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ADSORBED LAYERS OF D2, H2, O2, AND 3He ON
GRAPHITE STUDIED BY NEUTRON SCATTERING
M. Nielsen, J. Mctague, W. Ellenson
To cite this version:
M. Nielsen, J. Mctague, W. Ellenson.
ADSORBED LAYERS OF D2, H2, O2, AND 3He ON
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 38, octobre 1977, page C4-10
ADSORBED
LAYERS
OF Dz, Hz, 0 2 ,
AND 3He
ON GRAPHITE
STUDIED BY NEUTRON SCATTERING
M. NIELSEN, J. P. McTAGUE (*) and W. ELLENSON
(**)
Research Establishment Risqi,4000 Roskilde, Denmark
R6sum6. - Les diagrammes de phase de couches monomol6culaires adsorb6es de D2, Hz, 02, et de 'He sur graphite ont kt6 mesurks par diffraction neutronique. Les couches de H, et de Ds ont une structure
-\/7
cohkrente B des degrks de recouvrement 0 faibles'; lorsque les couchesmonomolCculaires sont complktes elles ont une structure triangulaire dense qui est incommensurable avec le substrat. Entre ces deux extrsmes, il y a une large rkgion en Bayant une structure triangulaire, dont le paramktre de rkseau :arie avec 0. I1 a 6tC constatk que les couches adsorbkes de O2 ont trois phases distinctes, qui sont toutes incommensurables avec le rkseau du substrat. GrAce B la grande section efficace d'adsorption de 'He, les dkterminations par diffraction
B
I'aide de neutrons provenant des couches 3He, sont beaucoup plus difficiles, mais on a pu observer non seulement la structurefl
cohkrente, mais aussi la structure triangulaire dense au voisinage de 0 = 1.Des rksultats de diffusion de neutrons inklastiques sont prksentks pour des couches adsorbks de Hz et de D2.
Abstract.
-
The phase diagrams of adsorbed monolayers of D2, HZ, OZ, and 'He on graphite have been measured by neutron diffraction. Hz and D2-layers have a registeredfl
structure at low coverages, and at monolayer completion they have a dense triangular structure, which is incommensurate with the substrate. Between the two densities there is a broad region of coverages where the structure is triangular but the lattice parameter varies with coverage. Adsorbed O2 layers are found to have three distinct phases which are all incommensurate with the substrate lattice. Due to the large absorption cross section of 'He the neutron diffraction measurements from the 3He layers are much more difficult, but both the registeredfi
structure and the dense triangular structure near monolayer completion have been observed.Inelastic neutron scattering results are presented for adsorbed Hz and Dz layers.
1. Introduction. - Neutron scattering results q e
presented for monolayers of H,, D,, 0, and 3He adsorbed on Grafoil. Some results have already been published for the three first gases [I,
21.
All the systems have several phases and many problems remain t o be solved. The measurements are being continued and this report will give the main results at the present status.The measurements were done at the DR 3 reactor at Ris0, mostly at the cold source beam. The use of a low energy neutron beam which is nearly free of higher order neutrons gives a low substrate scattering because we get below the cut off for the Bragg reflections from the hexagonal planes. Consequently the elastic diffraction measurements were performed on a triple axis spectrometer with an incoming energy of 4.7 or 5 meV with Be-filter in the monochromator.
f*) Guest scientist from University of California, Los Angeles,
California 90024, U.S.A.
(**) Present address : Brookhaven National Laboratory, Upton, New York 1 1973, U.S.A.
The Grafoil substrate was obtained from Union Carbide. The rocking curve for a c-axis reflection has a full width at half maximum of 27" and the total area per gram is 28 m2. The sample cell is filled with circular discs of grafoil, 0.2 mm thick and 30 mm in diameter. They are oriented parallel to the scattering plane and the total weight is 41.4 g. The grafoil was degassed a t 1 000 "C under vacuum and loaded in the sample cell in a glove box. For the 3He measurements a special sample cell was used. The scattering from the substrate is measured with no gas adsorbed and this intensity is subtracted before the neutron groups are plotted.
2 . Hz and D2 layers.
-
In all the measurements the gas was converted into p-H, or o-D,. In the'first measurements the rotational state of the adsorbed molecules was determined, and the results are described in [I]. The adsorbed molecules are freely rotating molecules in their rotational ground state.A detailed study of the structure of adsorbed D,
monolayers has been made by elastic neutron diffraction.
