X- ray diffraction of krypton and xenon mixtures adsorbed on graphite

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X- ray diffraction of krypton and xenon mixtures adsorbed on graphite

T. Ceva, M. Goldmann, C. Marti

To cite this version:

T. Ceva, M. Goldmann, C. Marti. X- ray diffraction of krypton and xenon mixtures adsorbed on graphite. Journal de Physique, 1986, 47 (9), pp.1527-1532. �10.1051/jphys:019860047090152700�.

�jpa-00210351�

X- ray diffraction of krypton ^{and xenon} mixtures adsorbed ^on graphite

T. Ceva, ^{M. Goldmann} (*) and C. Marti

Groupe ^de Physique des Solides de l’Ecole Normale Supérieure,

Université Paris 7, 2, place Jussieu, 75251 Paris Cedex, ^France

(Reçu le 8 novembre 1985, révisé le 24 avril 1986, accepté le 29 avril 1986)

Résumé.

En étudiant, par diffraction des rayons X, ^les mélanges xenon-krypton ^{absorbés sur} graphite ^{à 45} K,

nous avons observé deux solides incommensurables ainsi qu’un solide commensurable. La coexistence de chaque incommensurable avec le commensurable montre que la transition ^est dans chaque ^{cas du} premier ordre. L’obser- vation de spectres ^de diffraction à bas taux de couverture (environ 0,1) ^montre que les petits grains sont recouverts en premier ^et qu’ils favorisent un solide incommensurable. La concentration limite de la structure incommensurable

« type xénon» semble contradictoire avec celle observée sur le mélange argon-xénon. L’explication pourrait ^être

une structure moins ordonnée dans ce dernier cas.

Abstract

Mixtures of xenon and krypton ^{adsorbed on} graphite ^{at 45 K are studied} by X ray diffraction. Two kinds of incommensurate and one kind of commensurate solids were observed The coexistence of each incommen- surate with the commensurate structure indicates first order C - I transitions. Diffraction spectra ^with low coverage

(about 0.1) show that small platelets ^are first covered and that they ^{favour an} incommensurate solid The limit of the incommensurate xenon-like structure seems inconsistent with results on an argon-xenon mixture. Explanation

could be a less ordered structure for the latter mixture.

Classification Physics ^Abstracts

68.20

68.45

82.65

1. Introduction.

Since adsorption isotherms for rare gases ^on graphite

have shown a 2D phase transition [1, 2], many theore- tical and experimental studies have been devoted to these systems. Experimentally, ^{the most} prominent

progress ^was due to the direct observation of the 2D solid using ^{electron, neutron and,} since 1978 [3] X-ray

diffraction and now atom scattering [4]. ^Commen-

surate and incommensurate structures have been

clearly observed and transitions between them, ^studied especially ^for krypton [5, 6], ^xenon [7, 8], ^hexane [9] ^and

ethane [10] ^on graphite, ^{lead to define} concepts ^like static distortion ^waves and walls [11]. ^{A second rota-}

tional transition in the incommensurate 2D solid has even been demonstrated [12]. Contrary ^{to the 3D} crystal, theoretical predictions also indicate that the 2D solid presents ^a limited order and Kosterlitz and Thouless proposed ^an attractive model of the 2D fusion [13] that stimulated _many experiments [14-22]

and computer simulations [23-32]; the existence and location of tricritical points ^{has been searched} [33].

(*) ^{Present address :} Institut Laue Langevin, ¹⁵⁶ X,

38042 Grenoble Cedex, ^France

Helium layers ^are in themselves a question [34]. ^Pure layers have been studied, ^but little work has been done ^on 2D mixtures [35-37] ^where chemical compo- sition adds a parameter ^{which is} easy ^to control. The mixture of xenon and krypton ^on graphite ^{is a} good

candidate for diffraction studies, ^as co-adsorption

isotherms have been measured for this system [35].

Adsorption isotherms of krypton ^{on xenon} pre- covered graphite ^have nearly ^been interpreted ^{as if} krypton occupies ^{the area left} by ^xenon [35]. ^Thermo- dynamics indicates that the two pure ^2D solids should not coexist for all concentrations; ranges for single

solid solutions should exist, ^at least for small concen-

trations of xenon in krypton ^{or of} krypton ^{in xenon.}

Our first goal was ^to establish the limit of solubility

of these two rare gases in the 2D solid ^state. Another observation was the shift of the commensurate- incommensurate transition (C-1 kink) ^{towards a} higher pressure when xenon is preadsorbed. ^{We also}

wanted to precise ^{the nature} of the solid phases ⁱⁿ

each domain.

