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First order incommensurate-commensurate and rotational epitaxy transition in an ethane monolayer adsorbed on graphite: A leed study
Surface Science 162 (1985) 439-445 North-Holland, Amsterdam
439
F I R S T O R D E R I N C O M M E N S U R A T E - C O M M E N S U R A T E AND R O T A T I O N A L EPITAXY T R A N S I T I O N IN AN E T H A N E M O N O L A Y E R A D S O R B E D ON G R A P H I T E : A LEED STUDY J. S U Z A N N E ,
J.M. GAY and R. W A N G *
DOpartement de Physique **, Case 901, Facultb des Sciences de Lumin.v, F- 13288 Marseille COdex 09, France Received 1 April 1985; accepted for publication 15 April 1985
Low Energy Electron Diffraction experiments have been performed on an ethane monolayer adsorbed on graphite single crystals for 70 < T < 85 K. The substep previously observed between the first and second layers on volumetric isotherms, at higher temperature, is identified as being the transition between an incommensurate phase 12 and a v~ x vr3- commensurate solid phase S 3. From photometric isotherms, the isosteric heat of adsorption has been determined (Q,t = 7.6 _*0.5 kcal/mol), in agreement with the previous measurements. From LEED patterns, it is shown that there is not only a first order jump in the lattice parameter at the incommensurate-commensurate transition, but also an abrupt change of 30 ° in the orientational epitaxy: S3 is 30 ° rotated with respect to the graphite axes; 12 is not rotated even when its parameter differs only by 3q~ from the S~ one. This striking behaviour may be due to the nature of 12 which could be a rather well correlated fluid like phase.
Ethane C 2 H 6 adsorbed on graphite in the monolayer range has been studied by numerous techniques: adsorption isotherm measurements [1], elastic [2-4] and inelastic [5] neutron scattering and LEED [6,7]. The phase diagram of this two-dimensional (2D) system is shown in fig. 1. It features three solids S 1. S 2 and S 3, two intermediate phases I t and 12 and fluid phases L and F. Motivated by the work of Regnier et al. [1], we present here a detailed study of the 12 --', S 3 transition for 70 < T < 85 K. Using LEED experiments, we are able to identify unambiguously the substep observed by Regnier et al. on the plateau of their volumetric isotherms between the first and second layer as being the 12 - , S 3 transition. Before presenting our results, let us recall [6] that S3 is a triangular f3- × v~R30 ° commensurate solid phase with molecules having their C - C axis perpendicular to the graphite surface. The 12 phase is obtained from the solid S 2 * Present address: Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA. ** Unite associ6e du CNRS 794.
0039-6028/85/$03.30 ~9 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
440
J. Suzanne et al. / LEED .~tudv of ethane monolay¢'r on graphue
S3+ 2 n ° L A Y E R 1.2 1.0 u,,I (.9
$2+S~ S= SI+S=
0.8
S i I =+ S~....,..~
rr
LU > O O
I 0.6 SI+2D
0.4
I
GAS
+2D
!
L
GAS! + 2 D
0.2
I I
Tc o
2'0
4'0
'
6'0
" 8'0
TEMPERATURE
" 1()0 ' 1~)0
140
(K)
Fig. l. Tentative phase diagram of ethane monolayer adsorbed on graphite. Coverage of one monola~er corresponds to that of the phase S3 (commensurate (3 :x;~/3 ).
