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Adsorbed layers of O2 on graphite studied by heat capacity measurements
Solid State Communications, Vol. 33, pp.229—231. Pergamon Press Ltd. 1980. Printed in Great Britain. ADSORBED LAYERS OF 02 ON GRAPHITE STUDIED BY HEAT CAPACITY MEASUREMENTS R. Marx and R. Braun Labor für Tieftemperaturphysik der Gesamthochschule Duisburg, Lotharstr. 65, D.4100 Duisburg 1, Germany (Received 16 July 1979 by B. Muhlschlegel) Using a comparative method (quotient method) we determined the temperature dependence of the heat capacity of different layers of 02 adsorbed on Grafoil between 23.5 and 26.5 K. The specific heat of layers below monolayer completion shows a large delta-function shaped anomaly at the phase boundary between the 5 phase and the fluid phase. The anomaly is tentatively interpreted as due to a two-dimensional phase transition at the quadruple point of the adsorbate (the triple point of the monolayer). The investigation of other monolayers including the magnetic transition between a02 and 1302 and the S + ~3coexistence region is presently being carried out. 1. INTRODUCTION RECENTLY it has been discovered that physisorbed films can form states of two-dimensionally like character [1]. This was proved by investigation of vapour pressure isotherms and by heat capacity measurements of monolayer films adsorbed on substrates such as FeCl2, alkali halides and Grafoil (exfoliated graphite). tion isotherms show a defmed stair-step pressureAdsorpdependence indicating a layer-by-layer adsorption process. Heat capacity studies give evidence for two-dimensional phase transitions analogous to the solid—liquid—vapour transitions in the three-dimension world [2] but also for transitions of the order—disorder type [3]. An especially interesting system is 02 adsorbed on Grafoil. Neutron diffraction studies [4] revealed a large variety of two-dimensional phase boundaries for the first and second monolayer (Fig. 1). There are three distinct solid phases, labelled a, 13 and 5. The a region corresponds to a bulk 02, which is antiferromagnetic and the (3 region to (3 bulk 02, which is paramagnetic. The a, S transition line occurs at monolayer completion. The detailed nature of the S region is not yet known, it is possibly a phase of magnetostrictive fluctuations [4]. The present investigation is related to the 6— fluid transition line. With special emphasis on further characterizing this phase boundary we undertook a heat capacity study of the first monolayer. The essential features of the neutron diffraction findings were substantiated. The other details of the phase diagram require further investigations.
weak link connected samples, one unknown (Si) and one known (S2). S1 was replaced for the present investigation by a thin-walled adsorption cell, machined out of pure copper, which contained small disks of Grafoil. To achieve rapid thermal equilibrium the disks were embedded into a small amount of granulated copper. The total area the for knee the first monolayer was 2 asadsorption deduced from in the adsorption 224 m isotherm which occured at about 86 cm3 STP 02. This corresponds to 53.4 cm3 STP for the first monolayer of N 2 g~.The giving m volume 862,cm3 STPa specific adsorbedarea 02 of is 30 equivalent to a filling of p = 1.61 [4]. Filling is defined as the adsorbed gas measured in units of that gas amount which is needed to complete a monolayer of the commensurate ‘~J3structure, i.e. above every third carbon hexagon of the graphite surface a gas molecule is located [1], even if this structure is not found for adsorbed 02 layers. The Grafoil sample was degassed at 450°Cunder vacuum for several days and then handled under argon atmosphere. The heat capacity was calculated from the raw data as follows (fornotation refer to [5]). In the case of the degassed cell:
c
1 = ~(C2 + C02), C02 ~ 0 (1) (C1 heat capacity of the adsorption cell including Grafoil disks and addenda, C2 heat capacity of the reference sample S2, C02 heat capacity of the addenda of sample ~2, C02 represents small amounts of manganin wire, GE varnish, one half of the weak link and aluminium
2. EXPERIMENTAL
foil. It is negligible compared to the large reference sample S2, which consisted of 11.2 g copper. Copper is
The twin calorimeter used has been described in detail earlier [5]. The calorimeter consisted of two by a
especially suitable for the reference sample, because for temperatures above 10K its specific heat depends only 229
230
ADSORBED LAYERS OF 02 ON GRAPHITE
Vol.33, No.2
o~3b~5o T(K) 40
Fig. 1. Phase diagram for the first and second monolayer of 02 adsorbed on Grafoil as determined by neutron diffraction studies due to McTaque and Nielsen [4]. p is the filling as defined in text. The dots indicate the phase boundary due to this work (refer to Chapter 3).