2. Experimental set-up.

The sample ^{is a stack of} Papyex ^discs (HWMH ⁼

19 degrees, ^coherence length ^{= 350 to} 400 A) ^with

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019860047090152700

1528

the _average optical ^{axes C} perpendicular ^{to the wave-}

vector. To get ^a plane face in front of the beam, ^the

stack was cut perpendicular ^{to the} discs with a massi- cot. A draw-back of this method is that we inevitably

fold the graphite ^basal planes ^back along ^the face, perpendicular ^{to the} wave-vector (see Appendix).

The graphite ^{discs were heated at} 1450 OC in a vacuum better than 10-4 torr for 12 hours, ^before being stacked in the sample ^cell. Each time ^we started a new series of experiments they ^{were heated to} approximately 100 OC under the same vacuum over-

night.

The sample ^{cell is} made of copper, with mylar

windows.

We use the K-alpha ^{emission from a copper X ray} tube (A ^{= 1.5418} A), ^{run at 45 kV with} a 26 mA current selected by ^a graphite monochromator and a powder goniometer (omega, theta) controlled by ^a computer system. Diffraction spectra are recorded between theta ⁼ 20 and 30 degrees ^{with a} step ^{of 0.05} degrees.

Accumulation on each point ^{lasts 400 seconds. In this} angular ^{domain, we observe the} (002) graphite peak

diffraction and the (01) peak ^{of the 2D} structures. The substrate spectrum ^is subtracted after normalization

on the integrated ^{intensity of the} (002) peak. ^{This last} peak ^is slightly ^modified by ^the monolayer ^contribu- tion, ^{and a} strong perturbation around 26.60 degrees persists ^after subtraction of the graphite spectrum.

The cryostat ^{is a} closed helium refrigerator. ^A digital temperature controller using ^a platinum ^resis-

tance maintains the temperature within 0.02 K. Two

thermocouples ^{fixed above} and below the sample ^cell

control the vertical temperature gradient.

3. Experimental procedure.

To obtain a composite ^{solid we start from a 2D} liquid layer mostly ^{of xenon} (as ^{xenon is adsorbed at a} higher temperature ^than krypton, ^most of this last component is in the 3D _gas state). ^The thermodynamic equilibrium

is easily ^reached by exchange between the liquid monolayer and the 3D gas. We then reduce the temperature slowly enough ^{to maintain} equilibrium,

while the pressure of the gas is decreased, ^{in order to} solidify ^{the 2D} liquid When the 2D solid is achieved,

we freeze it to 45 K.

The detailed procedure ^{is : first, we} introduce the

xenon and the krypton ^{in the} sample, keeping ^{it at}

45 K. We close the cell and heat it to 115 K for 30 minutes (to ^{ensure the} equilibrium ^{and the mixture}

of the two gases). We cool it to 80 K at the rate of 0.5 K/min ^and then, directly (about ¹ K/min) ^{to 45 K.}

After the diffraction spectrum ^is recorded, krypton ^can

be added, ^{and so} on, until the layer ^is completed

Two tests show if we succeed in forming ^{a mono-} layer :

-

we control the intensity ^{of the} (002) peak during

the procedure, ^we consider its increase as the contri- bution of the monolayer ^{to the} peak, ensuring ^{that the} cooling ^{rates are slow} enough.

-

the peaks ^resulting from the diffraction treatment

are clearly ^{of the Warren} type.

We think that this procedure ^{is as efficient in pro-} ducing ^an equilibrium ^{state as} annealing ^{to 130 K}

described in [37].

4. Experimental ^results.

We explored the Xe-Kr mixtures for total _coverage between 0.1 and 2 (1 ^{= one atom of the} layer ^for

6 surface carbons or 3 graphite hexagones) ^{and for}

many chemical compositions. ^We distinguish ^three types ^of peaks, corresponding ^to three different 2D solids.

-

The first type ^of peak ^has its maximum at

Q ⁼ 1.7 A-’ (theta

^34.05 degrees); ^the position ^is

locked when the coverage ^or the composition ^{of the} layer ^{is varied over} its entire _range of existence. We take this invariance as the « signature ^{of a com-}

mensurate structure C (j3 ^x 3 - ^{30 degrees).}

-

The peak with its maximum at the lowest angle

indicates a xenon-like solid (X) which is dilated

compared ^{with the} commensurate structure : the spectrum ^of pure ^xenon submonolayer ^{has a maxi-}

mum at 23.05 degrees (Q ^{= 1.63} A-1).