ADSORBED LAYERS OF D2, H2, 02, AND 3He ON GRAPHITE C4-11
0 1 I I I I
0 10 20 30 LO
TEMPERATURE (K)
FIG. 1.
-
Phase diagram for Dz and Hz adsorbed on Grafoil. Filling is the amount of gas adsorbed measured in units of that gas amount which is needed to complete the commensurate fi structure. The broken line indicates where promotion to the second layer starts. The symbols show the following : Dz and AHZ layers in the fi phase, x D2 and
+
H2 layers in the a and b phases, 0 D, and A HZ in the Fluid phase, (Xi deformed groups with high background.We observe the phase diagram shown in figure 1. In all cases only the (10) Bragg reflection of the even lateral triangular structure was observed. If different
2-D structures existed they would give additional reflections which have not been observed. Figure 2 shows examples of diffraction scans and figure 3 shows the length of the reciprocal lattice vector ~ ( 1 0 ) as function of the square root of the filling. The filling is the amount of gas adsorbed. As a unit for this (p) we use the amount of gas needed to complete a monolayer of the comkensurate
lh
structure. In this structure a gas molecule is located above every third carbon hexagon of the graphite surface [3], giving an even lateral triangular structure with a neighbour distance of a,, = 4.26A
and ~ ( 1 0 ) = 1.703A-'.
The same structure has been found in N:, Kr5, and He adsorbed on Grafoil. In figure 1 this phase is indicated by full circles. Forp
<
1 we also observe this phase which means that we have coexistence between d-monolayers and a dilute 2-D gas. We do not see a broadening of the Bragg peak at p<
1. The coherent length of the adsorbed 2-D layers (i.e. the diameter of the individual -layers of adsorbed material) remains the same and it is probably determined by the substrate. When the temperature is increased the (10) diffraction peak disappears over a 2-3 K region around the phase line separating thefi
region from the Fluid region in figure 1 . This is seen in figure 2 (the p = 0.54 groups). In the melting region there is no significant change of the coherence length.he
behaviour of the D, monolayers in the commensuratefi
region is quite analogous to what was found for adsorbed N, layers131.
When the number of adsorbed particles goes down either by decreasing the coverage, or by melting, then theLOO I , , , , ,
,
p = 1.75 200 0",
200 I- 2 0 3g
200 0 200 0 200 0 16 1 8 2.0 2.2 2.LSCATTERING VECTOR (A-')
FIG. 2 . - Observed diffraction groups from adsorbed DZ layers.
FIG. 3. -The position of the diffraction peaks from monolayers of D2 and Hz as function of the square root of the amount of gas
adsorbed.
coherence length stays unchanged while the intensity of the Bragg peaks decreases. This means that the number of the adsorbed layers with the 2-D crystalline order decreases, but the extent of the remaining ordered layers stays unchanged until they eventually melt. At temperatures above the melting line no broad scattering profile, indicative of a liquid phase [3], is observed so the Fluid phase is probably gas-like.
As the filling is increased beyond p = 1 the reciprocal lattice vector ~ ( 1 0 ) increases gradually as shown in figure 3. This means that the molecules are forced out of registry and they form a triangular structure covering the total area available for adsorption with a monolayer. In this regime which is called b in figure 1 the neighbour distance varies between a,, = 4.26
A
and a,, = 3.40h;.
The nearest neighbour distances in different phases are shown in table I.TABLE I
The nearest neighbour distance a,, in Angstram
Monolayer Monolayer Bulk solid, hcp,
Element densest T
C4-12 M. NIELSEN, J. P. McTAGUE AND W. ELLENSON
It is a very broad range of densities over which the ordered 2-D structures are found. The commensurate
fi
structure is a very open structure where the neighbour distance is far beyond the inversion point of the pair-potential, and it is the substrate which stabilizes the structure. Diffraction groups at small intervals in p are shown in figure 4. In figure 4A the groups around p = 1 are shown and it can be seen that the Bragg peak moves away from the T = 1.703k1
position as soon as p gets larger than one. It is obvious that the diffraction group broadens when the 2-D structure is forced out of registry.FIG. 4. - Neutron diffraction groups for adsorbed D2 layers in the region b of the phase diagram. Figures A and B show the measured groups and the curves fitted to the groups. The numbers in the figures give the value of p determining the filling. In figure C the fitted value of the reciprocal lattice vector T is plotted
us C p . Figure D gives the coherence length L, (0) and the
integrated intensity, ( A ) us p.
