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Figures
Figure 1: The dashed lines show the centers of four bilayers
stacked in a perfectly crystalline array. The dot-dash lines show a snap-shot
of paracrystalline fluctuations in which the second and third bilayers
are displaced with a resulting local D-spacing 
.
The solid lines show a snap-shot of the fluctuations of the Caillé theory
that also involve undulations.
Figure2: The structure factor S(q) times q for paracrystalline theory
(PT) (dashed lines) and modified Caillé theory (MCT) (solid lines) versus
for 
= 4.0 Å, 
= 4270 Å, and 
= 3600 Å.
Figure3: The solid lines show typical S(q) for modified Caillé theory
(MCT) for the first three peaks, (a) h=1, (b) h=2, and (c) h=3, for D =
60 Å and 
.
The peak heights are normalized to unity and the peak maxima are shifted
to zero for comparison of peak shapes for different orders h. Values of
the parameters are 
= 0.050 (
=4.0
Å), 
= 4270
Å, and 
=
3600 Å. The dashed lines show the best fit to the solid curves using PT
which yields 
= 1.2 Å, 
= 8440 Å, and 
= 1560 Å. The dotted lines show the zero levels for each order.
Figure 4: High resolution X-ray configurations M---Si monochromator
crystal, S1---sample slits, SH---automatic shutter, IC---Ion chamber detector,
S2---scatter slits, A---Si analyzer crystal, FP---flight path (filled with
N2 gas) S3---detector slits, NaI---scintillator detector. (a)
Non-dispersive configuration. (b) Dispersive configuration.
Figure 5: The solid lines show modified Caillé theory (MCT) fit
to DPPC data with 0% PVP and D=64.5 Å. The peak heights are normalized
to unity and the peak maxima are shifted to zero for comparison of peak
shapes for different orders h. The dashed lines show the best fit using
the paracrystalline theory (PT). Parameter values are listed in Table I.
The dash-dot line shows the resolution function. The dotted lines show
the background subtracted zero levels for each order. For clarity counting
statistics error bars are shown only for three data points at the ends
and middle of each peak.
Figure 6: 0% PVP sample data, D=67.2 Å. Solid lines: MCT fits; dashed
lines: PT fits; dash-dot lines: resolution function; dotted lines: background
subtracted zero levels for each order. Parameter values are listed in Table
I. Error bars are shown for three data points for each peak.
Figure 7: 25% PVP sample data, D=58.2 Å. Solid lines: MCT fits;
dashed lines: PT fits; dash-dot lines: resolution function; dotted lines:
background subtracted zero levels for each order. Parameter values are
listed in Table I. Error bars are shown for three data points for each
peak.
Figure 8: Same sample as in Fig. 5. Solid lines: MCT fits; dashed
lines: ordinary Caillé theory fits.