phase through a first order transition driven by an increase of temperature at constant coverage, or from the I~ phase which becomes compressed with an increase of pressure at constant temperature. We have previously [7] interpreted I~ as being a lattice fluid with a 2 × 2 modulation. For 70 < T~< 85 K. the 12 phase gives a L E E D pattern analogous to that of I~ (hexagonal structure) with rather broad spots. This latter result is in agreement with the neutron diffraction experiments [4] indicating a short coherence length ( L -- 35 ,~ at T = 60 K). In the 12 phase, the distance between molecules is less than in the I~ phase. The L E E [ ) system and experimental procedures have been described previously [6,8]. At first, we present the results of L E E D isotherms measurements. For a given temperature, we have recorded with a spot photometer the intensity of a L E E D superstructure spot of the ~ × v~- $3 commensurate phase versus pressure. This procedure has allowed us to determine 11 adsorption isotherms around the l,---, $3 transition in the temperature range 70 85 K. These isotherms feature a sharp vertical step, signature of a first order transition. One of them ( T = 75.5 K) is shown in the inset of fig. 2. We have determined the isosteric heat of a d s o r p t i o n for 12 ---, $3 from the slope of the Clausius Clapeyron line In p versus I / T , where p is the pressure at the transition (fig. 2). We find Q,,(I~ --, $3) = 7.4 _+ 0.2 k c a l / m o l . This value agrecs rather well with that of Regnier et al. [1] at higher temperatures (87 < T < 90 K) for the sccond small substep they observed on their isotherms before second
J. Suzanne et a L / L E E D stud)" of ethane monolaver on graphite
10-2
•~.1 \\
T=75.5K
¢0
\ \
10-3
441
>I--
\ \
\
'" Z
0
~--
A--
_
10-4 0 I'-I.U rr
~lO-E W I1: Q.
10-7
10-8 INVERSE TEMPERATURE x l 0 3 (K -1) Fig. 2. Vapor pressure inverse temperature phase diagram for the 12 ---,S~ transition. The dashed line represents the measurements of Regnier et al. I1] for 87 < T< 90 K. Above --87 K, the transition becomes continuous. The inset shows the intensity of the L E E D superstructure S3 Sl:X~t versus C 2 H 6 pressure at 75.5 K. The vertical step at p = 1 × 10 -~' Torr is the signature of a first order 12 ---'$3 transition.
layer c o n d e n s a t i o n : Q~t = 6.87 +_ 0.12 k c a l / m o i . The s m a l l difference b e t w e e n the t w o values of Q~t is p r o b a b l y d u e to a p h a s e transition occurring in the S.~ p h a s e a r o u n d 87 K. A b o v e this temperature, Regnier et al. have f o u n d that the substep is not vertical [1], that is, the 12 ---, S 3 transition is no longer first order. Indeed, neutron diffraction e x p e r i m e n t s [4,9] h a v e s h o w n that the m e l t i n g of S 3 p r o b a b l y occurs b e t w e e n 83 and 87 K [9]. T h e s e e x p e r i m e n t s s e e m to s h o w that at 87 K, 12 transforms itself c o n t i n u o u s l y into a solid like p h a s e with increasing coverage [4]. Hence, T = 87 K m a y be identified at that of a tricritical point.
442
J. Suzanne et al. / LEED stud)" of ethane monolayer on graphtte
15
.__,?.X 2
a
#10 I.-I.L tO
O,
-73.8K ,77.9K -80.7K =82.8K
10 -8
&..--
10-'
10 -6
A.-_
16 -5
;=.--. L ,
16- 4
PRESSURE (Torr)
b
10 v I--LI_ 09
7'5 8'0 TEMPERATURE
85 (K)
Fig. 3. (a) Misfit between the lattice parameters of the 12 and S3 phases versus pressure for different temperatures. The arrow indicates the misfit for a lattice parameter 4.92 A (i.e. 2×2 commensurate phase 11). The dotted lines represent the first order 12 -. St transitions. Above them. there is a non-rotated 12 phase; below, a ~/3 x~/3 R 30° S~ phase, tlence, there is a first order incommensurate-commensurate and rotational epitaxy transition. (b) Misfit m t at the ] 2 ~ S 3 transition
versus
temperature.
A f t e r h a v i n g d e t e r m i n e d a set o f a d s o r p t i o n i s o t h e r m s , we h a v e u n d e r t a k e n a careful a n a l y s i s of the L E E D p a t t e r n s in o r d e r to m e a s u r e the v a r i a t i o n of the o v e r l a y e r p a r a m e t e r d with p r e s s u r e for d i f f e r e n t t e m p e r a t u r e s . T h e results are given in fig. 3a in t e r m s of misfit m b e t w e e n the 12 i n c o m m e n s u r a t e p h a s e a n d the ¢c~ × ~ c o m m e n s u r a t e S 3. m is d e f i n e d as ( d l , - d s , ) / d s . T h e misfit d e c r e a s e s c o n t i n u o u s l y at first, t h e n there is an a b r u p t c h a n g e at the transition. T h e v a r i a t i o n of the misfit m. at the t r a n s i t i o n versus t e m p e r a t u r e is r e p o r t e d in fig. 3b. m t d e c r e a s e s at first f r o m 70 to 80 K, then it r e m a i n s e s s e n t i a l l y c o n s t a n t f r o m 80 to 85 K. T h i s c u r v e gives the p h a s e b o u n d a r y o f the c o e x i s t e n c e r e g i o n 12 + S 3. T h e s e results h a v e a l l o w e d us to c o m p l e t e the t e n t a t i v e p h a s e d i a g r a m of fig. 1 p r e s e n t e d p r e v i o u s l y in ref. [6]. R e g n i e r et al.
