Direct observations of dislocations in thermotropic smectics using freeze-fracture replication

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Direct observations of dislocations in thermotropic

smectics using freeze-fracture replication

Joseph A. N. Zasadzinski

To cite this version:

747

Direct observations of dislocations

in

_thermotropic

smectics

using

freeze-fracture

_replication

Joseph

A. N. Zasadzinski

Department of Chemical and Nuclear

_{Engineering, University}

of California, Santa Barbara CA

93106, U.S.A.

(Reçu

le 18 _{septembre 1989, accepté} sous

_{forme définitive}

le 12 décembre

₁₉₈₉₎

Résumé. 2014 Les méthodes modernes de _trempe suivie de

_réplication

_{par fracture} sont _{idéales pour}

la visualisation directe de la structure tridimensionnelle et des défauts dans les _phases cristal

liquide

smectique

et

_{cholestérique.}

La _{résolution y} est

_proche

des distances moléculaires. On a

trempé

le nonanoate de cholestérol à

_partir

du

_voisinage

de la transition

_{smectique-cholestérique}

pour mettre en évidence des couches

_smectiques

étendues et bien définies, distordues par des

dislocations coins et vis _ayant une densité très élevée. Les dislocations vis ont des vecteurs de

Burgers de couche

_{unique organisée}

comme des

_parois

twistées. Il est tentant _{de penser que le}

twist

_présent

dans la

_phase

_{cholestérique} induit un twist résiduel dans la _{phase smectique}

_qui

est

incompatible

avec la mise en forme de couches. On a observé aussi des boucles de dislocations

vis-coin _{organisées également} en

_parois

twistées. On a

_suggéré

_que ces _parois soient

_responsables

de la

_disparition

de l’ordre

_smectique

amenant la

_{phase cholestérique.}

Abstract. 2014 Modern

_{rapid-freezing}

methods followed _by freeze-fracture

_replication

_techniques

are

_ideally

suited to allow the direct visualization of the three-dimensional structure and defects of

thermotropic

smectic and cholesteric

_liquid

_crystalline

_phases

with resolution

_approaching

molecular dimensions. Cholesterol nonanoate was

_quench

frozen from near the smectic-cholesteric transition to reveal extensive, well defined smectic _layers distorted

_by

a

_{high density}

of screw and _edge dislocations. The screw dislocations

_typically

had Burgers vectors of a _{single layer}

and

_commonly

_organized as twist walls. This is

_suggestive

that the twist _present in the cholesteric

phase

induces a residual twist in the smectic _phase

_incompatible

with

_{perfect layering. Screw-edge}

dislocation

_loops

were also _commonly observed, also

_organized

into twist walls. These twist walls have been _suggested as

_{being responsible}

for the breakdown of smectic

_ordering

_leading to the cholesteric

_phase.

J. _Phys. France 51

₍₁₉₉₀₎

747-756 15 AVRIL _1990,

Classification

Physics Abstracts

61.30E - 61.30J - 61.16D

Introduction.

Smectic and cholesteric

_phases

and the

_phase

transition from smectic to cholesteric

_(or

nematic)

has been

_extensively

studied

_by

a

_variety

of

experimental techniques,

most

_notably

by optical

microscopy

and

_X-ray

and

_{light scattering}

_techniques

_{[1, 2]. Unfortunately,}

none of

these

_techniques

_{reveal the structure,}

_number,

or interactions of defects such as dislocations

that

_might

be

_important

to the

_stability

of these

_phases,

or _may even mediate the

_phase

transitions. Freeze-fracture electron

_microscopy,

however,

is

_ideally

suited for

_{investigations}

of the defect structure in

_liquid

_crystals

_[3],

and has been used

_extensively

in

_{investigations}

of

lyotropic

nematic,

smectic and lamellar

_phases

_[3-12].

Freeze-fracture electron

_microscopy

can be

_usefully

_applied

to

_{thermotropic liquid}

_crystals,

_although

there are far fewer

examples

in the literature

_[13-16].

This _{may be} due to the more

_complex

fracture behavior of

thermotropic

materials as

_compared

to the

_{multiphase dispersions normally investigated}

with

freeze-fracture

_{techniques [16].}

However we show here that for smectic

_phases,

the fracture

appears to follow the

_layers

as is observed in

_lyotropic

smectics and the fracture

_patterns

relate

_simply

to the molecular order in these

_phases.