-

The peak with its maximum at a greater angle corresponds ^{to a} krypton-like ^solid (I) ^{which is} compressed relatively ^{to the} commensurate structure : the most incommensurate pure krypton layer peaks ^at

25.25 degrees (Q ^{= 1.78} A-1).

As those last two structures can be compressed ^or dilated, ^the corresponding peaks ^{can shift.}

Even if _coverage and concentration are the correct

thermodynamic parameters ^{for this} experiment, ^the experimental procedure ^{contrains to} vary them simul-

taneously.

-

For a pure ^xenon layer ^{with a} coverage (Ox.)

of 1.1, ^we observe, ^{a maximum} corresponding ^{to a}

commensurate structure, ⁱⁿ accordance with LEED studies [8], ^{but with a limited coherence} length (about

110 A). ^{When we add} krypton, ^{the structure remains}

commensurate but an increase of the coherence length

is observed : 195 A for oKr ^{= 0.07, 245 A for} 6Kr ⁼ 0.15, 340 A at higher krypton ^{coverage. We do not} interpret ^a gradual increase of the intensity ^{at about}

25.50 degrees ^{as a second} peak, ^{but as a second} layer

contribution (the total coverage is greater ^than 1).

In figure ^{1, we} present the evolution of the spectrum with the addition of krypton ^{in a 0.86 xenon initial}

coverage. For pure ^{xenon, a} peak ^{at 23.10} degrees corresponding ^{to the} incommensurate ^xenon solid with a coherence length ^{of 245 A is observed If we}

add a very small quantity ^of krypton, ^{a shift of the} peak

to higher angles ^{is observed,} indicating ^{a xenon-like}

structure (X). ^{For a 0.07} krypton coverage, this peak (shifted ^{to 23.40} degrees ^{and with a coherence} length

decreased to 195 A) clearly coexist with a commen- surate peak (C). ^When krypton coverage reaches 0.09,

the two peaks ^{have about the same} intensities and the

Fig. ^1.

Diffraction spectrum ^{at 45 K with a} precoverage of xenon (0xe

0.86). Displacement ^{of the X} peak ^while

the krypton coverage increases and coexistence of X with C

are observed

X one shifts to 23.50 degrees ^{with a coherence} length

of 160 A only. ^For OK,, ⁼ 0:11, ^{the X} peak appears just

as a low angle tail of the C peak. ^From OK,. ^{= 0.21 to} higher coverage, only ^{this last structure is} observed,

with an increase of the coherence length up ^to 340 A.

No krypton-like ^{structure was} observed for this

xenon coverage : the mixture is always commensurate in this domain.

As the peak of the xenon-like structure moves with coverage, the composition of this solid also varies, ^so only ^two phases ^are present : ^{for such a} high coverage,

no 2D gas coexist with the 2D solids. The C peak

appears for OKr ^{= 0.045, the} higher krypton ^concen-

tration in the single ^{solid X is then about 5} %. ^Little krypton ^is enough ^to provoke the transition to the commensurate phase, but, ^{as we are} very ^near the

complete xenon-like monolayer (the ^total coverage is

more than 0.9 and the area of the _pure xenon solid is about 4 % ^{more than the} commensurate one), ^{a small}

coverage increase lead to a high 2D pressure. From the small intensity ^{of the X} peak ^for OKr

^0.11,

we estimate that the xenon-like solid would disappear

for OK,, - ^{0.15. Then,} the concentration for the commensurate phase in the coexistence region ^would

be 14 % krypton ^{and 86} % ^xenon (there may be less

krypton ^as part ^{of it} may be in the second monolayer).

We compare the concentration of krypton ^{in the} single ^{solid X with a surface} averaging model without vacancies :

where d is the X (average) parameter ^lattice (measured),

ci the concentration of the ⁱ atoms, dxe ^the pure ^xenon 2D solid parameter (measured) ^or effective diameter

(4.43 A), dKr ^the pure krypton ^{2D solid} parameter (which ^must lay between the commensurate and the most compressed ^solid observed).

