Self-diffusion in naphthalene single crystals

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Self-diffusion in naphthalene single crystals

A. Bendani, L. Bonpunt

To cite this version:

A. Bendani, L. Bonpunt. Self-diffusion in naphthalene single crystals. Journal de Physique I, EDP

Sciences, 1993, 3 (4), pp.1059-1070. �10.1051/jp1:1993105�. �jpa-00246770�

Classification

Physics

Abstracts

61.708 66.30H

Self-dilTusion in naphthalene single crystals

A. Bendani and L.

Bonpunt

Laboratoire de

Cristallographie

et de

Physique

Cristalline (*), Universit6 Bordeaux 1, 351 Cours de la Liberation, 33405 Talence, France

(Received 6 October1992,

accepted

in

final form

4 December 1992)

Abstract. Molecular mobility in

organic

molecular

crystals

_was studied

by

_means of tracer diffusion

experiments

_: self-diffusion of

naphthalene

into

naphthalene single crystals

_was

measured. Wree self-diffusion tensors are determined from measurements in different

crystallogra- phic

directions, at three temperatures (338, 343 and 348 K). The

principal

_axes and the

anisotropy

of self-diffusion _are deduced. The

experimental

activation

energies

are determined and

compared

with results from the literature.

1. Introduction.

Solid state matter diffusion has been

widely

studied in many different

materials, metals,

semi-

conductors, halides, simple

oxides... Most of these materials

crystallize

in

high symmetry

structures, most often in the cubic space groups. ^{Then diffusion is}

isotropic. Organic crystals usually belong

to the lower

symmetry

systems, ^I-e-

orthorhombic,

monoclinic and triclinic.

Then diffusion is

anisotropic

and must be measured

by

a second rank tensor.

Experimental

methods issued from

crystal physics

must be

applied

in order _to determine the diffusion tensor.

The present paper

reports

an

example

of such _a

study.

We

present

a combination of classical methods of diffusion studies and tracer

counting technique,

which takes into account the

crystal

orientation and the

cutting

of

single crystal plates.

The

organic crystal

chosen is

naphthalene.

It is very

representative

of

organic

^solids : the molecular

packing,

the space group

P211a,

and the

only

_presence of _van der Waals interactions _are characteristic of _a great ^number of this

type

^of

crystals.

Moreover, it is

easily

obtained as

large single crystals

of

good

crystalline quality

and excellent

purity.

There is _no

plastic phase

known between _room

temperature

^{and the}

melting

temperature at 353 K. Some

previous

studies _on the _same

compound [1-3]

_were relative _to self-diffusion in the

unique crystallographic

direction

c*, preventing

the

anisotropy

of self-diffusion to be determined in this

crystal.

The

study

of

diffusion

anisotropy

in the

crystal

^of a very similar

compound,

anthracene, _was

published

in 1965-66

[4, 5]. Only

two

crystallographic

directions _were considered. A weak

anisotropy

_was

(*) URA 144 CNRS.

detected _; but in these monoclinic

crystals,

the

complete

determination of the diffusion tensor needs four

independent

directions to be studied. A _more recent

study [6, 7]

on heterodiffusion at infinite dilution of

2-naphthol

in

naphthalene single crystal

^{allowed the} determination of the

heterodiffusion _tensor at 343 K. A theoretical model

giving

a

partial interpretation

of the results _was

proposed.

In this paper, the

experimental

method and the results of _a self-diffusion

study

in

naphthalene,

^carried out at three different

temperatures (338,

343 and 348

K)

_are

presented.

The

microscopic interpretation

of these

results,

in terms of _a vacancy model is

presented

in

anpther

paper which is devoted _to the determination of the molecular

jump frequencies

from the

knowledge

of diffusion _tensor.

2.

Experimental.

2,I PREPARATION OF DIFFUSION SAMPLES.

Naphthalene

was

purified by

zone

refining.

Single crystals

were grown

following Bridgman's

method. The detection and measurement of

impurity

content were obtained

by

_gas

phase chromatography coupled

with _mass

spectrometry.

