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Low temperature hydrogen which has not solidified
Physica B 165&166 North-Holland
LOW
(1990)
TEMPERATURE
D F BREWER, University
569-570
HYDROGEN
J RAJENDRA,
of Sussex,
Physics
WHICH
N SHARMA Division,
HAS NOT
and
Brighton,
SOLIDIFIED
A L THOMSON
Sussex
BNI
9QH,
Great
Britain
We have measured the specific heat of hydrogen inside the small pores of Vycor glass at temperatures extending down to 4K. The latent heat associated with freezing when cooling, and with melting when warming, is clearly seen. When this latent heat is compared with that of bulk hydrogen it appears that only a fraction of the hydrogen inside our pores takes part in the solid-liquid transition. Furthermore the specific heat measured at temperatures below the latent heat anomaly is clearly much larger than the specific heat of the bulk solid phase. It is also much larger than the Ta specific heat expected for the monolayer of hydrogen next to the glass wall. If the large specific heat is due to phonon modes, they are unusually soft. It it interesting that the data also fit a roton-type specific heat, with a roton gap of about 23K.
Over the past few years interest in the properties of hydrogen in confined geometries has been steadily growing. It has already been established that the freezing and melting properties are considerably altered and the experimental situation (1) shows that, inside the porous media examined so far, the melting and freezing temperatures are different from each other and both are depressed to lower temperatures than those of the bulk phases. These lowered temperatures at which the solid- liquid transition takes place imply that the liquid phase exists at anomalously low temperatures inside small pores, and a principal reason for research on this system is that this liquid phase might exhibit superfluid properties. One of the first experiments (2) which sought such a phase was a flow result although experiment which produced a null similar experiments (3) on helium in several porous media have shown the flow expected of a superfluid. In this present paper we have measured the specific heat of hydrogen inside Vycor porous glass while both warming and cooling. The latent heat peaks associated with both melting and freezing were carefully measured with the liquid-solid and the entropy associated transition determined. In addition the temperature dependence and magnitude of the specific heat at temperatures below the latent heat peaks has been determined and indicates clearly that a considerable amount of the hydrogen sample does not exist in a simple solid phase. heat capacity in which the The apparatus made has a berylium-copper were measurements sample chamber which was filled with Vycor glass. On top of the chamber a needle valve was situated and this ensured that the amount of sample hydrogen The remained constant throughout each experiment. hydrogen entirely filled the Vycor pores and the space chamber and the around them inside the sample molecular state of the hydrogen was believed to be 100% para. Shown in Figure 1 is a log-log plot of the specific heat of our confined hydrogen as a function of temperature measured while warming. Also displayed in the graph is a solid line showing
0921-4526/90/$03.50
@ 1990 - El sevier Science
Publishers
-11 1, 0.6
0.8
LOG(T)
1-o
12
FIGURE 1 The logarithm of our specific heat plotted against the logarithm of the temperature. The dashed line represents a best fit for the lower temperature points. The dotted line represents the specific heat of the first adsorbed layer. The solid line represents the specific heat of hydrogen in its bulk phase. line the specific heat of bulk hydrogen. The vertical indicates the position of the triple point: there is good agreement between our data and the specific heat of liquid hydrogen at the highest temperatures. A notable feature in Figure 1 is the large anomaly associated with part of the hydrogen melting which occurs substantially below the bulk triple point, around 11.2K. In a similar experiment when cooling, the peak of the anomaly was shifted downwards to about lOK, and this behaviour is similar to that already observed by another group (1). At temperatures well below the melting anomaly, the specific heat is much larger than that of bulk solid hydrogen, and the temperature dependence is close to T2, unlike the solid dependence which is closer to T 2. A computer fit has been made to this low temperature specific heat and is represented by the dashed line which follows the equation
B.V. (North-Holland)
D.F. Brewer, J. Rajendra, N. Sharma, A.L. Thomson
570