The defect structure is visible to near

molecular dimensions and

_edge

and screw dislocations are

_easily

seen. The freeze-fracture

technique

may be an

_important

tool for studies of unusual smectic

_phases

_including

the

recently hypothesized

smectic-A*

_{phase [17, 18].}

Materials and methods.

The most

_important

_{step in any freeze-fracture}

_{investigation}

of

_high

_{vapor pressure materials} is the initial

_{rapid freezing}

or

_{quench step}

[3].

Cholesterol nonanoate

_{(CN) (recrystallized}

from

_solvent)

was

_{provided by}

J.

_Goodby.

A small

_droplet

_(0.1-0.5

_u1)

of CN heated to the

isotropic phase

was sandwiched between two _copper

_planchettes

_(Balzers

_{BUO-12-056T ;}

Hudson,

NH)

to form a 10-50 itm thick

layer.

Previously,

the copper

planchettes

had been

etched for 1 s in concentrated nitric acid to remove _any contamination and

_roughen

the

planchette

surfaces. The _apparatus used for

_freezing

was a modified version of a Balzers

Cryojet

QFD

020 jet

freeze device

_[21].

The

_sample

sandwiches were mounted on a Teflon

support arm and

_placed

in a _temperature controlled oven located

_vertically

over the

_jets

of the

freezing

device.

_Sample

_temperature was controlled

_prior

to

_freezing

to better than 0.1 °C.

The

_samples

were

_equilibrated

at the

_{appropriate temperature}

for a few minutes before a

solenoid-actuated mechanism

_opened

a Teflon door at the bottom of the oven and

_dropped

the Teflon arm and

_samples

between the

_opposed

_jets

of the Balzers

_cryojet.

A

_photodiode

switch initiated the

_{high velocity}

flow of

_liquid

_{propane, cooled}

_by

_{liquid nitrogen}

to -

180 °C,

which

_impinged

on the copper sandwich from both

_sides

to

_provide

a minimum average

cooling

rate of 15 000 °C/s. The initial

_cooling

rate, which is most

_important

for

_preserving

phases

of limited _{temperature range, is}

_likely

to be somewhat slower for the first few

_degrees

of

_cooling

_[22].

_{The frozen copper sandwiches} were stored under

_{liquid nitrogen}

until transferred into a

_{spring-loaded}

_{« mousetrap »} carrier. The loaded

_sample

carrier was

mounted onto the

_{liquid nitrogen-cooled coldfinger}

in a Balzers 400 freeze-etch device and

the vacuum chamber was evacuated to better than

10-7

torr. The _temperature of the

_sample

carrier and

_coldfinger

were

adjusted

to - 170 °C and the

_spring

mechanism was

_externally

actuated, thereby fracturing the

_samples.

The fracture surfaces were

_{immediately replicated}

by evaporating

1.5 nm of a

_platinum

carbon mixture from an electrode at a 45°

_angle

to the fracture

surface,

followed

_by

a 15 nm thick film of carbon at normal incidence to increase the mechanical

_stability

of the

_replica.

The

_samples

and

_replicas

were removed from the vacuum

chamber and the

_samples

_{and copper}

_planchettes

were dissolved in chromic

acid,

leaving

the

platinum-carbon

replicas

behind

_[23].

The

_replicas

were washed in chloroethanol-water

mixtures, rinsed in

_{doubly-distilled}

water, and collected on formvar-coated 50 mesh

_gold

electron

_{microscope grids}

_(Pelco,

_Tustin,

_California).

The

_replicas

were examined in a JEOL 100 CX

_scanning

transmission electron

_microscope

in the conventional transmission mode

using

80 kV electrons.

_Images

were recorded on Kodak electron

_{image plates.}

Shadows

749

Results and discussion.

Cholesterol nonanoate forms a cholesteric

_phase

at 91 °C and a smectic-A

_phase

at 73 °C on

cooling [19].

The

_untwisting

of the helical

_pitch

of the cholesteric

_phase

near the smectic-A

transition is well known

_[19].

The cholesteric twist is

_incompatible

with the

_layered

textures of the smectic-A

_{phase ;}

hence the twist and bend elastic constants

_diverge

_along

with the cholesteric

_pitch

at the transition

_{[19, 20].}

The smectic

_phase

does not

_supercool

or _appear to

grow

by

nucleation of smectic domains as the transition is second order. Hence, the transition is difficult to _{capture using}

_{rapid freezing}

followed

_by

freeze-fracture

_techniques

and we could not observe the

_untwisting

of the helical

_pitch.