The total

impurity

content of the final material is less than 5 ppm. The

crystalline quality

was

controlled

by

the

etch-pit technique [8, 9]

_{: no} dislocation association in

subgrain

boundaries

was detected in _our

samples,

and the dislocation

density

was about

10~ m~~ _[9].

_{In order to}

obtain the four

independent

coefficients of the diffusion _tensor in monoclinic

crystals,

^{it is}

necessary ^to

perform experiments

in four directions

(which

_are not part ^{of the} same

plane).

Our tracer diffusion

experiments

_were made _on

parallelepipedic plates

of about

6 _x 6 _x 3 mm3. The

largest

face _was

polished

in order _to be

highly planar,

which is _a

required

condition when

using

the classical treatment of _a

planar infinitely

thin

deposit.

The diffusion

was studied in the direction

perpendicular

to the

polished

face. The well-known

cleavage along

the

(001) planes

of

naphthalene together

with _a

simple optical

method

[10],

allows _{one to}

identify

^the a and b

crystallographic

_axes of the monoclinic unit

cell,

and also that of c*

simultaneously perpendicular

to a and b. The orientation of the unit cell is determined

by

the

X-ray

diffraction

(Laiie) technique.

In order _to

study

the

magnitude

of the diffusion _tensor

along

these three _axes, the

simple

orientation process described above is sufficient.

But,

on the other hand, ^if one wants to achieve the

complete

determination of the diffusion _tensor in _a monoclinic structure, the diffusion coefficient needs _to be measured

along

another

crystallographic

direction _: this xe direction was chosen such that it is contained in the _ac

plane,

and it makes _an

angle

of 135°

with _a.

A

sample

was cut with _a

plane

surface

perpendicular

to each direction. In order _to obtain

parallelepipedic samples,

the

cutting

of the

Bridgman crystals

was carried out

by cleaving

with

a razor blade and

sawing

with _a wire-saw. Good flatness of the diffusion

plane

_was then

obtained with _a microtome. The elimination of most of the dislocations

crqated during growth

and

cutting,

and caused

by

mechanical stress, was achieved

by submitting

the

sample

to a

thermal treatment in _a stainless steel matrix _{at a} temperature

just

below the

melting temperature (353 K).

This

annealing

consisted in

setting

the

crystal

for 8

days

at 348 K _or 12

days

at 343

K,

and

cooling

it

slowly

_over 3

days

to room

temperature (see

Tab.

Ii.

To prevent

sublimation,

the

plates

_are surrounded

by naphthalene powder (which

minimizes the empty volume around the

crystal

in the

matrix).

After

annealing etching

studies indicated that the dislocation _{content was} about

10~

_m~ ~ on

the face

perpendicular

to the direction studied.

2.2 TRACER DEPOSIT AND DIFFUSION PROFILES. The marked molecule used _was

naphthalene

14C-1(4, 5, 8) (specific activity

56

mcjmmole),

in

pentane.

^The

deposit

method used

[I II

Table I.

Annealing

temperatures

(T~)

and

diffusion

temperatures

(T~).

TR

(K

343 348

Annealing

time 12 9

in

days

T~ (K)

^{338 343 348}

Diffusion time 30 12 9

in

days

consisted in

deposing (three

_or

four) drops

of the radioactive solution _{on a}

glass slide, previously

cut

according

_to the

sample

face dimensions. The sublimation of the radioactive

naphthalene,

which is made of very thin

grains,

took

place

after the very

quick evaporation

of pentane ^{and induced} us to

proceed

in the

following

_{way :} first

siliconizing

the slide _to get a

localized

drop,

then

cooling

the solution before

deposit

with

dry

ice.

The overall

deposit operation

must not exceed 30 _s.

Afterwards,

the

glass

slide _was tumed back to the

crystal

face and these _two

pieces,

surrounded

by naphthalene powder (to

_prevent

sublimation of the

sample),

_were inserted into the matrix.