J. Suzanne et al. / LEED stud)' of ethane monolaver on graphtte
443
\
I!
Fig. 4. LEED pattern at the transition 12 ~ S~ for T = 80.7 K and p = 2.85 × 10 5 Torr. Electrons energy is 109 eV. The twelve spots are due to the coexistence between 12 and S3 oriented 30° apart. The white arrow indicate.,,one of the six S3 spots and the triangles a graphite axis.
have tentatively i n t e r p r e t e d the substep observed as being a solificiation of the first layer with molecules s t a n d i n g up on the surface with an a r e a / m o l e c u l e of 15.15 + 0.7 ,~2 in the solid phase. T h a t is in c o m p l e t e agreement with the $3 structure. Moreover, the difference of density between 12 and S 3 at the transition (6% for T - 80 K) c o r r e s p o n d s well with the height of the substep of the volumetric isotherms of Regnier. As said before, the 12 ~ S 3 transition is first o r d e r below 85 K and we have observed the coexistence of the two phases at the transition. Fig. 4 shows a L E E D p a t t e r n of 12 coexistence with S 3. It is very striking to notice that the two phases are rotated 30 ° one from the o t h e r whereas their p a r a m e t e r s differ o n l y by 3% at T > 80 K. Hence, there is not only a first o r d e r phase transition in the lattice p a r a m e t e r of the two solid phases, but also in their epitaxial o r i e n t a t i o n with the substrate. It would be interesting to observe the change in the o r i e n t a t i o n s of the phases a b o v e 87 K at the tricritical line. U n f o r t u n a t e l y this d o m a i n of t e m p e r a t u r e is not accessible to L E E D ( p >_ 10 -3 Torr). The m e c h a n i s m of the 12 --, S~ transition is not c o m p l e t e l y u n d e r s t o o d . A m o r e detailed k n o w l e d g e of the 12 phase would be largely helpful to explain the transition. In the 12 phase, the molecules have p r o b a b l y some kind of precession m o t i o n a r o u n d an axis p e r p e n d i c u l a r to the g r a p h i t e surface. This
444
J. Suzanne et al. / LEED study of ethane monolaver on graphtte
motion is hindered with increasing coverage and the tilt angle of the C - C axis with the perpendicular to the surface decreases. At the transition all the molecules tend to align perpendicular to the surface in a cooperative first order transition. Furthermore, the 12 phase which may be obtained by compressing the 2 × 2 lattice fluid [7] has, like I~, some degrees of translational mobility in addition to the rotational one [10]. Hence, we think now that 12 is a rather well correlated liquid like phase with an hexatic order. The fact that 12 is not rotated with respect to the graphite axes, even when its parameter differs only by 3% with that of the v~- x ~ R 30 ° $3 solid phase, shows that the modulation of the substrate potential has little effect on the orientation of 12. It is likely that a theory of orientational epitaxy as that of Novaco and Mc Tague [11] does not apply. The stabilization of 12 oriented along the graphite axes may be due to the presence of steps. Such an explanation has been given in the case of the ,~' phase of 02 adsorbed on graphite [12]. It is worth noticing that a similar phenomena has also been observed in the case of the floating S u phase of monolayer methane/graphite [131. As a conclusion, we have identified the substep observed by Regnier et al. between the first and second layers as being the 12 ( f l u i d ) ~ S t (solid) transition. In our experiment, it appears to be first order unlike Regnier et al. results, implying the existence of a tricritical point around 87 K above which 12 transforms itself continuously into a solid phase. We have shown that there is a first order j u m p in the lattice parameter at the incommensurate-commensurate ~3 × ~ transition and also an abrupt change of 30 ° in the orientational epitaxy.