The best agreement ^{with the} experimental ^values (from 0 % ^{to 5} % ^of krypton) ^{is obtained for} dK, ⁼

4.07 A.

For °Xe ⁼ 0.6, ^the spectrum ^{of the} pure ^xenon

monolayer ^{exhibits a} peak ^{at 23.05} degrees ^{with a}

coherence length ^{of 340 A. This} peak ^{has a maximum}

of 25 photons/s (ph/s). ^{When we add a} coverage of 0.05 krypton, ^we already observe the coexistence of the commensurate peak with the xenon-like peak; ^this peak ^{decreases to 15} ph/s and shifts to 23.25 degrees

while the C peak reaches 10 ph/s. ^This large intensity

of the C peak insures that a great number ^{of xenon}

atoms participate ^{in this} structure; likewise, ^{the shift}

of the X peak (from ^the pure ^xenon one) proves this solid to be a mixture. For oKr ⁼ 0.15, the maximum of the X peak ^{decreases to 5} ph/s (but ^{with no shift,} indicating ^that 2D gas (V) ^{must coexist} with the solid

phases ^{at such} coverage), ^{while the} intensity ^{of the C} peak ^increases slightly. This indicates that from

Oy, ^{= 0.2} (corresponding ^{to a} concentration of 25 % krypton), the C solid would be the only ^solid phase.

Indeed we observe, ^for OK, ^{= 0.21,} only ^{a C} peak ^with

a very small tail to low angles. The total coverage is then 0.81. As we know the composition ^{of the com-}

mensurate solid near the limit between X +C + V and C + V, ^{we can then} estimate, ^from the evolution of the C peak intensity, ^a concentration of krypton ^{in X}

between 5 % ^{and 7} %.

No other features is observed when krypton ^is

increased to a total _coverage of 2.2 monolayers, except the deformation of the commensurate peak ^{due to the}

second layer.

For an initial _coverage of 6xe ^{= 0.25, the} pure

xenon layer ^{has a} maximum of 12 ph/s ^{and a coherence} length ^{of 245} A only. ^{If we add 0.06} monolayer ^of krypton, ^the spectrum ^{shows a C} peak reaching

5 ph/s while the X maximum decreases to half its value and shifts to 23.40 degrees.

For oKr ⁼ 0.13, ^{the C} peak grows ^to 15 ph/s, ^while

the X solid _appears ^{as a} hump ^{at low} angle ^{in the}

commensurate peak. Subtraction of a « clean » com- mensurate peak ^{shows an X} peak ^with very low

intensity (3 ph/s ^{at a} maximum of 23.450). ^{As a} result,

the single ^solid phase ^{C would start at about} OK, ⁼ 0.15, indicating ^{more than 33} % krypton, quite ^different

from the 25 % ^we found when 0xe ^{= 0.6. Studies on}

each series of spectra (in subtracting commensurate

peaks ^{with variable} intensity) ^{do not} permit ^{to recon-}

ciliate those values. In the same way, from the intensity

of the C peak ^for OK,, ^{= 0.06,} the concentration of

krypton ^{in X must be about 7} %, ^rather larger ^{than the}

value observed for Oxr ^{= 0.6.}

For lJKr ^{= 0.17, the C} peak appears clearly ^alone

with a 245 A coherence length. ^The commensurate

phase remains stable with coherence length ^{of 340} A,

while the krypton coverage is increased to 0.85 (note

that then, ^{the total} coverage is about 1).

1530

For higher krypton concentration, ^the growth ^{of a} peak corresponding ^{to an} incommensurate krypton-

like structure I (maximum ^{at the} larger ^of angle

25 degrees) ^{is observed} (Fig 2). ^The misfit of the I-

phase coexisting ^{with the} C-phase ^{is then} nearly ⁴ %, higher ^{than was found} by Stephens et ^al. [37], ^{i.e. about}

2 %; the difference _may be related to the difference of temperature. Though ^{this structure is} clearly observed,

it is difficult to determine at what _coverage this peak

first appears : the ^I peak increases under the C peak’s

Warren tail, ^{and the} subtraction of a pure C spectrum would be relatively unaccurate, ^as normalization ^on the graphite peak ^has important effects in this angular

range.

At _very low _coverage (Ox,, ⁼ 0. 1), ^{we observe a} pure

xenon peak, contrary ^to Stephens et ^{al. at 84.5 K} [37],

but it is shifted from 23.10 degrees ^{to 23.20} degrees

and the coherence length of this 2D-solid is limited to 80 A. When we add a 0.1 layer ^of krypton, ^{the com-}

mensurate peak ^is largely predominant ^{but a} wing ^at

lower angles (until ²³ degrees) indicate the existence of the X structure, and the limit of krypton ^{in C would}

be more than 50 %.