Thermal _{treatment was} carried _out from 200 to over 800 hours

(see

Tab.

Ii.

^{The time}

necessary to reach the diffusion

temperature

^and to cool the

sample

to room

temperature,

^after the diffusion treatment, was short

(4 hi compared

with the diffusion time.

Following

the diffusion

period,

^the

edges

_were removed _to avoid contributions from surface diffusion to the

activity

of each slice. The

crystal

_was cut with _a microtome. Four micrometer slices _were removed each time and dissolved in ethanol. This solution _was divided into _two parts : the first one, to which _a

liquid

scintillator _was

added,

was used _{to measure} the

radioactivity

of the slice

by counting

it in _a

liquid

scintillation spectrometer. ^{The second} part ^{of the ethanol solution} was

analysed by

UV

absorption,

in order to eliminate _errors due _{to an}

imperfect

collection of the

whole slice. On the

spectra,

a

peak corresponding

to

naphthalene absorption

_at 328nm

allowed _us to detect _a decrease in _mass and

eventually

to correct the _raw

radioactivity corresponding

_{to a}

given

slice.

Every

slice

activity

_was

proportional

to the concentration of

diffused

naphthalene

molecules.

The diffusion coefficient

(D)

was determined from the

slope

of the Ln

(A)

_{vs. x curve,} where _x is the

penetration

and A the

radioactivity

of each slice.

Figure

I shows _a

typical

self-

diffusion

profile

in

naphthalene

at 338 K. The contribution of dislocations _to the observed

mobility

was subtracted

by

Leclaire and Rabinovitch's method

[12, 13],

and the true bulk

diffusion coefficient

(D)

found.

Very

often this correction _{was not} necessary as the

contribution of the dislocations could _not be observed when their

density

is less than 0.9 _x

10~

_m~ ^~ The

uncertainty

about the bulk diffusion coefficient is deduced from the

slope

of the linear

regression.

It is obvious that this method

only

allows for the

alignment

of the

points

_on which the linear

regression

is made. In

fact,

this is _{more a}

quality

factor of the measurement than its real

uncertainty.

The bulk diffusion coefficient characteristic of the direction

Dx;

studied _was the result of several

experiments

carried out in the _same direction and _on different

samples.

For this purpose, the proper method consisted in

working

out a

single

_curve

representing

the different functions Ln

(A~~,)= f(x~/t~).

_A~~, is the

activity along

the

sample,

corrected for the

contribution of the dislocations. The factor

tj~

is _a normalization factor which takes into

Loi

v.a.

~

a ^. corrected

. a not corrected

a

.

D "

D o

a

o soo

o

o

30

60 90 _{1 ~m}

Fig,

I.- Self-diffusion

profile

in

naphthalene single crystal (t=720h, T~=338K, crystal

84, direction al.

account the different diffusion times of the different

experiments.

The _same remark _as for the

D about the

given uncertainty

_can be made.

The

simplest

choice of the reference frame for _our

study

^is

(0,

_{xi, x~,}

x~)

=

(0,

_a,

b,

c*

).

We have made

experiments

in these three directions. The fourth _one is xe as defined above.

3.

Experimental

results.

3.I BULK SELF-DIFFUSION COEFFICIENTS. Tables

2, 3,

4 show the bulk self-diffusion

coefficients obtained _at

338,

343 and

348K, corresponding

to the directions xi, x~,

x~ and xe. The values of the coefficients obtained at 348 K and 343 K show, for _a

given direction,

_a

fairly

marked

dispersion

since the scatter between coefficients reach I _to 2 _x 10~ ^~~

m~

_{s~ ~.}

Impurities

in

quite

low concentrations

[9, III (the highest

does not exceed 30

ppm),

could not

explain

this

dispersion.

Due _to this

fact,

_we have realized two to five

experiments (usually four)

ⁱⁿ order to obtain _a suitable

precision

for each coefficient

Dx;.

^{At 0.99}

T/(T~(K)

is the

melting temperature

^{of the}

material),

the molecular

mobility

seems to be

higher

in the xi and xe directions

(3.4

and 3.8 _x 10~ ^~~

m~

_s~

respectively).

