A first order two-dimensional melting transition : methane adsorbed on (0001) graphite

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A first order two-dimensional melting transition :

methane adsorbed on (0001) graphite

A. Glachant, J.P. Coulomb, M. Bienfait, J.G. Dash

To cite this version:

A. Glachant, J.P. Coulomb, M. Bienfait, J.G. Dash. A first order two-dimensional melting transition :

methane adsorbed on (0001) graphite. Journal de Physique Lettres, Edp sciences, 1979, 40 (20),

pp.543-544. �10.1051/jphyslet:019790040020054300�. �jpa-00231684�

L-543

A

first

order

two-dimensional

_melting

transition :

methane

adsorbed

on

(0001) graphite

_(*)

A.

_Glachant,

J. P.

Coulomb,

M. Bienfait

Département de _Physique, CRMC, Faculté des Sciences de _Luminy, Université d’Aix-Marseille II, 13288 Marseille, France and J. G. Dash

Department of _{Physics, University} of _{Washington, Seattle, Washington 98195,} USA (Re~u le 6 juillet 1979, accepte le 3 _{septembre 1979)}

Résumé. 2014 La diffraction

neutronique

permet de mesurer la _perte de l’ordre à

_longue

distance d’un solide bidi-mensionnel localisé de méthane adsorbé lors de sa fusion. Les

_expériences

montrent _{que la fusion} est une

transi-tion du

_premier

ordre et _{que l’on peut} définir le

_{point triple}

de la _couche, soit 56 ± 0,4 K. Abstract. 2014 The variation of

long

range order of a

_registered

solid _submonolayer of methane adsorbed on the

graphite

basal _plane is measured at

_melting

_by neutron elastic

_scattering.

The sudden loss of order indicates a

first order

_melting

transition and defines the two-dimensional

_{triple point}

of the

_layer,

_namely 56 ± 0.4 K.

LE JOURNAL DE PHYSIQUE - LETTRES

TOME 40, 15 OCTOBRE 1979,

Classification

Physics Abstracts

82.65Dp - 68.40+e

Among

the

_phase

transitions in

_monolayer

films discovered a few _{years ago}

_[1],

_melting

involves

_long

standing

theoretical

_{questions ~2].}

For an

incommen-surate

_monolayer,

_melting

_corresponds

to the loss of

_long-range

directional

_[3]

or

_{topological [4]}

order. For such _systems, the

_melting

transition can be either

continuous or first order

[4-7].

In the case of

_registered

films with

_{long-range positional}

order,

melting

to a

disordered fluid

_phase

can occur via a continuous

transition,

as, for

_example

the order-disorder

tran-sition of the

_J3

x 3 registered

_phase

of He on

graphite [8, 9].

However,

it is also

_possible

that such

phases

could melt via a

_sharp

first order

_phase

transi-tion.

_Experimental

results for various solid

mono-layers

adsorbed on

graphite

indicates that

solid-fluid

_phase

transitions are more or less

_abrupt,

depending

on the adsorbate

and/or

substrate

quality

[10-22].

It has been

_emphasized

that size effects and substrate

_{heterogeneity}

can blur a first order

_phase

change

and make it appear to be continuous

_[19].

Other characteristics of first order

_phase

_changes,

which _may be less

_subject

to

_{heterogeneity,}

are the

coexistence of two distinct

_phases,

and a linear

depen-dence of extensive variables on the total

quantity

of

adsorbate

_[2].

(*) Experiments performed at I.L.L. Grenoble.

A recent Letter

_reported

a coexistence

region

between 2D incommensurate solid and 2D

_liquid

for

a

_monolayer

of NO adsorbed on

_{graphite [23].}

Here

’

we _report a more

_{complete study of melting}

of methane

adsorbed on

_graphite,

where we find a coexistence

region

between 2D

_registered

solid and 2D

_liquid,

and at lower coverage a sudden loss of

_long

_range

order within a narrow _temperature

_interval,

indica-tive of a first order

_melting

transition at a 2D

_triple

point.

The

_liquid

_phase

is characterized

_by

its

_density,

short _range order and lateral

_mobility.

Our

_experimental

_system was deuterated methane

(CD4)

adsorbed on

_{Papyex [24],}

a

_compressed

and

partially aligned powder

of exfoliated

_graphite

simi-lar to Grafoil

_{[2, 10, 12].}

It has

_{large specific}

adsorp-tion area

_{( ~ 20}

m2/g,

1.1

g/cm3)

_{predominantly}

of basal

_{plane (0001)}

surfaces,

with mean orientation

parallel

to the

_plane

of the sheet. It has been used

previously

for neutron or

_X-ray

_scattering

studies of

films

_{[23, 25-27].}

The neutron diffraction

_experiments

were

perform-ed in such a _way that the incident beam and the

scatter-ing

vector

_Q(I

_Q

_{I =}

4 7c sin

0//L)

were

_parallel

to the

mean orientation of the

_graphite

basal

_planes

(in-plane

geometry).

We used the deuterated form of methane

_(CD4)

which is a

_good

coherent scatterer. ,

Almost all the measurements were done for a _coverage x = 0.6

monolayer

within the 51.6-60.8 K

L-544 JOURNAL DE _{PHYSIQUE -} LETTRES

ture range. Two other

experimental

conditions were

also

_{chosen, x}

=

0.83,

T = 55.8 K and T = _{58.7 K.}

The interest of this choice will be obvious in the course

of the discussion. In our

notation,

x = 1

corresponds

to a 0.07

A-2

molecular

density,

i.e. to a

_compressed

out-of-registry monolayer.