From BKr ^{= 0.18 to} 6Kr ^{= 0.9,} only ^{the C} peak ^is

observed (coherence length growth ^{from 175 A for} Ol{r ^{= 0.18 to 340 A until} OKr ⁼ 0.55). ^When OK,, ^{= 1,}

the peak reached 25 degrees (coherence length ^is

limited to 195 A), and then confirms the existence of the single krypton-like ^solid (I) phase. The coherence

length increases with krypton coverage, ^as the peak

shifts to high angles (25.25 degrees ^{and 245 A for} 0Kr ^{= 1.08, 25.30} degrees ^for 6Kr ⁼ 1.15).

Other spectra ^can be found in [38].

5. Discussion.

We present ^the phase diagram ^{at 45 K} (Fig. 3) ⁱⁿ oblique coordinates : one coordinate is the partial

coverage of krypton, the other the partial coverage of _xenon; this representation is familiar to all physical

chemists when they ^discuss ternary ^mixtures (here ^the

third quantity ^{could be} thought ^{of as} vacancies, ^but

it is better to note that an intermediate vertical axis

corresponds ^{to the total} coverage). ^The advantage ^of

these coordinates is that all important quantities ^are

constant on straight lines i.e. partial ^{or total} coverage, relative concentration and, moreover, the limits of the domains of coexistence of three phases.

The limit of the 2D gas ^{was not} determined by

diffraction but is arbitrary ^drawn (in ^dotted line) ^to help understanding. ^{It must be} determined by precise

isotherm measurements. We observed three types ^of 2D single ^solid phases in this mixture :

-

a commensurate solid, ^from pure krypton up ^to

70 % ^{xenon in the} submonolayer, ^and up ^to pure

xenon for higher coverage.

-

an incommensurate xenon-like structure, ^{for a} few % krypton ^{in the} monolayer

-

an incommensurate krypton-like structure, ^for

Fig. ^2.

Diffraction spectrum ^{at 45 K with a} precoverage of xenon (0xe

0.25). ^At high krypton coverage, coexistence of the C peak ^{and the I} peak ^{is observed}

Fig. ^3.

^{A cut at T}

^{45 K in the} (T, 0,,r ,, OK,) phase ^dia-

gram. 0,,,

^{number of xenon atoms} per 3 graphite ^hexa-

gons ; °Kr

^{number of} krypton ^atoms per 3 graphite hexagons; ^C =.J3 x.J3 commensurate structure; ^X

« xenon like » incommensurate structure ; ^I

« krypton

like » incommensurate structure; ^V

2D gas (estimated);

crosses are experimental points.

coverage greater ^{than 1 and} approximately up ^to 20 %

xenon in the mixture.

The J3 ^{x J3} commensurate structure predomi-

nates in this diagram. ^We confirm the shift of the C-I kink observed by ^isotherm measurements [35]. Displa-

cement of the X peak upon introducing ^some krypton

proves that the ^two kinds of atoms contribute to the solid In the same way, integrated intensity ^{of the}

commensurate peak shows that xenon and krypton ^are

mixed in this structure.

The single ^solid phases ^are separated ^{in the} diagram by coexistence regions, ^then, X-C and I-C are first order transitions in a mixture. We note that the I-C transition appears ^more clearly first order than for pure krypton ^{at low} temperature ^{and even} with deute- rium _gas added on the krypton monolayer ^{at 40 K} [39].

A small amount of krypton ^is enough ^to stabilize the C solid and this ^{even occurs} for low coverages where the free area left by ^the 2D gas is large enough ^to support ^a complete ^{X solid.} Similarly, addition of

xenon in the compressed krypton ^solid provokes ^a

transition to a commensurate structure, ^{dilated com-}

pared ^{with I.}

The Gibbs phase rule, restricted to a 2D system, is,

in the case of a two-component ^{mixture :}

« Degrees of freedom »