The

same is true for the x~ and xe directions at 0.97 T~ ^{and 0.96} _T~, with 2.6 _x 10~ ^~~

m~

_{s~ and}

1.7 _x 10~ ^~~

m~

_{s~ ~,}

as average

respective

self-diffusion coefficients. We _can notice _{a more}

marked

_diffusion

anisotropy

at 338 K than at 343 K _or 348 K.

3.2 VARIATION _OF THE BULK SELF-DIFFUSION COEFFICIENT WITH TEMPERATURE. At the

microscopic level,

we know that diffusion is most

probably

achieved

by

successive molecular

jumps

^from an

occupied

site to a vacant site. If _a

single

_type of

jump

_occurs, then D varies with T

according

to an Arrhenius law.

Conversely,

in _a low symmetry

crystal

such _as

naphthalene

^{where several} types ^of

jumps

are

possible,

the variation of D with T does _not

necessarily

follow this law.

But, given

the accuracy of the diffusion coefficients and the limited

temperature

range

[338 K,

348

K],

we can assume that the temperature

dependence

is

represented by

_an Arrhenius law

(see Fig. 2).

With this

assumption

_we obtain _:

~ 74 kJ mol~

2 ~- ^l

~~l

~ ~'~ _~ ~~ ~~~

RT ^"'

~~ 46 kJ mol~

~2

_~- i

~X2

_~ ~.~ _~ ~~ ~~~

~T

D~~

=

14 _x

ios

exp

~~ " '~~°~~

m~

_s~

RT

/~~~

= 2_8 _x IO ^~ eXp

~~ ~ ~~~

m~

_S~

RT

The standard deviations relative to these values _{are :} 16 kJ mol~ for xi, II kJ mol~ ^I for x~, 20 kJ mol~ for x~ and 6 kJ mol~ for xe. In the x~

direction,

the

experimental points

do _not lie _{on a}

straight

line.

Nevertheless,

we think that it would be

interesting

to mention the _mean

activation energy which is 144 kJ mol~

Supposing

_a

single

_average

jump mechanism,

the

value of the

pre-exponential

factor

Do,

is

probably

in the range

[10~

^~° to I

m~

_s~

_Thus,

_the

1.4

x10~m~s~l

_{value of}

Do

related _to this direction

probably

comes from _an inexact

extrapolation

_: within this range of temperatures, a

major

curvature of Arrhenius'

graph

^exists.

The uncertainties of these values _are rather

large.

These values could be

improved by enlarging

the range of temperatures. ^{We think that it is}

interesting

to

give

these values

(though they

do not have any immediate

physical meaning),

for two reasons : first

they

allow _{us to use an}

approximate expression allowing

_us to

predict by interpolation

_or limited

extrapolation,

values

corresponding

to D _at temperatures ^{different from those of the}

study second,

the

comparison

with other data

published

in the literature is

possible.

3.3 BULK SELF-DIFFUSION TENSORS IN NAPHTHALENE. The self-diffusion tensor is

easily

calculated from the self-diffusion coefficients measured in four different

crystallographic

directions. It expresses the

anisotropy

of the

phenomenon

in _a mathematical way.

Ii Self-di#fizsion

tensor at 348 K _: The

dita

_relative

to 348

K, presented

in table II,

give

^for the diffusion tensor referred to the reference _axes

(0,

_{xi, x~, x~}

(equivalent

to _a

crystallographic

referential

(0,

_a,

b, c*11

_:

3.3 ° °.45

~ _{~~-17 ~2}

~- ⁱ

~

~~~~

~

~45 ~~ ^~4 ~°'

_~'

~'

~ ^*

The

principal

_axes

Xi, _X~

and

X~

^{of this} tensor have been determined.

X~

^is

parallel

to the symmetry ^{axis b.}

Xi

and

X~

are contained in the _ac

plane,

and the

angle

_q7

=

(a, Xi )

^is found to be

equal

to 58°. With

respect

to the set of

principal

axes, the _tensor is written _as :

3.8±0.8 0 0

i~ ~ i

D

(348

K

)

= 0 2.9 _± 0.2 0 ^~ ~~ _{~ ~}

0 0 2.9 _± 0.7

(°, '~1, '~2, '~3~

2) Self-di#fizsion

_{tensor at} 343 K _: from the data

presented

in table

III,

_we obtain _:

1.9

^{0 -0.45}

i~ ~ i

D

(343 K)

₌ 0 2.6 0 ^~ ~°

f~

^~

0.45 0 2.4

~°'~' ~'

_~

~'

a

'8

D,

ios T

338 T~KI

b

^"

~~i'

~ '

2.85

m

~*

8

'

8

fl

Fig.

2. Variations of the bulk self-diffusion (o) and heterodiffusion coefficients (al with temperature in the _a, b and c* directions. The continuous line represents the self-diffusion coefficient (S), the dotted

line the hererodiffusion coefficient (H).

Table II. Bulk

self-diffusion coejficients

at 338 K in

naphthalene.

Crystal

Diffusion D

Dx;

direction time in h in 10-17 m2 s-I in 10-17 m2 s-1

571 1.6 _± 0.I

xi 571 1.3 _± 0. I 1.5 _± 0.1

813 1.7 _± 0.1

720 1.3 _± 0.2

780 1.7 _± 0, I

x~ 730 1.8 _± 0. I 1.7 _± 0.1

730 1.4 _± 0.2

780 1.7 ± 0.1

814 0.7 _± 0.1

813 0.8 _± 0. I

x~ 720 0.5 _± 0,1 0.7 _± 0.1

720 1.0 _± 0.1

720 0.8 _± 0.1

800 1.6 _± 0. I

xe 723 1.8 _± 0. I 1.7 _± 0.1

723 1.9 ± 0.1

800 1.9 + 0.1

Table III. Bulk

self-diffusion coefficients

at 343 K in

naphthalene.

Crystal

Diffusion D

Dx;

direction time in h in 10-17 m2 s-I in 10-17 m2 s-1

484 1.3 ± 0. I

xi 329 1.6 ± 0.4 1.9 _± 0.2

329 2.4 _± 0.2

328 2.2 _± 0. I

x~ 220 2.2 _± 0.2 2.6 ± 0.1

220 2.8 _± 0.1

328 2.0 ± 0.4

x3 305 2.8 _± 0.1 2.4 _± 0.2

300 2.9 _± 0.2

xe 300 2.4 _± 0.2 2.6 _± 0.1

312 2.8 _± 0.1

360 2.8 ± 0.1

With _q7

= 60°

2.7 ± 1.6 0 0

l~~

~ ,

D

(343 K)

₌ 0 2.6 ± 0.1 0 ^~ ~° _{~ ~}

0 0 1.6 _± 0.7

(°, '~1, X2, X3)

3) Self-dijfizsion

_tensor at 338 K _: from the data

presented

in table

IV,

_we obtain _:

1.5 0 0.60

li~

~ i

D

(338

K

)

₌ ⁰ 1.7 0

(

^'°

~

f~

^~

0.60 0 0.7 '

~'

'

~

~'

Table IV. Bulk

set-diffusion coefficients

at 348 K in

naphthalene.

Crystal

Diffusion D

Dx;

direction time in h in 10-17 m2 s-I in 10-17 m2 s-1

233 4.3 _± 0.2

xi 329 3.9 _± 0,1 3.3 _± 0.3

306 2.6 _± 0,1

234 2.5 _± 0.7

234 2.0±0.I

x~ 216 3.0±0.2 2.9±0.2

216 3.2±0.1

216 2.9±0.1

336 3.5 _± 0.I

x~ 259 3.0 _± 0.1 3.4 _± 0.2

330 3.8 _± 0.6

216 4.0 _± 0.4

xe 216 4.6 _± 0.1 3.8 _± 0.2

234 3.7 _± 0.2

234 3.6 _± 0.2

With _q7

= 28°

1.8 _± 1.5 0 0

~~ ~

D

(338

K

= 0 2.6 _± 0.1 0 ^~ ~° _{~ ~}

0 0 0.4 _± 1.5

(0, Xi, X2, X3)

Figure

3

represents

^{the flux}

ellipsoid,

in order _to show the

preceeding

tensors. It

corresponds

to the

spatial

distribution of the flux of _matter due _{to an}

isotropic unitary

concentration

gradient.

The symmetry ^{of the diffusion}

phenomenon

is

clearly

indicated

by

these

ellipsoids,

the

binary

axis b of the structure

being

also _one of the symmetry axes of the

ellipsoids.

The other _two

symmetry

axes of the

ellipsoid, Xi