Acknowledgements We are grateful to M. Bienfait and J.P. Coulomb for the communication of their quasi-elastic neutron scattering results prior to publication. One of us (R.W.) thanks NSF for financial assistance through the U S - F r a n c e scientific program.
References [1] J. Regnier. J. Menaucourt, A. Thorny and X. Dural, J. Chim. Physique 78 (1981) 629. [2] J.P. Coulomb, J.P. Biberian, J. Suzanne, A. Thorny, G.J. Trott, H. Taub. II.R. Danner and F.Y. Hansen, Phys. Rev. Letters 43 (1979) 1878. [3] H. Taub. G.J. Tron, F.Y. Hansen, H.R. Danner, J.P. Coulomb, J.P. Biberian, J. Suzanne and A. Thorny, in: Ordering in Two Dimensions, Ed. S.K. Sinha (North-Holland, New York, 1980) p. 91. [4] G.J. Trott, PhD Thesis, University of Missouri-Columbia (1981).
J. Suzanne et al. / LEED stud)' of ethane monolaver on graphite
445
[51 F.Y. Hansen, R. Wang, H. Taub, If. Shechtcr, D.G. Reichel, I-t.R. Danner and G.P. Allredge, Phys. Rev. Letters 53 (1984) 572. [61 J. Suzanne, J.L. Sequin, H. Taub and J.P. Biberian, Surface Sci. 125 (1983) 153. [7] J.M. Gay. J. Suzanne and R. Wang, J. Physique I,ettres 46 (1985) L429. [8] S. Calisti. J. Suzanne and J.A. Venables, Surface Sci. 116 (1982) 455. 19] J.P. Coulomb, T h e e . Faculte des Sciences de Luminy, Universit6 Aix-Marseille II (1981). [10] J.P. Coulomb, M. Bienfait and P. Thorel, to be published. [111 J.P. McTague and A.D. Novaco, Phys. Rev. BI9 (1979) 5299. [12] J.F. Toney and S.C. Fain, Phys. Rev. B30 (1984) 1115. [13] J.M. (Jay, J. Krim and J. Suzanne, to be published.
439
F I R S T O R D E R I N C O M M E N S U R A T E - C O M M E N S U R A T E AND R O T A T I O N A L EPITAXY T R A N S I T I O N IN AN E T H A N E M O N O L A Y E R A D S O R B E D ON G R A P H I T E : A LEED STUDY J. S U Z A N N E ,
J.M. GAY and R. W A N G *
DOpartement de Physique **, Case 901, Facultb des Sciences de Lumin.v, F- 13288 Marseille COdex 09, France Received 1 April 1985; accepted for publication 15 April 1985
Low Energy Electron Diffraction experiments have been performed on an ethane monolayer adsorbed on graphite single crystals for 70 < T < 85 K. The substep previously observed between the first and second layers on volumetric isotherms, at higher temperature, is identified as being the transition between an incommensurate phase 12 and a v~ x vr3- commensurate solid phase S 3. From photometric isotherms, the isosteric heat of adsorption has been determined (Q,t = 7.6 _*0.5 kcal/mol), in agreement with the previous measurements. From LEED patterns, it is shown that there is not only a first order jump in the lattice parameter at the incommensurate-commensurate transition, but also an abrupt change of 30 ° in the orientational epitaxy: S3 is 30 ° rotated with respect to the graphite axes; 12 is not rotated even when its parameter differs only by 3q~ from the S~ one. This striking behaviour may be due to the nature of 12 which could be a rather well correlated fluid like phase.
Ethane C 2 H 6 adsorbed on graphite in the monolayer range has been studied by numerous techniques: adsorption isotherm measurements [1], elastic [2-4] and inelastic [5] neutron scattering and LEED [6,7]. The phase diagram of this two-dimensional (2D) system is shown in fig. 1. It features three solids S 1. S 2 and S 3, two intermediate phases I t and 12 and fluid phases L and F. Motivated by the work of Regnier et al. [1], we present here a detailed study of the 12 --', S 3 transition for 70 < T < 85 K. Using LEED experiments, we are able to identify unambiguously the substep observed by Regnier et al. on the plateau of their volumetric isotherms between the first and second layer as being the 12 - , S 3 transition. Before presenting our results, let us recall [6] that S3 is a triangular f3- × v~R30 ° commensurate solid phase with molecules having their C - C axis perpendicular to the graphite surface. The 12 phase is obtained from the solid S 2 * Present address: Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA. ** Unite associ6e du CNRS 794.