However, we were able to freeze in the

cholesteric

_phase

from 77 °C

_{(Fig. 1). Samples}

frozen from 75 °C showed intermediate textures

_{(Fig. 2)}

and were difficult to

_interpret.

_Samples

frozen from

_{approximately}

1 °C below the transition _temperature

_{(Figs. 3-5)}

showed well defined smectic

_layering

_punctuated

by

numerous screw and

_edge

dislocation defects.

To

_interpret

freeze-fracture

_images

of

_{thermotropic liquid crystals}

it is _necessary to relate

the

fracture surface to the molecular structure. Berreman et al.

_{[16] proposed}

that in a

spatially varying, anisotropic,

brittle

material,

the

_specific

surface _energy was

_directly

related

to the number of molecules

_separated

_by

the

_advancing

crack. This is

_equivalent

to

_saying

that the

_binding

_energy per molecule is

independent

of the molecular orientation. Each molecule is assumed to _occupy an

_ellipsoidal

volume that reflects the local

anisotropy

of the fluid. In

nematic or cholesteric

_{liquid crystals,}

the molecules

spontaneously align

along

a

_preferred

direction. The ratio of the

_major

to minor axes of the

_ellipsoid

is related to the molecular

alignment

of the material. A crack normal to the

_major

axis of the

_ellipsoid

_separates more

molecules that a crack

_parallel

to

_{it ;}

hence the fracture would

_prefer

to

_propagate

_along

the

major

axis of the

_{ellipsoids, providing}

that the new area created was not too

_large.

The

Fig. 1. - Freeze-fracture

product

of surface area and this

_specific

surface _energy was calculated

_by

Berreman for cholesteric and blue

_{phase liquid crystals using anisotropy}

_parameters measured

indepen-dently by optical

diffraction or

predicted

by theory

(cf.

Berreman et al.

_[16])

and the

computed

fracture _patterns matched those observed in cholesteric and blue

_{phases quite}

closely.

For smectic

_phases,

however,

the

_{layering imposes}

a

_density

modulation that appears

to influence the crack

_propagation

more than the local orientation. The fracture surface

propagates

primarily

between

_layers,

the

_region

of lowest

_density,

as is observed for

_lyotropic

smectics

_{[3, 4].}

Figure

1 is a freeze-fracture electron

microscope image

of CN frozen from 77°. The

images

showed textures

_typical

of other cholesteric

_phases

we have

_imaged

_previously

_[13,

15,

16].

The

_{regular undulating}

fracture surface is related to the

_{regular twisting}

of the molecules

along

the cholesteric axis. These undulations can extend for several microns before the cholesteric axis or the fracture surface

_changes

directions. Calculations

_by

Berreman et al.

[16]

suggest that this

_pattern

is the result of fracture

_roughly

normal to the cholesteric

_axis,

and that the undulation

_period

of about 130-140 nm is

_{roughly equivalent}

to half of the cholesteric

_pitch.

This is in

_good

_agreement

with the results of Pindak et al.

_[19]

who

measured an

_{optical pitch}

of 360 nm

_{(the optical pitch}

is related to the actual

_pitch

_by

poptical

=

nP actual’ in

which _n is fhe _average refractive

index,

here about

1.5-1.6).

It _was

somewhat

_surprising

that we were able to visualize the cholesteric

_phase

as the transition to

the smectic

_phase

is continuous and does not

_supercool.

_Apparently,

the finite _{time necessary} for diffusion and _{rearrangement} in these viscous materials is sufficient to allow us to lock in

high

temperature

phases

even if the lower _{temperature phase} does not form

_by

a first order

transition,

provided

that the

_cooling

rate is

_rapid

_enough.

Samples

frozen from 75 °C revealed a mixture of smectic-like and cholesteric-like fracture

patterns.

Figure

2 shows one such

_region

in CN in which the undulations characteristic of the

Fig.

2. -

Freeze-fracture

_image

of CN

_quenched

from 75°C. The fracture surface is much less

_regular

than

_figure

1 _{and appears} to be a mixture of smectic and cholesteric textures. The

_{irregular spacing}

of the undulations

_may

be related to fluctuations associated with the _phase transition, or with _temperature

751

cholesteric

_phase

at the bottom of the

_image

_give

_way to a smoother, almost

_layer-like

structure at the _top of the

_image.