and X~ are contained in the _ac

plane. They correspond

to the directions of the

highest

and lowest mobilities of

naphthalene

molecules in the

naphthalene crystal.

The fact that their directions _are not

neighbouring

_or confused with

significant

directions of the

crystalline

structure

description,

_can be

explained by

the fact that

3

b

a

a

~

a

Fig.

3. Flux

ellipsoids

characteristic of the bulk sew-diffusion at 3 temperatures.

the observed effect is due _{to a}

composition

of several directions of molecular

jumps,

which _are

necessarily

linked to the

crystallographic

directions. These _{axes are more}

easily

observed _on sections of these flux

ellipsoids. Figure

4 shows the _ac

plane

sections of these

ellipsoids,

which coincide with the extremities of the matter flux _vectors when _we

impose

_an

isotropic unitary

concentration

gradient

of

spherical

_symmetry. The

principal (or symmetrical)

directions of the resultant flux _are

clearly

seen. The variation of these directions with temperature appears very small. The

tendency

to

isotropy

when T increases is

emphasized.

4.

Comparison

and discussion.

4,I SELF-DIFFUSION _IN NAPHTHALENE SINGLE CRYSTAL. The

complete

measured self-

diffusion tensors in

naphthalene single crystals presented

ⁱⁿ this paper are, to our

knowledge,

the first

published

ⁱⁿ the literature. So

they

cannot be

compared

with other measurements of this

phenomenon. Nevertheless,

the self-diffusion coefficient in the _c * direction _was measured

by

Sherwood and White

[I]

in the temperature range 330-348 K. The variation with

temperature ^of their self-diffusion coefficient

obeys

_an Arrhenius'law described

by

:

D

=

2.5 _x lo ^~~ exp

(-

^~~~

_~(f°~ ^m~

s~

In their

study, according

to this

equation,

at 343 K, D is

equal

to 14

x10~~~m~s~~.

Hampton

and Sherwood

[3]

have carried _out the measurement of this coefficient _on

crystals

of similar

quality,

in the c* direction.

They

obtained _a value of lo _x

10~l~ m~ s~~

_{within the}

same

temperature

range. Their values _are from 6 _to lo times

higher

than _ours. The influence of

,'X5(338K)

/ /

, /

', _/

,

/

, a

,

/ /

,

/ ,

/

',J,(338K)

/ / /

,

Xi

(343K(~'~'~~~~~~

- corresponds to a flux of

lxlT17

_molenfles

rn2s'I Fig.

4. Sections of the flux

ellipsoids by

the ac

plane.

impurities

_on diffusion in this type ^of

crystals

_was

emphasized by

Sherwood and White.

They

showed that

impurities considerably

increased the diffusion coefficients measured. Further-

more, these two teams have

probably

not well taken into account the influence of the extended

defects _on the determination of the characteristic bulk self-diffusion coefficients

[14, 15].

Therefore,

_we think that _our values _are

certainly

closer to the true intrinsic diffusion coefficients.

4.2 SELF-DIFFUSION AND HETERODIFFUSION OF 2-NAPHTHOL IN NAPHTHALENE. The Vari-

ation of

D~ (D~

is the heterodiffusion coefficient at infinite dilution of

2-naphthol

in

naphthalene)

with temperature ^{in the studied} range

[7]

_can be

represented by

_an Arrhenius law.

In table

V,

the

expressions