The full lines in figure 4A and I3 are curves fitted to the measured groups. Only three parameters are varied, namely the position r,,, the amplitude I,, and the coherence length L. The line shape is described by Warren's formula [4], modified to take the partial orientation of the layers into account,
x
exp - ((r - r0)2/A ')x l/[Q(Q2 - T')"'] d + d r (I) where A is a normalizing factor, 7, is the reciprocal
lattice vector of the 2-D structure, and A = 2 &/L,
where L is the coherence length. The factor exp - (0
'/
W2) is a weighing function describing the misalignment of hexagonal graphite planes in the Grafoil. W = 16", (measured by diffraction), and cos 0 = r / Qx
cos 4. The line shape is a saw toothwith a steep edge to the left and a sloping right side. The leading left edge has a width determined by L,
and the right hand side is given predominantly by W.
In fitting formula (1) to the groups, most weight is given the points along the leading left edge, in order to get a value of L. The fitting is difficult because there is a very large substrate scattering around 1.88
A-',
and in a region around this value of Q the uncertainty on the measured points is very large. For the same reason we cannot measure diffraction groups with T vectors around 1.88h;-I.
Further,additional scattering, which is not described by formula
(I),
is present. The values of the parametersL and I, are given in figure 4D as circles and triangles, respectively. In the calculation, the Debye-Waller factor and the molecular form factor are not included, since they do not vary rapidly over a single peak.
From the data in figure 4 we conclude that as the adsorbed layers are forced out registry by increasing the filling beyond p = 1 we find an ordered triangular structure with a gradually decreasing average nearest neighbour distance a,,. The coherence length and the intensity decrease abruptly at p = 1. The .r vector is almost proportional to the square root of p, giving an area-density proportional with the number of adsorbed particles. However, the small deviation of the points from the straight line in figure 4C is, we believe, significant. The sign of the deviation change in the non-accessible region around T = 1.88 and this together with the break of the curves in figure 4D in the same region could indicate that a phase change takes place.
The upper knee of the line in figure 4C at r = 2.13
k1
and p = 1.55 indicates where pro- motion t o the second layer starts. At this point we have dense monolayers with a triangular structure with a,, = 3.40A.
As more molecules are added to the second layer, the density of the first layer continue to increase slightly. At higher temperatures the density goes down (see Fig. 3). An exampie of the observed neutron group in this phase is shown in figure 2, p = 1.75. Here 12 per cent of the adsorbed molecules are in the second layer. Between 6 K and 3 1.5 K the r vector decreases from 2.13 to 2.05A-',
which means that 7.5 per cent more molecules are promoted to the second layer. The melting occurs in a region of about 4 K around the melting line in figure 1. Also here the coherence length in the solid phase is not affected significantly by the melting.ADSORBED LAYERS OF D2, H2, O2 AND 3He ON GRAPHITE C4- 13
groups. This is indicated in figure 1 by squares. As the temperature is increased the background disappears and the groups sharpen to the usual shape.
A series of diffraction scans were measured with adsorbed H, in the same Grafoil cell. Because the coherent scattering amplitude of H, is small the measurements are less detailed. The results are very similar for H, and D, as seen in figures 1 and 3. It is remarkable that the melting temperature of the commensurate
fi
layers is the same within 1 K forD, and H, layers at p = 1.
From figure 3 it is seen that where the 2nd layer promotion starts, we have 7 = 2.066
A-',
givinga,, = 3.51
A.
This means that the lattice spacing is6.3 per cent smaller in the 2 D layers than in the hexagonal layers of bulk Hz. The corresponding number for D, layers is 4.7 per cent, but due to the different compressibilities of bulk solid H, and D, we find in both cases that the necessary pressure to give the same value of a,, as in the 2-D layers is 700 bar [6].
Also in the dense monolayer regime, at p = 1.8,
we find that the melting temperature is about equal for H, and D, layers.
Inelastic neutron scattering experiments on adsorbed monolayers in order to measure the 2-D phonons have s o far only been reported for argon layers on Grafoil [7]. The results are interpreted by a 2-D phonon model including the force constants from the nearest neighbours only, and no forces parallel with the layers from the substrate. Argon does not form the commensurate
1/7
structure, but has a dense triangular structure with a,, = 3.88&almost the same as in bulk argon. It is therefore plausible that the nearest neighbour forces between the argon atoms are dominant in determining the dynamic response within the planes of the adsorbed layers.