4 - « Number of phases

present ^{» ;} therefore, ^{in the} region ^{where three} phases coexist, ^{there is} only ^one degree ^{of freedom} (including temperature) ^{and the} composition ^{of each} phase ^is

fixed. This region should be delimited by ^three straight

lines limiting ^the two-phase regions. ^{Indeed, we}

observe that the global krypton concentration deter-

mining ^the limit between X + C + V and C + V

regions ^is not constant with the _coverage; 50 % ^{Kr for}

low _coverage (about 0,2) ^{and 25} % ^for higher coverage

(about 0.8) and, ^{if we} draw the frontier between those two regions, ^{the low comer of the} three-phase triangle (joining ^{X + C +} V, ^{X +} V, ^{C + V and} V) ^{is out}

of the phase diagram. ^The experimental spectra ^{do not} allow the modification of those limits in such a way

as to reinteger ^{this comer into the} phase diagram. ^It

can be explained ^when taking ^{into account another}

remarkable effect : spectra ^{recorded at low} coverages show a shorter coherence length ( ¹⁰⁰ A) ^{than at}

high coverage (350 A). ^{We assume that the coherence} length ^{is limited} by ^{the substrate} platelet size, ^and then, it would indicate that the smallest ones are

covered first But this introduces an additional _para- meter, ^{and the} experimental phase diagram ^{must be}

considered ^as the superposition ^{of each} diagram corresponding ^{to a} characteristic platelet ^{size. The}

concentration limits first mentioned are now plausible:

small platelets ^favour incommensurable structures

(probably ^{on account of border} effects), ^and therefore,

need more krypton ^to keep ^{the 2D solid commen-}

surate.

We now discuss the value of this limit.

-

Bohr et al. [36] studied mixtures of Ar and Xe adsorbed on graphite. ^{We sketch in} figure ^{4 the} phase diagrams ^{of both} mixtures; ^the diagram (a) ^{for Ar-Xe}

is just ^{what we can draw from} [36] ^to present ^{it in more}

adequate coordinates; ^the diagram ^{for Kr-Xe is}

what we think would be found for a powder of platelets

with an homogeneous large ^size. Pure argon does not form a commensurate structure; this leads ^to the A-

phase part ^{of the} diagram ^{and a} second coexistence domain (gas-A-C). Differences between the two mixtures are understandable, except ^{for the} heavy-

drawn limits between C and X phases. ^{For Ar-Xe the}

Fig. ^4.

^Schematic phase diagrams ^{for Ar-Xe} (a) ^deduced

from (17) ^{and Kr-Xe on} large platelets (b).

commensurate C-phase replaces totally ^{the X solid}

for about 33 % ^of argon. In ^our experiments, ²⁵ % krypton ^is enough ^to replace ^{the X solid} by ^{a com-}

mensurate one (to compare those values, ^{we must}

consider the large platelet limit, ^as Ar-Xe mixture has been studied on ZYX). ^{This seems} astonishing : ^as

argon ^{atoms are} smaller than krypton ^{atoms and since}

the X structure is dilated from the commensurate structure, the opposite ratio would be expected.

A mean-field model has been devised [40], playing

with :

-

the pair interaction (Lennard-Jones parameters),

-

the elastic _energy to drive the incommensurate solid to the commensurate parameter,

-

the depth ^of potential ^for registration,

-

the mixing entropy,

-

the model is quite successful to explain ^the krypton-xenon limits but no reasonable values of these parameters ^{can be found to} produce ^the larger

concentration of argon necessary ^to drive xenon commensurate.

For argon-xenon mixture, the disorder _may be stronger leading ^{to a} reduction of registration energy and an increase of the apparent ^{size of} argon ^atoms.

Appendix.

Negative intensity ^is observed in figures ^{1 and 2}

before the 2D peak. ^It indicated that X _ray absorption

is different in this region than around the (002) peak.

This can be explained ^{if the} background ^is supposed

to come only ^{from a} volume effect and that (002)

reflection can be separated ^{in two} parts : ^the isotropic

disorientation of the graphite planes (which ^{is a}

volume sample contribution) and the contribution of the planes which have been folded back perpen- dicular to the wave-vector by ^{the massicot,} (and then,

is only ^a sample ^face contribution). ^{If the} intensity

diffracted from the first contribution is affected by

1532

introducing ^the gas (which ^{is a « volume »} phenome- non) ^{in the same} way that the background, ^{this is not}

the case for the intensity diffracted by ^the sample ^face planes, ^{which is} evidently ^{less absorbed} by ^the gas.

As we take into account the total variation of the

(002) intensity to correct the spectrum before sub-

tracting ^the graphite signal, ^the normalization is not

completely ^correct in the other region.

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