of the self-diffusion and heterodiffusion coefficients measured in Table V. Arrhenius

expressions

in bulk

heterodijfizsion

and

set-diffusion

in

naphthalene.

Crystal DH

_in

In~

_S

~~

_'~

^~~

_~

d;rection 17] _1~

l

~ ~ ~~- ³ 92 kJ mol~ ^I

~ ~ ~- ⁶ 74 kJ mol~

~ ~ ~~~

RT ^~ ~~~

RT

~ 97 kJ mol~ mo

2.3 _x 10~ ^'° eXP

~~

$T

b I.I _x IO eXP

RT

c*

4.0 _x 10~ ^~ _exp ^~~

$)°~

IA _x

10~

_exp ^{~~ " ~°~}

RT

three directions xi, x~ and x~ are

given experimental points

are shown in

figure

2. The

influence of the limited

temperature

range

probably explains

the

dispersion

of the

Do

^{and AH~~' for} the two

phenomena.

The _same order of

magnitude

is

clearly

found for the two molecules in the _same lattice. In the directions _{x~ and x~, it seems} that the activation

enthalpies

are different. In the xi direction, the

experimental dispersion yields

the

equality

of the activation

enthalpies.

The

analysis

of these data carried _out with _a

single procedure

will allow

us to

distinguish

the

jump frequencies

of the _two molecules. But the tensor of heterodiffusion is not yet ^known at the three temperatures.

In

figure 5,

the sections

by

_ac and ah

planes

of the flux

ellipsoids

of self and heterodiffusion at 343 K _are

given.

A great

similarity

_appears. The

angle

between the

principal

axes is 21°.

C*

X31H343),

', /

', ,'

' /

' ,/ ,X31343K)

j , ,/

t

',

' II,

a

' /

/ ,

/ '

1'

"

/~

' _"

,' _'(i(H3431

- oo«esponds _{to a} flux of W~17 _molecules

m 2s'l

(I)

, ^,

/ '

,'

^"

1 '

/ ~H343

j j ^a

t ,

' /

I'

/

- oo«e~pontlsto aflux of

WT17

_molecules

m

2f' (it)

Fig.

5. Sections of the self-diffusion and heterodiffusion flux

ellipsoids by

the _ac and ab

planes

at

343 K _{: ac} plane (ii, ab

plane

(iii.

This difference between the _tensor orientation indicates _a different contribution of the different molecular

jumps

in the two

phenomena.

But the _common

crystalline medium,

and the

slight

difference between the molecular forms of

naphthol

and

naphthalene (see Fig. 6),

_are the essential fact which is

clearly

_seen in the tensor

similarity.

A further

interpretation

of these results will be

given

in the paper ^{relative to the}

microscopic

aspect ^{of these} mobilities.

~°~ f

,'

/

,~

/

(I)

(11)

Fig.

6. Chemical formulae for

2-naphthol

(ii and naphthalene molecules (iii.

5. Conclusion.

The most

important

result is the

description

of the obtention of _a self-diffusion _tensor in _a monoclinic

crystal.

It _seems to _us that _our self-diffusion coefficients _are measured in

crystals

of

a better chemical and

crystalline quality

than those in Sherwood's

experiments.

The extension of the temperature range is necessary ⁱⁿ order _to obtain _{a more}

precise frequency

factor and the activation

enthalpy. Nevertheless,

the

anisotropy

of self-diffusion in

naphthalene single crystals

is measured. It is _{not so}

high,

and has _a

tendency

to decrease when

temperature

^increases. The

similitary

observed between the tensors measured _at 343 K of self and heterodiffusion is _an

interesting

result. It demonstrates the

important

_part

played by

the

crystalline