The undulations in the cholesteric are not as uniform as

_they

are in the

samples

frozen from

_higher

_temperatures

(see

Fig.

1).

There are often _{gaps between}

undulations and the cholesteric

_pitch

is not well defined. It is not clear if this

_region

_represents the textures that result from fluctuations

_during

the

_unwinding

of the cholesteric

_pitch

as it

transforms to the smectic

_phase,

of if there. was a small _temperature

_gradient

across the

sample

during

freezing resulting

in a mixture of smectic and cholesteric textures. The

cholesteric

_pitch

more than doubles when CN is cooled

slowly

from 75° to 74°

[19],

and

eventually diverges

as the _temperature is lowered to 73 °C.

Previously,

we have shown

₍₂₂₎

that a

_rough

estimate of the maximum

_temperature

gradient

across the

_sample

thickness is

Fig.

3. - Freeze-fracture

image of CN

_quenched

from 72.5 °C. The fracture surface is that of well-defined

_layers

_{punctuated by} numerous dislocation defects. A twist wall of screw dislocations is located

along the asterisks between A’s. A small arrow marks where one of these screw dislocations

_pierces

the

fracture surface. _Screw-edge dislocation loops are _present at B. In the _magnified inset of B, the twist wall _{abruptly changes} the _layer

_organization

from

_being

_roughly

_parallel

to the fracture _plane to almost

in which Bi is the Biot modulus of the

_{sample (hd/k, h}

is the heat transfer

coefficient,

d is the

_sample

half-thickness,

and k is the

_sample

thermal

_{conductivity),}

and

_{Ts - Tc}

is the

difference between

_sample

_{and cryogen} temperatures. For a

_typical

_sample,

Bi = 0.01-0.02,

hence the maximum

_gradient

across the

_sample

thickness is about 1-2 ’C.

Laterally,

we _expect

the

_gradients

to be of the same

_magnitude

as the entire surface of the

_sample

is contacted

simultaneously

by

a stream of

_liquid

_propane cooled

_by

_{liquid nitrogen.}

This uniform

exposure to the cryogen,

coupled

with the

_{high conductivity}

of _{the copper support} should

minimize any lateral _temperature

_gradients.

In the

_samples

frozen from

77 °C,

we saw no

variation in the

_pitch

of the cholesteric helix across the

_samples,

which is consistent with this

approximation.

Figures

3-5 are

_typical

of

_samples

frozen from 72.5 °C.

Figure

3 shows a low

_{magnification}

view of flat

_layers

_punctuated

_by

numerous

edge

and screw dislocation networks. Between

defects, the

_layers

_appear

_flat,

which is not

_{completely expected}

as the smectic-A

_phase

is

known to be better described

_by

a

density

modulation than

by

well defined

layers [1, 2].

This

may be the result of the limited vertical resolution of the freeze-fracture

image

or

_by

some

enhancement of

_{layer ordering}

due to the

_freezing

_{process. The} low _{temperatures may}

_quench

any fluctuations in the

layer

thickness,

resulting

in better defined

layers.

Smooth variations in

vertical

_topography

1 nm in

height

are difficult to resolve

_by

metal

_shadowing,

hence small,

Fig.

4. - Screw dislocation _steps in CN frozen from 72.5 °C

_converging

with

_neighboring

steps to form

753

Fig. 5. - A combined

screw-edge loop

in CN frozen from 72.5 °C. This _arrangement is shown

schematically

in cross section in

_figure

5b. The

_{screw-edge loop}

in _figure 5

_begins

at B+ where the screw

dislocation line emerges from the fracture plane. The small _plateau of

_{additional layers}

can be _thought of as an _edge dislocation line with _Burgers vector of _{several layers.} The

_loop

ends at B-, where a second screw dislocation line of

_opposite

_sign to B+

_disappears

into the fracture surface.

_Figure

5a shows

schematically a

pure screw dislocation line such as the one at A in the freeze-fracture

_image.

Most of the

screw dislocations we observed had _Burgers vectors of a

_single

_layer, about 2.5 nm in thickness.

long wavelength

variations in the

_layer

thickness would not be visible in the freeze-fracture

images

[3].