20
0,7 23,5
000 0
0
24,5
25,5 —
26,5 1(K)
0
0
0
0
0
0
0
0
0 0
0,3
0
0
0
0 0
0
0
00
0
0
0
Fig. 3. Heat capacity of the 02 fIlm (p = 0.45) at phase transition in units of kb as a function of temperature.
00
0 0
The temperature resolution for the results reported here was about 60 mK, the accuracy ±5%. The accuracy and temperature resolution of the absolute specific heat measuring methods, however, is not yet achieved [2], mainly due to the finite voltage resolution of the preamplifier which amplifies the voltage needed to be known for determination the heat flux through the weak link. An improved preamplifier is in preparation. 3. RESULTS
0
0
0 00
0,1
____________________________________ 5,0
The raw data needed for calculation the heat capacity of the 02 film corresponding to a filling of p = 0.45 are given in Fig. 2. At the top of the figure there are plotted the two quantitiesA 1 and A2 in
2,5
0 23,5
arbitrary units as functions of temperature. A1 and A2 are proportional to the integrated heat fluxes Q01 and Qo2 [51 The slight scattering of the measuring points is mainly due to the zero instability of the preamplifier. .
24,5
25,5
1(K) 26,5
Fig. 2. Raw data as a function of temperature needed for calculation the heat capacity for the filling ~ = 0.45 as explained in text;
Nevertheless, the S function shaped singularity is clearly revealed. At the bottom of the figure there is plotted the accompanying quotient ,f of the integrated heat fluxes as a function of temperature. The ~ values of the empty cell are given too. The heat capacity Cfilm is calculated from equation
little on the special preparation and composition [6]). In the case of adsorption of 02
c.film Hence C .
film
+ c1
=
7?
(~f
—
2•
~)C 2
~ (3~ “
Onceto thecalculate n-valuesCfof thefrom empty easy jim ~7X cell and are C known it is very 2. The detailed temperature dependence of the heat capacity of the empty cell need not to be known.
/
(3) and is shown in Fig. 3. We got this result for a fillmg of p = 0.45. It should be pointed out that the heat capacity for one particle of 02 rises as high as 69kb at the phase transition temperature. The other investigated filling oftransition p = 0.3 shows similar features (Ctiim = 7kb at phase temperature). At a filling of S p = 1.69 the singularity disappeared and the residual vapour pressure of the adsorbate increased from 8 x 10~mbarfor fillings below p = 1.69 to values
Vol. 33,No. 2
ADSORBED LAYERS OF 02 ON GRAPHITE
above 1 mbar (outside the measuring range of the used instrument), indicating completion of the first monolayer. 4. DISCUSSION In principle there are two possibilities for the coexistence of two phases at the phase boundary in question. The first possibility is a film composed of condensed liquid or solid 02 in equilibrium with its low density two-dimensional vapour. Secondly one could think of a solid film phase coexisting with a twodimensional fluid. The first possibility was ruled out by the findings of the neutron diffraction study. For the possibility left one has to distinguish between two cases, namely, surface phase melting at constant area or surface phase melting at constant spreading pressure [1]. In the former case the specific heat shows a distinct maximum at the phase transition temperature but remains fmite. The specific heat jumps to higher values when the melting starts and drops down to nearly the same value as before when the melting process is fmished. In the latter case one is concerned with melting at the quadrupole point of the adsorbate, i.e. at the triple point of the monolayer. When the system is heated the temperature remains fixed as soon as the triple point is reached, because the whole energy pumped from outside into the system will be used for melting until the last trace of the solid phase has been disappeared. Therefore, the specific
231
heat must reveal an infinite jump at the triple point temperature ,just as is the case for C~in a first order process in a three.dimensional system. Because of the observed large jump of the specific heat at the phase transition temperature (refer to Fig. 3), we believe that the peaks are consistent with ideal S function shaped singularities degraded to some extend by instrumental resolution and perhaps some substrate heterogeneities. Therefore, the underlying phase transition is interpreted as melting at the triple point of the two-dimensional system, the final classification, how. ever, requires further efforts. Acknowledgements The authors wish to thank E.F. Wassermann for his current interest, constructive criticism and expert advice. .—
REFERENCES 1. 2. 3. 4. 5. 6.