0039-6028/85/$03.30 ~9 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
440
J. Suzanne et al. / LEED .~tudv of ethane monolay¢'r on graphue
S3+ 2 n ° L A Y E R 1.2 1.0 u,,I (.9
$2+S~ S= SI+S=
0.8
S i I =+ S~....,..~
rr
LU > O O
I 0.6 SI+2D
0.4
I
GAS
+2D
!
L
GAS! + 2 D
0.2
I I
Tc o
2'0
4'0
'
6'0
" 8'0
TEMPERATURE
" 1()0 ' 1~)0
140
(K)
Fig. l. Tentative phase diagram of ethane monolayer adsorbed on graphite. Coverage of one monola~er corresponds to that of the phase S3 (commensurate (3 :x;~/3 ).
phase through a first order transition driven by an increase of temperature at constant coverage, or from the I~ phase which becomes compressed with an increase of pressure at constant temperature. We have previously [7] interpreted I~ as being a lattice fluid with a 2 × 2 modulation. For 70 < T~< 85 K. the 12 phase gives a L E E D pattern analogous to that of I~ (hexagonal structure) with rather broad spots. This latter result is in agreement with the neutron diffraction experiments [4] indicating a short coherence length ( L -- 35 ,~ at T = 60 K). In the 12 phase, the distance between molecules is less than in the I~ phase. The L E E [ ) system and experimental procedures have been described previously [6,8]. At first, we present the results of L E E D isotherms measurements. For a given temperature, we have recorded with a spot photometer the intensity of a L E E D superstructure spot of the ~ × v~- $3 commensurate phase versus pressure. This procedure has allowed us to determine 11 adsorption isotherms around the l,---, $3 transition in the temperature range 70 85 K. These isotherms feature a sharp vertical step, signature of a first order transition. One of them ( T = 75.5 K) is shown in the inset of fig. 2. We have determined the isosteric heat of a d s o r p t i o n for 12 ---, $3 from the slope of the Clausius Clapeyron line In p versus I / T , where p is the pressure at the transition (fig. 2). We find Q,,(I~ --, $3) = 7.4 _+ 0.2 k c a l / m o l . This value agrecs rather well with that of Regnier et al. [1] at higher temperatures (87 < T < 90 K) for the sccond small substep they observed on their isotherms before second
J. Suzanne et a L / L E E D stud)" of ethane monolaver on graphite
10-2
•~.1 \\
T=75.5K
¢0
\ \
10-3
441
>I--
\ \
\
'" Z
0
~--
A--
_
10-4 0 I'-I.U rr
~lO-E W I1: Q.
10-7
10-8 INVERSE TEMPERATURE x l 0 3 (K -1) Fig. 2. Vapor pressure inverse temperature phase diagram for the 12 ---,S~ transition. The dashed line represents the measurements of Regnier et al. I1] for 87 < T< 90 K. Above --87 K, the transition becomes continuous. The inset shows the intensity of the L E E D superstructure S3 Sl:X~t versus C 2 H 6 pressure at 75.5 K. The vertical step at p = 1 × 10 -~' Torr is the signature of a first order 12 ---'$3 transition.
layer c o n d e n s a t i o n : Q~t = 6.87 +_ 0.12 k c a l / m o i . The s m a l l difference b e t w e e n the t w o values of Q~t is p r o b a b l y d u e to a p h a s e transition occurring in the S.~ p h a s e a r o u n d 87 K. A b o v e this temperature, Regnier et al. have f o u n d that the substep is not vertical [1], that is, the 12 ---, S 3 transition is no longer first order. Indeed, neutron diffraction e x p e r i m e n t s [4,9] h a v e s h o w n that the m e l t i n g of S 3 p r o b a b l y occurs b e t w e e n 83 and 87 K [9]. T h e s e e x p e r i m e n t s s e e m to s h o w that at 87 K, 12 transforms itself c o n t i n u o u s l y into a solid like p h a s e with increasing coverage [4]. Hence, T = 87 K m a y be identified at that of a tricritical point.