However, in

_comparison

to similar

_{magnification images}

of

_lyotropic

smectic

phases prepared

in identical _ways

_{[3, 4],}

the

_replicas

of CN in the smectic

_phase

_appear

_grainy

and

_{perhaps rough}

on the

_length

scale of the

_platinum

_crystallites

that make _{up the}

_replica

film

_(see

_{Figs. 4,}

_5).

This same

_roughness

does not _{appear in the}

_images

of the cholesteric

phase

(Fig. 1),

and

_might

be

_interpreted

as a fine scale variations in the

_layer

thickness.

Abrupt steps

between

_{single layers,}

such as the screw dislocations _present at the arrows in

figures

3-5,

are

_easily

visible. The smallest _step

height

(measured

_by

the thickness of the white

shadow between the arrows in

_Fig.

₅₎

is

_{approximately}

2.5 nm, or

_roughly

one molecular

As has been

_predicted

for smectic-A

_{phases [2],}

and observed for

_{single-phase lyotropic}

smectics

_{[4, 5],}

a

high density

of screw dislocations are found. A screw dislocation in a smectic

phase

resembles a

_spiral

_staircase,

with the dislocation line

_being

the axis of the staircase

_(see

Fig.

5a and

_Fig.

5.20 of Ref.

_[2]).

The dislocation can be

_thought

of as

_being

formed

_by

_cutting

a stack of

_layers

_{perpendicular}

to the

_layers,

then

_reattaching

each cut

_edge

to the

_layer

above

(or below)

it. In a freeze fracture

image,

a screw dislocation _appears as either a

_light

or dark

line which terminates

_abruptly

into an unbroken

_layer

at the

_point

where the screw dislocation

line

_pierces

the fracture surface

_(arrows

in

_Figs.

3,

4).

The dark and

_light

lines are caused

_by

the

_shadowing

effect of the metal

_deposition

on the _step

_produced

where the dislocation

pierces

the fracture surface. Because of the choice of shadow

_angle

relative to the

_sample

plane,

the

_length

of the shadow at these _steps is

_roughly

_equal

to the

_height

of the _step

_(this

assumes that the local fracture

_plane

is

_{roughly parallel}

to the

_sample

_plane).

_Hence, the

Burgers

vector of the dislocation is

_{roughly equivalent}

to the thickness of the shadow on the

images.

Most of the screw dislocations appear to have

_Burgers

vectors of one or at most a few

layers,

and the

_sign

of the

_Burgers

vector can be

_assigned

_by

the shadow _pattern at the _step,

dark and

_light

shadows

_{corresponding}

to dislocations of

_{opposite signs.}

Screw dislocations of

small

_Burgers

vector, b, are

_predicted

as their energy goes as

_{[2] :}

in which B is the elastic

_{compressibility}

modulus and _rc is a core radius.

As the screw dislocation _{steps propagate along} the fracture

surface,

they

often _converge with

_neighboring

_steps to form « rivers _», with a well-defined coalescence

_angle

as shown in

figure

4

_([24],

also

_Figs.

5.19 and 5.20 in Ref.

_[2]).

As the rivers

_coalesce,

the _apparent

thickness of the main « river » _grows

by

the thickness of the

tributary

« river » added. This

increase

_(or

decrease for dislocations of

_{opposite sign)}

in the river thickness

_corresponds

to an

equivalent

increase in the _step

_height,

because of the metal

_shadowing.

The increases in step

height

between the

_layers

result in a tilt between the

_layers

on

_opposite

sides of the step. The

average tilt between the

layers

is

_{given by}

6 =

b/d,

in which b in the

Burgers

vector of the

screw dislocation

_(about

25

À) ,

and d is the average distance between unit screw dislocations.

These twist boundaries between

_layers

_might

be a _way of

_{incorporating}

the residual twist of

the cholesteric

_phase,

while still

_maintaining

the

_layered

structure of the smectic

_phase

_{[2, 17,}

18].

In CN at 72.5

°C,

we often found

_large

numbers of screw dislocations of similar

_sign

aligned

in

_long

rows

_(Fig.

_3,

_asterisks).

Screw dislocations

_aligned

in this _way can form twist

walls,

allowing

the

_layering

direction to

_change

direction over

_relatively

short distances. Such

twist walls are visible

_along

the asterisks between A’s in

_figure

3. These twist walls _{may be} result of the

_proximity

of the cholesteric

_{phase ;}

the twist wall is one _way of

_making

a

_degree

of

_twisting

_compatible

with the

_layered

structure of the smectic

_phase.

