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Dissipation in submonolayer helium films adsorbed on graphite
PflYSICA
Physica B 194-196 (1994) 681--682 North-Holland
Dissipation in submonolayer helium films adsorbed on graphite P. Mohandas, B. P. Cowan, C. P. Lusher and J. Saunders Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham Hill, Egham, Surrey TW20 0EX, UK.
We have investigated the influence of an adsorbed helium film on the damping of a torsional oscillator containing exfoliated graphite. The damping depends crucially on the phase of the adsorbed film; in the incommensurate solid a significant dissipation is m e a s u r e d which increases with decreasing temperature. The origin is believed to be internal friction in the two dimensional solid rather than surface friction. The results provide a novel probe of the 2D melting transition. They are being extended to lower temperatures, including an investigation of the domain wall solid phase in order to elucidate the dissipation mechanism. 1. I N T R O D U C T I O N
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The phase diagrams for submonolayer helium films adsorbed on graphite are fairly well established, due to measurements of heat capacity, 1 nuclear magnetic resonance 2 and neutron scattering) Here we have used a conventional torsional oscillator to investigate energy dissipation in the film, providing a new probe of its dynamics. We have attempted to investigate the effect of surface morphology by using two different substrates, Grafoil and UCAR ZYX, 4 the latter having uniform platelets believed to be larger in diameter b y a factor of ten. 2. R E S U L T S The energy dissipation and period shift due to the adsorbed film were inferred from measurements of the amplitude and period of the oscillator, which had a resonant frequency ~ l k H z and Q - 2 x 105 . The experimental details have been described elsewhere. 5 The period shift AP at 4K was observed to be nearly proportional to the mass of the film, showing that the film is well locked to the substrate at all densities. This indicates
i
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T/K Figure 1. (i) Energy dissipation versus temperature for 4He on Grafoil, (ii) 4He on UCAR ZYX. Film densities are the following; (a) 0.030/~-2, (b) 0.034]k -2, (c) 0.064~ "2, (d) 0.094/~ -2. that the oscillator is in the regime or~ << 1, where x is some characteristic relaxation time of the film-substrate coupling. The contribution of the film to Q-] was
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSD1 0921-4526(93)E0921-3
682 inferred by subtracting the background due to the empty oscillator from the total measured Qd. A selection of data is illustrated in Figure 1. Measurements taken for 3He films adsorbed on Grafoil showed little variation from the data on 4He. On the Grafoil substrate, a broad maximum in dissipation was observed at a temperature near 3K for the low density fluid coverages, such as 0.030/k-2. This feature displays a systematic dependence on film density, the temperature of the maximum gradually decreases and its magnitude increases with increasing density. The peak persists up to and beyond the coverage corresponding to perfect registry (0.064A'2), and there is no discernable signature of the order-disorder transition at this particular coverage. On the ZYX substrate, a significantly smaller dissipation was observed for the corresponding coverage range. For the higher density incommensurate solid films, such as at 0.094/~-2, there is a large increase in dissipation for temperatures below the melting temperature of the incommensurate solid. The density dependence of this feature has led us to conclude that the dissipation is dependent upon the phase of the adsorbed film. The magnitude of Q-1 was found to be approximately the same on both Grafoil and ZYX substrates at the lowest temperatures. Consider a description of the dissipation in the general form,
the film mass, an extra temperature dependent deviation in period AP' away from full mass loading was observed, the period decreasing with decreasing temperature. The magnitude of this shift, at 0.094/k -2 and the lowest temperatures investigated, was - l n s for the Grafoil substrate, whereas AP ~ 150ns. AP" was found to be approximately proportional to Q-1 for the solid film. The constant of proportionality was essentially coverage independent. The fact that they have approximately the same temperature dependence suggests that Qd and AP" have the same origin and that • is temperature independent. However at the corresponding film densities on ZYX, AP" was unobservable (within the resolution limits of the background subtraction of _+ 0.1ns) which is inconsistent with the simplest model. 3. CONCLUSION We have established that the dissipation in a submonolayer film is significant in the incommensurate solid, where it increases with increasing surface density and decreasing temperature. This effect depends strongly upon surface morphology. Extension of these measurements to 100mK and below, will attempt to locate the dissipation maximum and permit an investigation of the dynamics of the partially registered or domain wall solids.
REFERENCES Qfilm
0
where ~ is some function of the variables of the system, o~ is the frequency, Po is the oscillator period and x is some model dependent characteristic time constant. As AP/P 0 is smaller by a factor of 19 for 4He on ZYX owing to the small adsorption area compared to Grafoil, then our results suggest that • must increase by a similar factor, i f .~ is independent of the surface morphology. In addition to the period shift AP due to
1. D. S. Greywall, Phys.Rev.B 47, 309 (1993). 2. M. G. Richards, J. Phys (Paris), Colloq. 39, C6-1342 (1978). 3. H. J. Lauter et. al, Physica B 165-166, 597 (1990). 4. Grafoil and UCAR ZYX are trademarks of Union Carbide. 5. P. Mohandas, C. Lusher, B. Cowan and J. Saunders, J. Low Temp. Phys. 89, 613 (1992).
Physica B 194-196 (1994) 681--682 North-Holland
Dissipation in submonolayer helium films adsorbed on graphite P. Mohandas, B. P. Cowan, C. P. Lusher and J. Saunders Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham Hill, Egham, Surrey TW20 0EX, UK.