c, = 2 log T - 1.37
log which
may be C,
re-written
= 4.3
(1)
as
x 10e2T2
Jmole-‘K-l
(2)
It is therefore quite clear that a considerable part of our hydrogen does not exist in an ordinary bulk phase and it is interesting to speculate on what the character of this phase must be. A specific heat with a T 2 dependence has previously been observed for a monolayer of helium in Vycor (4) with a Debye 8D of about 28K. If we analyse the hydrogen results in the same way and estimate flD = 120K, close to that of bulk solid, 122K (5), the result is the dotted line in figure 1. It is apparent that our data are higher than this line by a factor of about 3. The data of Figure 1 were derived on the basis that all of the sample is in some homogeneous phase. Clearly this is not the case since the part of the sample that melts in the region of 11K is presumably In an attempt in a solid phase at lower temperatures. to ascertain the amount of hydrogen taking part in the melting process we have integrated the data in the region of the latent heat peak of the melting inside the pores and have hence derived the amount of entropy associated with the melting. The peak region was identified as starting where the specific heat points began to increase with temperature faster than Tr and ending where they assumed a fairly constant value. = 2.5 _I mole-lK-r for the The result is AS= 1.7 warming (melting) experiment and lsu = J mole-‘K-i for the cooling (freezing) experiment. Both of these values are very far below the entropy difference of 8.5 J mole-‘K-i which exists in the bulk phase (6) at the triple point and hence it is reasonable to assume that only a fraction of our sample, probably less than on half, takes part in the melting process. However, since this fraction should have a small heat capacity at low temperatures, the must have a remaining part of the sample correspondingly larger specific heat. 86
3 0.10
0.14
0.18
0.22
4 (X-3
The natural logarit??oy(&T312) plotted agarnst The straight line represents a inverse temperature. experimental points and its slope best fit to the indicates a roton gap energy of about 23K.
Although our data give quite a good fit on a T 2 plot, it is interesting to take a different approach and to examine the extent to which they might be excitations are explained by a model in which the rotons. Evidence has previously been obtained for the existence of rotons in helium inside Vycor glass at low pressures (7),(g) where plots of In(CvTs/2) versus T-l satisfactory fit to experimental data. showed a in Figure 2 a similar plot for Accordingly we present our hydrogen data and the fit is reasonably good with the slope of the line indicating a gap energy for the This is considerably rotons of approximately 23K. larger than the values of about 6K to 7K of the confined helium but, bearing in mind the larger Van der Waals forces in hydrogen, is not unreasonable. Of course, rotons are normally regarded as excitations that exist in the superfluid phase of liquid helium. CONCLUSIONS The first result of this work is that the amount of entropy change associated with the melting of the hydrogen inside the porous glass indicates that a considerable fraction does not take part in this process. The second result is that at our lowest temperatures this fraction has a comparatively large specific heat and we can interpret this in different ways. The fact that it may be fitted to a T 2 dependence points to the possibility that it is produced by some interface layer(s) in which two dimensional phonons may prove to be the main excitations. However the data also appear to fit an analysis in which rotons are the principal excitations. On the relative quality of the fits to the two different ways of plotting our data it is, at this not clear to regard one as being stage, significantly better than the other. Clearly to resolve this it will be necessary to acquire more accurate data over a wider temperature range. ACKNOWLEDGEMENTS The authors wish support of SERC grant
to gratefully number GR/F
acknowledge 51845.
the
REFERENCES. (1) J.L. Tell and H.J. Maris, Phy.Rev. B Vol 28, (1983) 5122. (2) M. Bretz and A.L. Thomson, Phy. Rev, B Vol 24, (1981) 467. (3) D.F. Brewer, Cao Lie&o, C. Girit and J.D. Reppy, Physica 107B (1981) 583. (4) D.F. Brewer, A. Evenson and A.L. Thomson, J. Low Temp. Phys. Vol 3, (1970) 603. (5) R.J. Roberts and J.G. Daunt, J. Low Temp. Phys. Vol 6 (1972) 97. (6) R.F. Dwyer, G.A. Cook, B.M. Shields and D.H. Stellrecht, J.Chem. Phys. Vol 42, (1%5) 3809. (7) D.F. Brewer, A.J. Symonds and A.L. Thomson Phys. Rev. L&t. Vol 15, (1965) 182. (8) R.H. Tait and J.D. Reppy, Phys. Rev. B Vol 20, (1979) 997.