Kléman _suggests that

twist walls _may be associated with the transition from smectic to cholesteric

_{(or nematic)}

phases.

Renn and

_Lubensky

_[17]

have

_postulated

that

_regular

twist walls of screw dislocations

may be

responsible

for the structure of the

_newly

discovered smectic-A*

_{phase [18],}

which

appears to be a

_{hybrid phase structurally}

between a normal smectic-A and a normal

cholesteric

_phase.

The

_topology

of dislocations is such that dislocations cannot end or

_begin

within a

_given

sample

of

material ;

dislocation lines must close on themselves to form

_loops

or end at a free

surface or another dislocation

[2].

Screw dislocations line in smectics are

_{always perpendicular}

to the smectic

_{layers ;}

_edge

dislocation lines are

_always

_parallel

to the

_layers.

A combined

screw-edge loop

can be made

_by

_connecting

two screw dislocations of

_{opposite signs}

with an

755

figure

5b. The

_screwedge

_loop

in

_figure

5

_begins

at B+ where the screw dislocation line

emerges from the fracture

plane.

The small

_plateau

of

_{additional layers}

can be

_thought

of as an

_edge

dislocation line with

_Burgers

vector of

_{several layers.}

The

_loop

ends at B-, where a

second screw dislocation line of

_opposite

_sign

to B+

_disappears

into the fracture surface. Such

screw-edge loops

have also been observed in

_lyotropic

smectics and have a similar appearance

[25].

The

_Burgers

vector of

_{screw-edge loops}

is

_complicated

_by

the fact that the _{energy of}

screw dislocations as shown above is minimized for defects with

Burgers

vectors of a

single

layer,

while

_edge

dislocations

_prefer

to have

_multiple

_{layer Burgers}

vectors. _{The energy} of an

isolated

_edge

dislocation is

_given

_{by :}

b is the

_Burgers

vector of the dislocation and

_{T c is}

a core _energy

independent

of b. À is a

_length,

on the order of the

_bilayer

thickness,

over which the

compressibility

(B )

and bend elastic moduli

_{( K )}

are

_{comparable [1, 2].}

This shows that

E(2b)2E(b);

hence a

_{single edge}

dislocation of

_{large Burgers}

vector is of lower _{energy than} two

_{(or more)}

edge

dislocations of the same total

_Burgers

vector. This _promotes a small number of

_edge

dislocations of

_large

_Burgers

vector. _Hence, the

_Burgers

vector of the

_loop

_{may be} some

energetic compromise

between these two

_preferences,

or the screw dislocation _{may be}

dissociated into _many smaller screw dislocations that merge

together.

Several dark _steps

arrear to _converge near B- in

_figure

5.

Conclusions.

Freeze-fracture electron

_microscopy

have made it

_possible

to see the three-dimensional

structure and

_organization

in a wide _range of _systems that have

previously

thwarted

analysis.

Here we _present some of the first

images

of the three-dimensional

organization

of defects in

thermotropic

smectic

_phases

near the cholesteric-smectic transition. Screw dislocations are numerous, with most

_{being organized}

either in twist walls or in

_screw-edge

dislocation

_loops.

The screw dislocations _appear to have

_Burgers

vectors of a

_{single layer,}

as

_expected

from

energy arguments. It _{also appears} to be

_possible

to

_quench

in

_high

_temperature

_phases

even if

the lower _temperature

_phase

is entered

_by

a second order

transition,

if the

_quench

is initiated

far

_enough

from the transition _temperature. Freeze-fracture electron

_microscopy

should be an

ideal tool to

_investigate

other

_thermotropic

and

_{lyotropic liquid crystalline phases, especially}

the

_recently

discovered smectic-A*

_phase

which is believed to be stabilized

_by

screw

dislocations.

Acknowledgements.

1 would like to thank J.

_Goodby,

M. J.

Sammon,

S.

Meiboom,

D. W. Berreman, and R. Pindak for generous use of their time and

_talents,

their comments and

_continuing

discussions

on the role and

_{possibilities}

of freeze-fracture. The

experimental

work described here was

done at AT & T Bell Labs. The referees were also

_helpful

in

_clarifying

the

_{interpretation}

of

the images.

Financial _support was

_{provided by}

the donors of the Petroleum Research Fund,

the Exxon Education Foundation, the DuPont

_Company,

and

_by

a National Science

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