For the commensurate D, and H, layers in the
fi
regime of the phase diagram on figure 1 the nearest neighbour distance is very large, a,, = 4.26A,
and the substrate forces must be dominating in stabilizing the structure. We have measured the inelastic neutron scattering from the layers, and results are shown in figures 5 and 6. For both H, and D, it is the coherent scattering function which is measured. The neutron scattering vector Q was parallel to the substrate so we measure the in-plane-motion of the molecules, predominantly. Measurements were made for different lengths of the scattering vector so that we could measure the longitudinal and the transverse motion with different weight. The same response was seen.The result in figure 5 shows clearly that the molecules behave as Einstein oscillators with the energies h w @ d = 4.0 meV and k w ( H 3 = 4:9 meV. For p
>
1 the response is completely different and at the dense monolayer completion, p = 1.58, the-
0 1 2 3 L 5 6 7 8 9 1 0 1 1 ENERGY (rneV1
FIG. 5. - Inelastic neutron scattering groups measured for adsorbed D, and H2 layers at 5 K. T h e filling (p) is given in the
figure.
I
L L K4
FIG. 6. - Inelastic neutron scattering groups for adsorbed H,
layers a t p = 1 .O. The temperature is given in the figure.
result resembles the 2-D phonon scattering of argon, but with a cut off frequency of
8
meV. However, the intensity is too low to resolve this spectrum.C4-14 M. NIELSEN, J. P. McTAGUE AND W. ELLENSON
This width can be caused both by neighbour interactions, which must be present because we have a long range ordered structure, and by anharmonic potentials. The difference in line width for D, and Hz indicates, that anharmonicity is probably most important. The thermal amplitude of the H, molecules in the harmonic approximation is
= 0.46 b;.
The inelastic response of the adsorbed Hz layers was also measured by incoherent scattering. Above the conversion line at 14.6 meV we can observe the incoherent scattering spectrum, and this occurs with the strong incoherent cross section of hydrogen. Strong inelastic groups are observed around 20 meV when p = 1 and a broad featureless spectrum is observed for p
>
1. This confirms the model of a localized oscillator for p<
1. It should be noticed that the Hz and D, frequencies do not scale as the square root of the masses. This is in agreement with the fact that the anharmonicity is important.The variation of the inelastic scattering group with temperature for p = 1 is shown for
Hz
layers on figure 6. A similar behaviour is found for D,layers. Considerable broadening of the oscillator group occurs before the melting is completed and above the melting a broad spectrum at low frequencies is observed. This is similar t o what is observed from adsorbed argon layers near and above the melting temperature (private communication, K. Carneiro, J. K. Kjems and J. P.
McTague).
3. 0, Layers.
-
We have studied adsorbed 0,layers on Grafoil by elastic diffraction measurements, and the major results are published [2). Bulk solid 0, has both in the a and
P
phase the molecules oriented perpendicular to the densest packed planes, see figure 7. Each malecule has a magnetic moment of 2 E*, and the moments are ordered antiferromagnetically in the a phase as indicated by the arrows in figure 7. At the a to
P
transition which occurs at 24 K the basal plane structure changes from a skew into an even lateral triangular structure and at the same time the long range magnetic order disappears.
The phase diagram for the adsorbed 0, layers on Grafoil is shown in figure 8. It is still tentative, with several unsolved problems. Monolayer completion coincides with the phase line between the 6 and the a region at p = 1.61. The same unit is used here for the filling as above, which means the p = 1
gives the amount of gas needed to complete a monolayer of the commensurate
lh
structure, although this structure is not found for adsorbed 0, layers. In the a-phase we find that the first layer of 0, molecules has a structure almost identical to the basal plane structure for bulk 0, in the a -phase. An example of the diffraction peaks observed is shown in figure 9 at p = 1 .%. The groupFIG. 7.
-
(a) The a and 0 structure of bulk solid Oz. (b) The closest packed planes in a -02 and /3 -02. The molecular axes are perpendicular to the plane. Arrows indicate the direction of the magnetic moments. The 6 phase has no long-range magneticorder.
0
0 10 20 30 LO SO TEMPERATURE (K)
FIG. 8. -The phase diagram of adsorbed Oz layers. The filling is measured in units of the gas amount needed to complete a commensurate 1/?; structure. The monolayer completion coincide
with the a to (6
+
vapor) phase boundary.FIG. 9.