LOW
(1990)
TEMPERATURE
D F BREWER, University
569-570
HYDROGEN
J RAJENDRA,
of Sussex,
Physics
WHICH
N SHARMA Division,
HAS NOT
and
Brighton,
SOLIDIFIED
A L THOMSON
Sussex
BNI
9QH,
Great
Britain
We have measured the specific heat of hydrogen inside the small pores of Vycor glass at temperatures extending down to 4K. The latent heat associated with freezing when cooling, and with melting when warming, is clearly seen. When this latent heat is compared with that of bulk hydrogen it appears that only a fraction of the hydrogen inside our pores takes part in the solid-liquid transition. Furthermore the specific heat measured at temperatures below the latent heat anomaly is clearly much larger than the specific heat of the bulk solid phase. It is also much larger than the Ta specific heat expected for the monolayer of hydrogen next to the glass wall. If the large specific heat is due to phonon modes, they are unusually soft. It it interesting that the data also fit a roton-type specific heat, with a roton gap of about 23K.
Over the past few years interest in the properties of hydrogen in confined geometries has been steadily growing. It has already been established that the freezing and melting properties are considerably altered and the experimental situation (1) shows that, inside the porous media examined so far, the melting and freezing temperatures are different from each other and both are depressed to lower temperatures than those of the bulk phases. These lowered temperatures at which the solid- liquid transition takes place imply that the liquid phase exists at anomalously low temperatures inside small pores, and a principal reason for research on this system is that this liquid phase might exhibit superfluid properties. One of the first experiments (2) which sought such a phase was a flow result although experiment which produced a null similar experiments (3) on helium in several porous media have shown the flow expected of a superfluid. In this present paper we have measured the specific heat of hydrogen inside Vycor porous glass while both warming and cooling. The latent heat peaks associated with both melting and freezing were carefully measured with the liquid-solid and the entropy associated transition determined. In addition the temperature dependence and magnitude of the specific heat at temperatures below the latent heat peaks has been determined and indicates clearly that a considerable amount of the hydrogen sample does not exist in a simple solid phase. heat capacity in which the The apparatus made has a berylium-copper were measurements sample chamber which was filled with Vycor glass. On top of the chamber a needle valve was situated and this ensured that the amount of sample hydrogen The remained constant throughout each experiment. hydrogen entirely filled the Vycor pores and the space chamber and the around them inside the sample molecular state of the hydrogen was believed to be 100% para. Shown in Figure 1 is a log-log plot of the specific heat of our confined hydrogen as a function of temperature measured while warming. Also displayed in the graph is a solid line showing
0921-4526/90/$03.50
@ 1990 - El sevier Science
Publishers
-11 1, 0.6
0.8
LOG(T)
1-o
12
FIGURE 1 The logarithm of our specific heat plotted against the logarithm of the temperature. The dashed line represents a best fit for the lower temperature points. The dotted line represents the specific heat of the first adsorbed layer. The solid line represents the specific heat of hydrogen in its bulk phase. line the specific heat of bulk hydrogen. The vertical indicates the position of the triple point: there is good agreement between our data and the specific heat of liquid hydrogen at the highest temperatures. A notable feature in Figure 1 is the large anomaly associated with part of the hydrogen melting which occurs substantially below the bulk triple point, around 11.2K. In a similar experiment when cooling, the peak of the anomaly was shifted downwards to about lOK, and this behaviour is similar to that already observed by another group (1). At temperatures well below the melting anomaly, the specific heat is much larger than that of bulk solid hydrogen, and the temperature dependence is close to T2, unlike the solid dependence which is closer to T 2. A computer fit has been made to this low temperature specific heat and is represented by the dashed line which follows the equation
B.V. (North-Holland)
D.F. Brewer, J. Rajendra, N. Sharma, A.L. Thomson
570
c, = 2 log T - 1.37
log which
may be C,
re-written
= 4.3
(1)
as
x 10e2T2