We have investigated the influence of an adsorbed helium film on the damping of a torsional oscillator containing exfoliated graphite. The damping depends crucially on the phase of the adsorbed film; in the incommensurate solid a significant dissipation is m e a s u r e d which increases with decreasing temperature. The origin is believed to be internal friction in the two dimensional solid rather than surface friction. The results provide a novel probe of the 2D melting transition. They are being extended to lower temperatures, including an investigation of the domain wall solid phase in order to elucidate the dissipation mechanism. 1. I N T R O D U C T I O N
3.0
. . . .
J
. . . .
i
. . . .
(~) ,
The phase diagrams for submonolayer helium films adsorbed on graphite are fairly well established, due to measurements of heat capacity, 1 nuclear magnetic resonance 2 and neutron scattering) Here we have used a conventional torsional oscillator to investigate energy dissipation in the film, providing a new probe of its dynamics. We have attempted to investigate the effect of surface morphology by using two different substrates, Grafoil and UCAR ZYX, 4 the latter having uniform platelets believed to be larger in diameter b y a factor of ten. 2. R E S U L T S The energy dissipation and period shift due to the adsorbed film were inferred from measurements of the amplitude and period of the oscillator, which had a resonant frequency ~ l k H z and Q - 2 x 105 . The experimental details have been described elsewhere. 5 The period shift AP at 4K was observed to be nearly proportional to the mass of the film, showing that the film is well locked to the substrate at all densities. This indicates
i
. . . .
(i)
2.0
C3
1.0 <:3
(c)
C3
0 (b)
t-.
3.0
~:.
. . . .
i
. . . .
i
. . . .
!
. . . .
ao (:~
2.0
(d).
1.0 p-
<3 (c)
0
x,--
(o) 1 -
i
. . . .
"C~.o
i
2.0
. . . .
i
. . . .
3.0
I
4.0
. . . .
5.0
T/K Figure 1. (i) Energy dissipation versus temperature for 4He on Grafoil, (ii) 4He on UCAR ZYX. Film densities are the following; (a) 0.030/~-2, (b) 0.034]k -2, (c) 0.064~ "2, (d) 0.094/~ -2. that the oscillator is in the regime or~ << 1, where x is some characteristic relaxation time of the film-substrate coupling. The contribution of the film to Q-] was
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSD1 0921-4526(93)E0921-3
682 inferred by subtracting the background due to the empty oscillator from the total measured Qd. A selection of data is illustrated in Figure 1. Measurements taken for 3He films adsorbed on Grafoil showed little variation from the data on 4He. On the Grafoil substrate, a broad maximum in dissipation was observed at a temperature near 3K for the low density fluid coverages, such as 0.030/k-2. This feature displays a systematic dependence on film density, the temperature of the maximum gradually decreases and its magnitude increases with increasing density. The peak persists up to and beyond the coverage corresponding to perfect registry (0.064A'2), and there is no discernable signature of the order-disorder transition at this particular coverage. On the ZYX substrate, a significantly smaller dissipation was observed for the corresponding coverage range. For the higher density incommensurate solid films, such as at 0.094/~-2, there is a large increase in dissipation for temperatures below the melting temperature of the incommensurate solid. The density dependence of this feature has led us to conclude that the dissipation is dependent upon the phase of the adsorbed film. The magnitude of Q-1 was found to be approximately the same on both Grafoil and ZYX substrates at the lowest temperatures. Consider a description of the dissipation in the general form,
the film mass, an extra temperature dependent deviation in period AP' away from full mass loading was observed, the period decreasing with decreasing temperature. The magnitude of this shift, at 0.094/k -2 and the lowest temperatures investigated, was - l n s for the Grafoil substrate, whereas AP ~ 150ns. AP" was found to be approximately proportional to Q-1 for the solid film. The constant of proportionality was essentially coverage independent. The fact that they have approximately the same temperature dependence suggests that Qd and AP" have the same origin and that • is temperature independent. However at the corresponding film densities on ZYX, AP" was unobservable (within the resolution limits of the background subtraction of _+ 0.1ns) which is inconsistent with the simplest model. 3. CONCLUSION We have established that the dissipation in a submonolayer film is significant in the incommensurate solid, where it increases with increasing surface density and decreasing temperature. This effect depends strongly upon surface morphology. Extension of these measurements to 100mK and below, will attempt to locate the dissipation maximum and permit an investigation of the dynamics of the partially registered or domain wall solids.
REFERENCES Qfilm
0
where ~ is some function of the variables of the system, o~ is the frequency, Po is the oscillator period and x is some model dependent characteristic time constant. As AP/P 0 is smaller by a factor of 19 for 4He on ZYX owing to the small adsorption area compared to Grafoil, then our results suggest that • must increase by a similar factor, i f .~ is independent of the surface morphology. In addition to the period shift AP due to
1. D. S. Greywall, Phys.Rev.B 47, 309 (1993). 2. M. G. Richards, J. Phys (Paris), Colloq. 39, C6-1342 (1978). 3. H. J. Lauter et. al, Physica B 165-166, 597 (1990). 4. Grafoil and UCAR ZYX are trademarks of Union Carbide. 5. P. Mohandas, C. Lusher, B. Cowan and J. Saunders, J. Low Temp. Phys. 89, 613 (1992).