442
J. Suzanne et al. / LEED stud)" of ethane monolayer on graphtte
15
.__,?.X 2
a
#10 I.-I.L tO
O,
-73.8K ,77.9K -80.7K =82.8K
10 -8
&..--
10-'
10 -6
A.-_
16 -5
;=.--. L ,
16- 4
PRESSURE (Torr)
b
10 v I--LI_ 09
7'5 8'0 TEMPERATURE
85 (K)
Fig. 3. (a) Misfit between the lattice parameters of the 12 and S3 phases versus pressure for different temperatures. The arrow indicates the misfit for a lattice parameter 4.92 A (i.e. 2×2 commensurate phase 11). The dotted lines represent the first order 12 -. St transitions. Above them. there is a non-rotated 12 phase; below, a ~/3 x~/3 R 30° S~ phase, tlence, there is a first order incommensurate-commensurate and rotational epitaxy transition. (b) Misfit m t at the ] 2 ~ S 3 transition
versus
temperature.
A f t e r h a v i n g d e t e r m i n e d a set o f a d s o r p t i o n i s o t h e r m s , we h a v e u n d e r t a k e n a careful a n a l y s i s of the L E E D p a t t e r n s in o r d e r to m e a s u r e the v a r i a t i o n of the o v e r l a y e r p a r a m e t e r d with p r e s s u r e for d i f f e r e n t t e m p e r a t u r e s . T h e results are given in fig. 3a in t e r m s of misfit m b e t w e e n the 12 i n c o m m e n s u r a t e p h a s e a n d the ¢c~ × ~ c o m m e n s u r a t e S 3. m is d e f i n e d as ( d l , - d s , ) / d s . T h e misfit d e c r e a s e s c o n t i n u o u s l y at first, t h e n there is an a b r u p t c h a n g e at the transition. T h e v a r i a t i o n of the misfit m. at the t r a n s i t i o n versus t e m p e r a t u r e is r e p o r t e d in fig. 3b. m t d e c r e a s e s at first f r o m 70 to 80 K, then it r e m a i n s e s s e n t i a l l y c o n s t a n t f r o m 80 to 85 K. T h i s c u r v e gives the p h a s e b o u n d a r y o f the c o e x i s t e n c e r e g i o n 12 + S 3. T h e s e results h a v e a l l o w e d us to c o m p l e t e the t e n t a t i v e p h a s e d i a g r a m of fig. 1 p r e s e n t e d p r e v i o u s l y in ref. [6]. R e g n i e r et al.
J. Suzanne et al. / LEED stud)' of ethane monolaver on graphtte
443
\
I!
Fig. 4. LEED pattern at the transition 12 ~ S~ for T = 80.7 K and p = 2.85 × 10 5 Torr. Electrons energy is 109 eV. The twelve spots are due to the coexistence between 12 and S3 oriented 30° apart. The white arrow indicate.,,one of the six S3 spots and the triangles a graphite axis.