J.G. Dash, Films on Solid Surfaces. Academic Press, New York (1975). G.B. Huff&J.G. Dash,J. Low Temp. Phys. 24, 155 (1976). M. Bretz, J.G. Dash, D.C. Hickernell, E.0. Mclean & 0.E. Vilches,Phys. Rev. A8, 1589 (1973). J.P. McTaque & M. Nielsen,Phys. Rev. Lett. 37, 596 (1976). R. Marx, Rev. Phys. Appi. 13,298 (1978). Y.S. Touloukian & E.H. Buyco, Thermophysical Properties ofMatter, Vol. 4. IFI/Plenum, New York, Washington (1970).
weak link connected samples, one unknown (Si) and one known (S2). S1 was replaced for the present investigation by a thin-walled adsorption cell, machined out of pure copper, which contained small disks of Grafoil. To achieve rapid thermal equilibrium the disks were embedded into a small amount of granulated copper. The total area the for knee the first monolayer was 2 asadsorption deduced from in the adsorption 224 m isotherm which occured at about 86 cm3 STP 02. This corresponds to 53.4 cm3 STP for the first monolayer of N 2 g~.The giving m volume 862,cm3 STPa specific adsorbedarea 02 of is 30 equivalent to a filling of p = 1.61 [4]. Filling is defined as the adsorbed gas measured in units of that gas amount which is needed to complete a monolayer of the commensurate ‘~J3structure, i.e. above every third carbon hexagon of the graphite surface a gas molecule is located [1], even if this structure is not found for adsorbed 02 layers. The Grafoil sample was degassed at 450°Cunder vacuum for several days and then handled under argon atmosphere. The heat capacity was calculated from the raw data as follows (fornotation refer to [5]). In the case of the degassed cell:
c
1 = ~(C2 + C02), C02 ~ 0 (1) (C1 heat capacity of the adsorption cell including Grafoil disks and addenda, C2 heat capacity of the reference sample S2, C02 heat capacity of the addenda of sample ~2, C02 represents small amounts of manganin wire, GE varnish, one half of the weak link and aluminium
2. EXPERIMENTAL
foil. It is negligible compared to the large reference sample S2, which consisted of 11.2 g copper. Copper is
The twin calorimeter used has been described in detail earlier [5]. The calorimeter consisted of two by a
especially suitable for the reference sample, because for temperatures above 10K its specific heat depends only 229
230
ADSORBED LAYERS OF 02 ON GRAPHITE
Vol.33, No.2
o~3b~5o T(K) 40
Fig. 1. Phase diagram for the first and second monolayer of 02 adsorbed on Grafoil as determined by neutron diffraction studies due to McTaque and Nielsen [4]. p is the filling as defined in text. The dots indicate the phase boundary due to this work (refer to Chapter 3).
20
0,7 23,5
000 0
0
24,5
25,5 —
26,5 1(K)
0
0
0
0
0
0
0
0
0 0
0,3
0
0
0
0 0
0
0
00
0
0
0
Fig. 3. Heat capacity of the 02 fIlm (p = 0.45) at phase transition in units of kb as a function of temperature.
00
0 0
The temperature resolution for the results reported here was about 60 mK, the accuracy ±5%. The accuracy and temperature resolution of the absolute specific heat measuring methods, however, is not yet achieved [2], mainly due to the finite voltage resolution of the preamplifier which amplifies the voltage needed to be known for determination the heat flux through the weak link. An improved preamplifier is in preparation. 3. RESULTS
0
0
0 00
0,1
____________________________________ 5,0
The raw data needed for calculation the heat capacity of the 02 film corresponding to a filling of p = 0.45 are given in Fig. 2. At the top of the figure there are plotted the two quantitiesA 1 and A2 in
2,5
0 23,5
arbitrary units as functions of temperature. A1 and A2 are proportional to the integrated heat fluxes Q01 and Qo2 [51 The slight scattering of the measuring points is mainly due to the zero instability of the preamplifier. .
