyls) has a length 
over which it has a uniform area 
.
This model then allows for penetration of 
waters in the volume 
between the headgroups. From neutron diffraction (Buldt et al., 1979),
Å appears
to be a generously large estimate. Then, a corresponding pure water distance
is defined
where the total hydrocarbon thickness is defined by 
and is calculated using Eq. 6. A summary of
the values of these derived quantities as well as measured quantities is
given in Table II for the 
phase for two values of D near the extremes of our data as well as earlier
results (Sun et al., 1994) for the fully hydrated gel phase.
Table ii: Structural Quantities for 
and 
Phase