have tentatively i n t e r p r e t e d the substep observed as being a solificiation of the first layer with molecules s t a n d i n g up on the surface with an a r e a / m o l e c u l e of 15.15 + 0.7 ,~2 in the solid phase. T h a t is in c o m p l e t e agreement with the $3 structure. Moreover, the difference of density between 12 and S 3 at the transition (6% for T - 80 K) c o r r e s p o n d s well with the height of the substep of the volumetric isotherms of Regnier. As said before, the 12 ~ S 3 transition is first o r d e r below 85 K and we have observed the coexistence of the two phases at the transition. Fig. 4 shows a L E E D p a t t e r n of 12 coexistence with S 3. It is very striking to notice that the two phases are rotated 30 ° one from the o t h e r whereas their p a r a m e t e r s differ o n l y by 3% at T > 80 K. Hence, there is not only a first o r d e r phase transition in the lattice p a r a m e t e r of the two solid phases, but also in their epitaxial o r i e n t a t i o n with the substrate. It would be interesting to observe the change in the o r i e n t a t i o n s of the phases a b o v e 87 K at the tricritical line. U n f o r t u n a t e l y this d o m a i n of t e m p e r a t u r e is not accessible to L E E D ( p >_ 10 -3 Torr). The m e c h a n i s m of the 12 --, S~ transition is not c o m p l e t e l y u n d e r s t o o d . A m o r e detailed k n o w l e d g e of the 12 phase would be largely helpful to explain the transition. In the 12 phase, the molecules have p r o b a b l y some kind of precession m o t i o n a r o u n d an axis p e r p e n d i c u l a r to the g r a p h i t e surface. This
444
J. Suzanne et al. / LEED study of ethane monolaver on graphtte
motion is hindered with increasing coverage and the tilt angle of the C - C axis with the perpendicular to the surface decreases. At the transition all the molecules tend to align perpendicular to the surface in a cooperative first order transition. Furthermore, the 12 phase which may be obtained by compressing the 2 × 2 lattice fluid [7] has, like I~, some degrees of translational mobility in addition to the rotational one [10]. Hence, we think now that 12 is a rather well correlated liquid like phase with an hexatic order. The fact that 12 is not rotated with respect to the graphite axes, even when its parameter differs only by 3% with that of the v~- x ~ R 30 ° $3 solid phase, shows that the modulation of the substrate potential has little effect on the orientation of 12. It is likely that a theory of orientational epitaxy as that of Novaco and Mc Tague [11] does not apply. The stabilization of 12 oriented along the graphite axes may be due to the presence of steps. Such an explanation has been given in the case of the ,~' phase of 02 adsorbed on graphite [12]. It is worth noticing that a similar phenomena has also been observed in the case of the floating S u phase of monolayer methane/graphite [131. As a conclusion, we have identified the substep observed by Regnier et al. between the first and second layers as being the 12 ( f l u i d ) ~ S t (solid) transition. In our experiment, it appears to be first order unlike Regnier et al. results, implying the existence of a tricritical point around 87 K above which 12 transforms itself continuously into a solid phase. We have shown that there is a first order j u m p in the lattice parameter at the incommensurate-commensurate ~3 × ~ transition and also an abrupt change of 30 ° in the orientational epitaxy.
Acknowledgements We are grateful to M. Bienfait and J.P. Coulomb for the communication of their quasi-elastic neutron scattering results prior to publication. One of us (R.W.) thanks NSF for financial assistance through the U S - F r a n c e scientific program.
References [1] J. Regnier. J. Menaucourt, A. Thorny and X. Dural, J. Chim. Physique 78 (1981) 629. [2] J.P. Coulomb, J.P. Biberian, J. Suzanne, A. Thorny, G.J. Trott, H. Taub. II.R. Danner and F.Y. Hansen, Phys. Rev. Letters 43 (1979) 1878. [3] H. Taub. G.J. Tron, F.Y. Hansen, H.R. Danner, J.P. Coulomb, J.P. Biberian, J. Suzanne and A. Thorny, in: Ordering in Two Dimensions, Ed. S.K. Sinha (North-Holland, New York, 1980) p. 91. [4] G.J. Trott, PhD Thesis, University of Missouri-Columbia (1981).
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[51 F.Y. Hansen, R. Wang, H. Taub, If. Shechtcr, D.G. Reichel, I-t.R. Danner and G.P. Allredge, Phys. Rev. Letters 53 (1984) 572. [61 J. Suzanne, J.L. Sequin, H. Taub and J.P. Biberian, Surface Sci. 125 (1983) 153. [7] J.M. Gay. J. Suzanne and R. Wang, J. Physique I,ettres 46 (1985) L429. [8] S. Calisti. J. Suzanne and J.A. Venables, Surface Sci. 116 (1982) 455. 19] J.P. Coulomb, T h e e . Faculte des Sciences de Luminy, Universit6 Aix-Marseille II (1981). [10] J.P. Coulomb, M. Bienfait and P. Thorel, to be published. [111 J.P. McTague and A.D. Novaco, Phys. Rev. BI9 (1979) 5299. [12] J.F. Toney and S.C. Fain, Phys. Rev. B30 (1984) 1115. [13] J.M. (Jay, J. Krim and J. Suzanne, to be published.