For x = 0.60 and

51.6

T

55.7,

the diffraction

pattern exhibits a

_{sharp peak (Fig.}

la)

characteristic

of an

in-registry

/3

x

J3

R 300 2D solid illustrated in the inset. The same diffracted

_peak

is observed for

x = 0.83 and T = 55.8 K. For both

coverages

(x

= 0.60 and x =

0.83),

all the

graphite

surface

cannot be

_{occupied by}

a

_{CD4 registered}

solid whose

completion corresponds

to x ~ 0.9. Hence a low

density,

disordered

_phase

coexists with the 2D solid. This

_phase

is a 2D _gas and of course cannot be detect-ed

_by

neutron diffraction.

Fig. 1. - Neutron diffraction spectra from _CD4 adsorbed on

graphite. Background scattering from the substrate has been subtracted. Typical background level is 2-3 x 104 counts for the

present experimental conditions. Both curves are normalized to

the same incident flux. The solid curve _represents the best fit with the standard theoretical line [12] and yields the nearest _neighbor

distance a and the correlation _{rang L. a)} 01 peak of the in-registry

J3

x

J3

R 300 2D solid _(inset), T = 52.6 _± 0.4 K and

cove-rage = 0.60,

parameters of the fit : a = 4.26 A, L = ₂₅₀ A.

b) At

melting the _{preceding peak} broadens (T = 56.9 _{± 0.1 K,}

cove-rage =

0.60) indicating a short _spatial correlation range.

Parame-ters of the fit : a = _{4.33 ± 0.3} A, _{L ~ 20-25} A.

The

_{Bragg peak}

has been

_interpreted

with the

current

_theory

_(see

for instance

_[12])

of 2D diffraction and the

_experimental

data have been corrected for the instrumental resolution

(AO

=

0.3~)

and for the distribution of

_{crystallite angles}

about the

prefe-rential orientation. The width of the

_peak

enables us

to determine the

_spatial

correlation _{range L} of the 2D

_crystals,

i.e. the mean size of the

diffracting

_arrays.

Its value is about 250

_A,

_nearly

constant within the 51.6-55.7 K

_temperature

_range. Such a N 250

A

correlation _range has

_previously

been observed for

Kr

_[26]

and NO

_[23]

solids adsorbed on

Papyex.

The limited size of the 2D

_crystals

is

_probably

due to

the existence of defects on the

graphite

surface

pre-venting

a

_larger

extension of the 2D lattice.

Above T = 56

K,

the diffracted _pattern for x = 0.60

changes drastically.

It broadens and the correlation

range decreases.

Figure

lb

_presents

a

_typical

diffract-ed

_peak

observed between 56.4 and 60.8 K. It defines

a condensed

_phase

with a short

spatial

correlation

range

(L ~

20-25

A).

Mobility

measurements

[27]

have shown that this

_phase

is a 2D

liquid

which,

in

these T and 0 _ranges, coexists with a 2D _gas.

In

_figure

2,

the

_spatial

correlation _rang is

_plotted

as a function of T. It

_{drops abruptly by}

a factor 10

within 0.7 K

_indicating

a clear-cut

_melting

transition.

Fig. 2. -

Temperature variation of the _spatial correlation range

(or 2D cluster _size) in adsorbed _{CD4 submonolayer} for a _coverage = 0.60. The _{abrupt change at} 56 K within 0.7 K is the _signature of a 2D first order _melting transition.

This result is confirmed

_by

two

_experimental

facts :

i)

At

_melting,

the distance between

_CD4

molecules

jumps

from 4.26

A

_(~/3

in-registry

structure)

to

4.33 ± 0.03

A.

As in three

_dimensions,

there is a

sudden

_expansion

when a 2D solid melts.

ii)

At T = 58.7 K and for _x =

0.83,

_we observe

a diffracted

_peak

which can be

_interpreted

as

result-ing

from the

_scattering

of a mixture of 2D

liquid

and

solid.

_Figure

3 shows this

_peak

and a

comparison

with a

_composite

of

_1/3

of 2D solid and

_2/3

of 2D

liquid.

The

_sharpness

of our observed

_melting

transition

appears to be related to the

_{graphite quality. Melting}

of 0.7

_monolayer

of

_CD4

adsorbed on

_graphon

has been studied

_{previously by}

neutron

_{scattering [14].}

In this case, the

submonolayer

melts

_continuously

’

N° 20 A FIRST ORDER 2D-MELTING TRANSITION

Fig. 3. - Neutron

diffraction spectrum of the CD4 layer (T = 58.7 _± 0.1 _K,

coverage = _{0.83) in the solid-liquid}

coexis-tence region. The fit (solid curve) has been obtained from a

super-position of the solids lines of figures la and lb weighted by the relative amounts of solid and _liquid

_{(t and i}

_{respectively).} The small _peak near _{22° appears} to be a small error due to the subtrac-tion of the _{(0002) graphite peak.}

between 40 and 60 K.

_Graphon

is a

graphitized

carbon

black

_showing

_crystallites

with _very small

₍₀₀₀₁₎

uniform domains which

_prevents

the

_developments

of

long

range

order;

Marlow et al. report that their diffraction lines indicated coherence

_lengths

of about 35

A.

In _summary, we

_{experimentally}

demonstrated

_by

neutron diffraction that T = 56 _± 0.4 K is _a

phase

boundary

between the 2D

_gas-solid

and the 2D

liquid-solid coexistence domains. Hence 56 ± 0.4 K is the 2D

_{triple point}

of the first

_layer

of methane adsorbed

on the

(0001)

graphite plane.

We are

_{especially grateful}

to C.

_Marti,

P. Thorel and B. Croset for fruitful discussions and the D2 staff for

_helping

us in the neutrons measurements.

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