24,5
25,5
1(K) 26,5
Fig. 2. Raw data as a function of temperature needed for calculation the heat capacity for the filling ~ = 0.45 as explained in text;
Nevertheless, the S function shaped singularity is clearly revealed. At the bottom of the figure there is plotted the accompanying quotient ,f of the integrated heat fluxes as a function of temperature. The ~ values of the empty cell are given too. The heat capacity Cfilm is calculated from equation
little on the special preparation and composition [6]). In the case of adsorption of 02
c.film Hence C .
film
+ c1
=
7?
(~f
—
2•
~)C 2
~ (3~ “
Onceto thecalculate n-valuesCfof thefrom empty easy jim ~7X cell and are C known it is very 2. The detailed temperature dependence of the heat capacity of the empty cell need not to be known.
/
(3) and is shown in Fig. 3. We got this result for a fillmg of p = 0.45. It should be pointed out that the heat capacity for one particle of 02 rises as high as 69kb at the phase transition temperature. The other investigated filling oftransition p = 0.3 shows similar features (Ctiim = 7kb at phase temperature). At a filling of S p = 1.69 the singularity disappeared and the residual vapour pressure of the adsorbate increased from 8 x 10~mbarfor fillings below p = 1.69 to values
Vol. 33,No. 2
ADSORBED LAYERS OF 02 ON GRAPHITE
above 1 mbar (outside the measuring range of the used instrument), indicating completion of the first monolayer. 4. DISCUSSION In principle there are two possibilities for the coexistence of two phases at the phase boundary in question. The first possibility is a film composed of condensed liquid or solid 02 in equilibrium with its low density two-dimensional vapour. Secondly one could think of a solid film phase coexisting with a twodimensional fluid. The first possibility was ruled out by the findings of the neutron diffraction study. For the possibility left one has to distinguish between two cases, namely, surface phase melting at constant area or surface phase melting at constant spreading pressure [1]. In the former case the specific heat shows a distinct maximum at the phase transition temperature but remains fmite. The specific heat jumps to higher values when the melting starts and drops down to nearly the same value as before when the melting process is fmished. In the latter case one is concerned with melting at the quadrupole point of the adsorbate, i.e. at the triple point of the monolayer. When the system is heated the temperature remains fixed as soon as the triple point is reached, because the whole energy pumped from outside into the system will be used for melting until the last trace of the solid phase has been disappeared. Therefore, the specific
231
heat must reveal an infinite jump at the triple point temperature ,just as is the case for C~in a first order process in a three.dimensional system. Because of the observed large jump of the specific heat at the phase transition temperature (refer to Fig. 3), we believe that the peaks are consistent with ideal S function shaped singularities degraded to some extend by instrumental resolution and perhaps some substrate heterogeneities. Therefore, the underlying phase transition is interpreted as melting at the triple point of the two-dimensional system, the final classification, how. ever, requires further efforts. Acknowledgements The authors wish to thank E.F. Wassermann for his current interest, constructive criticism and expert advice. .—
REFERENCES 1. 2. 3. 4. 5. 6.
J.G. Dash, Films on Solid Surfaces. Academic Press, New York (1975). G.B. Huff&J.G. Dash,J. Low Temp. Phys. 24, 155 (1976). M. Bretz, J.G. Dash, D.C. Hickernell, E.0. Mclean & 0.E. Vilches,Phys. Rev. A8, 1589 (1973). J.P. McTaque & M. Nielsen,Phys. Rev. Lett. 37, 596 (1976). R. Marx, Rev. Phys. Appi. 13,298 (1978). Y.S. Touloukian & E.H. Buyco, Thermophysical Properties ofMatter, Vol. 4. IFI/Plenum, New York, Washington (1970).