Jmole-‘K-l
(2)
It is therefore quite clear that a considerable part of our hydrogen does not exist in an ordinary bulk phase and it is interesting to speculate on what the character of this phase must be. A specific heat with a T 2 dependence has previously been observed for a monolayer of helium in Vycor (4) with a Debye 8D of about 28K. If we analyse the hydrogen results in the same way and estimate flD = 120K, close to that of bulk solid, 122K (5), the result is the dotted line in figure 1. It is apparent that our data are higher than this line by a factor of about 3. The data of Figure 1 were derived on the basis that all of the sample is in some homogeneous phase. Clearly this is not the case since the part of the sample that melts in the region of 11K is presumably In an attempt in a solid phase at lower temperatures. to ascertain the amount of hydrogen taking part in the melting process we have integrated the data in the region of the latent heat peak of the melting inside the pores and have hence derived the amount of entropy associated with the melting. The peak region was identified as starting where the specific heat points began to increase with temperature faster than Tr and ending where they assumed a fairly constant value. = 2.5 _I mole-lK-r for the The result is AS= 1.7 warming (melting) experiment and lsu = J mole-‘K-i for the cooling (freezing) experiment. Both of these values are very far below the entropy difference of 8.5 J mole-‘K-i which exists in the bulk phase (6) at the triple point and hence it is reasonable to assume that only a fraction of our sample, probably less than on half, takes part in the melting process. However, since this fraction should have a small heat capacity at low temperatures, the must have a remaining part of the sample correspondingly larger specific heat. 86
3 0.10
0.14
0.18
0.22
4 (X-3
The natural logarit??oy(&T312) plotted agarnst The straight line represents a inverse temperature. experimental points and its slope best fit to the indicates a roton gap energy of about 23K.
Although our data give quite a good fit on a T 2 plot, it is interesting to take a different approach and to examine the extent to which they might be excitations are explained by a model in which the rotons. Evidence has previously been obtained for the existence of rotons in helium inside Vycor glass at low pressures (7),(g) where plots of In(CvTs/2) versus T-l satisfactory fit to experimental data. showed a in Figure 2 a similar plot for Accordingly we present our hydrogen data and the fit is reasonably good with the slope of the line indicating a gap energy for the This is considerably rotons of approximately 23K. larger than the values of about 6K to 7K of the confined helium but, bearing in mind the larger Van der Waals forces in hydrogen, is not unreasonable. Of course, rotons are normally regarded as excitations that exist in the superfluid phase of liquid helium. CONCLUSIONS The first result of this work is that the amount of entropy change associated with the melting of the hydrogen inside the porous glass indicates that a considerable fraction does not take part in this process. The second result is that at our lowest temperatures this fraction has a comparatively large specific heat and we can interpret this in different ways. The fact that it may be fitted to a T 2 dependence points to the possibility that it is produced by some interface layer(s) in which two dimensional phonons may prove to be the main excitations. However the data also appear to fit an analysis in which rotons are the principal excitations. On the relative quality of the fits to the two different ways of plotting our data it is, at this not clear to regard one as being stage, significantly better than the other. Clearly to resolve this it will be necessary to acquire more accurate data over a wider temperature range. ACKNOWLEDGEMENTS The authors wish support of SERC grant
to gratefully number GR/F
acknowledge 51845.
the
REFERENCES. (1) J.L. Tell and H.J. Maris, Phy.Rev. B Vol 28, (1983) 5122. (2) M. Bretz and A.L. Thomson, Phy. Rev, B Vol 24, (1981) 467. (3) D.F. Brewer, Cao Lie&o, C. Girit and J.D. Reppy, Physica 107B (1981) 583. (4) D.F. Brewer, A. Evenson and A.L. Thomson, J. Low Temp. Phys. Vol 3, (1970) 603. (5) R.J. Roberts and J.G. Daunt, J. Low Temp. Phys. Vol 6 (1972) 97. (6) R.F. Dwyer, G.A. Cook, B.M. Shields and D.H. Stellrecht, J.Chem. Phys. Vol 42, (1%5) 3809. (7) D.F. Brewer, A.J. Symonds and A.L. Thomson Phys. Rev. L&t. Vol 15, (1965) 182. (8) R.H. Tait and J.D. Reppy, Phys. Rev. B Vol 20, (1979) 997.