structure of the host in the observed

anisotropies

of the mobilities of the two molecules.

References

[Ii SHERWOOD J. N., WHITE D. J., Philos. Mag. is (1967) 745.

[2] CORKE N. T., SHERWOOD J. N., J. Mat. Sci. 6 (1971) 68.

[3] HAMPTON E. M., SHERWOOD J. N., J. Chem. Sac. Faraday Trans. 71(1975) 1392.

[4] REUCROFT P. J., KEVORKIAN H. K., LABES M. M., J. Chem.

Phys.

44 (1966) 4416.

[5] LEE C. N., REucRofT P. J., KEVORKIAN H. K., LABES M. M., J. Chem. Phys. 42 (1965) 1406.

[6] BONPUNT L., DAUTANT A., LOUMAID A. and FAURE F., J.

Phys.

Chem. Solids 50

(1989)

777-783.

[7] FAURE F., DAUTANT A., BENDANI A., BONPUNT L., J.

Phys.

Chem. Solids 51(1990) 1005-1010.

[8] LOUMAID A., Thbse Bordeaux 1 (1987).

[9] RAIMI K., Thbse Bordeaux 1 (1990).

[10]

KARL N.,

Crystal

Growth

Properties

and

Applications (Springer,

Berlin, 1980).

II ii BENDANI A., Thhe Bordeaux (1991).

[12]

LECLAIRE A. D., RABINOVrrCH A., J.

Phys.

C14 (1981) 3863.

[13]

LECLAIRE A. D., RABINOVrrCII A., J.

Phys.

C 16 (1982) 3455.

j14]

BONPUNT L., DAUTANT A., Theoretical and

Experimental

Studies of

Crystalline

Defects in

Organic

Molecular Solids, Defect Control in Semi-conductors, Ed. K. Sumino, Elsevier Science

Publishers B. V.

(North-Holland,

1990),

pp.1659-1665.

jls] CHADWICK A. V., Point Defects and Diffusion in Molecular Solids in Mass

Transport

in Solids, Ed.

F. Beni~re and Catlow, NATO ASI, B, Physics 97

(1983)

285.

regus

au

de I et II

Weak

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A.

BARONE,

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LARKIN,

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928 _pages, 320Dfl.

Comptes

rendus de la deuxi~me Conference Intemationale _sur la

radiographie

_par neutrons tenue h Paris

~juin

1986). Contient _{un panorama} des contributions des diff£rents pays sun le

sujet,

les r£acteurs et

autres instruments utilis£s, des

expos£s

_sur les

applications

dans diff£rents domaines, _{e. g.} corrosion, les

m£thodes

d'analyse

des r6sultats, _e.g.

tomographie.

The

Physics

and

Chemistry

of

Aqueous

Ionic Solutions M.-C.

BELLISSENT-FUNEL,

G. W.

NEILSON,

EdS.

Sdrie : NATO ASI

Series,

Series C Mathematical and

Physical

Sciences, vol. 205

(D. Reidel, 1987)

ISBN _:

90-277-2534-9,

475 pages, 210 Dfl.

Comptes

rendus d'un

symposium

tenu h

Carg~se

_en

juin-juillet

1986 _sur la th£orie des solutions

ioniques,

les _venes

ioniques,

les

poly£lectrolytes,

les simulations

num£riques

et les

exp£riences

off£rentes.

Rythmes

et Chaos dans les

systkmes hiochimiques

et cellulaires

A. GOLDBETER

Collection

Biologie Thdorique,

vol. 5

(Masson, 1990)

ISBN _:

2-225-82109-7,

304 pages, 330F.

Monographie sp6cialis6e

entre

biologie

et

math6matiques appliqu£es.

Neuf

chapitres

; introduction _; comportement

p6riodique simple birythmicit6

dans _un mod~le

biochirnique

h deux variables; du comportement

p£riodique simple

_aux oscillations

complexes

_;

signaux

d'AMP

cyclique

chez les amibes

Dictostelium discodeum, oscillations

complexes,

mod~le

d'ontogen~se

des rythrnes

biologiques;

s6crdtions

p£riodiques

d'horrnones conclusions _et

perspectives

;

bibliographie

et index.