-
Neutron diffraction groups from adsorbed O2 layers at4.2 K. The filling is given by the numbers in the figure ( p ) . The three arrows indicate the positions and the relative intensities of Bragg peaks from monolayers of O2 identical to the (a-b) planes of
ADSORBED LAYERS OF D2, H2, O2 AND 3He ON GRAPHITE C4-15
to the right shows the nuclear group which is a double peak consistent with the skew triangular structure. The group to the left with the much smaller intensity is a magnetic superlattice reflection which signals an antiferromagnetic ordering. The three arrows in the figure are calculated assuming a 2-D structure identical to that of the basal plane of bulk 0, (Fig. 7) and with the same magnetic ordering. The height of the arrows indicates the expected relative intensities.
In the 6-phase we measure diffraction groups as shown in the lower part of figure 9. We cannot on the basis of our results characterize this phase very well. The nuclear Bragg peak is similar t o that of an even lateral triangular structure but there is a tail of extra scattering intensity,on the high Q side. Also, there are indications of some magnetic scattering around the superlattice position. Presumably the 6-phase is a triangular structure with magnetic and magnetostrictive fluctuations. The p-phase is an even lateral triangular structure like the basal plane of bulk 0, in the P-phase. The nearest neighbour distances are given in table 11.
Between the 6 and the P-phase there is a coexistence region. This is analogous to a first order phase transition at constant volume. Figure 10 shows neutron groups for scans at points along a horizontal line in the phase diagram (Fig. 8) through the a-, the
p
+
6-, and the transition-region. At4.2 K we have the a-phase, at 25 and 29 K the coexistence between the
p
-
and 6-phases. At 32 Kwe have pure p-phase. In the region denoted transition in the phase diagram the intensity of the diffraction groups gradually goes to zero. This is also illustrated in figure 10.
The nearest neighbour distance a,, in Angstrsm
Phase a P S
2-D adsorbed O2 layer 3.20and 3.40 3.28 3.35 t03.43 Bulk solid 02, basal plane 3.20 and 3.43 3.30
-
The a
-P
-phase transition is probably a second order transition. Figure 11 shows how the intensity of the magnetic Bragg peak varies with temperature. Here the substrate scattering has not been subtracted. The indications are that the magnetic intensity varies continuously as the temperature goes through the transition at 10 K. If the skewness of the triangular structure of the cr -phase is caused by magnetostrictive forces then the distance between the peaks in the nuclear double group should follow the magnetic moment. From the nuclear groups shown in figure 1 1 this seems to be the case.Specific heat measurements on 0, adsorbed on Grafoil are presently being carried out (private communication, 0. E. Vilches).
FIG. 10. - Neutron diffraction groups for adsorbed O2 layers at the filling p = 1.66, and at the temperatures indicated in the
figure. The groups give a horizontal scan through the a, P
+
6, P, and transition region o f the phase diagram on figure 8.2000
--!
L---
TEMPERATURE (K)1.8 2.0 2.2 2.4 a (A-')
FIG. I I . - Temperature dependence of structural peaks (left) and of the peak intensity of the magnetic group (right). The
substrate scattering has not been subtracted.
4. 'He on Grafoil.
-
3He has a very large absorption cross section for neutrons. In liquid 3He the penetration length is only about 1/10 mm. However in measurements on thin adsorbed films only a vqry small fraction of the scattering comes from the films, and scattering from the substrate dominates. The exponential length for the decay of the neutron intensity in Grafoil is about 3 cm (at 5 meV). Filled with a monolayer of 3He this has decreased to about 1 cm. The coherent scattering cross sectios of 'He is reasonably large, 4.9 barn which makes the measurements feasible.A special sample cell was used in these measurements. The Grafoil sheets are still placed horizontally, parallel to the scattering plane of the neutrons. The cell is rectangular, 8 rnrn thick,
C4-16 M. NIELSEN, J. P. McTAGUE AND W. ELLENSON
In these, measurements the substrate scattering cannot be corrected for by measuring the scattering from the Grafoil alone and subtracting this, since the 3He absorption influences strongly the scattering from the: Grafoil. Instead the scattering at a temperature above the melting temperature is subtracted from the groups.
The phase boundaries for both 3He and "He on Graf oil is rather well known [S]. However, neutron diffraction contributes in measuring the nature of the long range ordered phases.
2 D Gas
FIG. 12. - Phase diagramsfor adsorbed 'He layers, p gives the filling in units of the gas needed to complete the commensurate
6
structure. The dotted 'line indicates where second layer promotion starts. In phase b ,the first layer has an even lateral triangular structure with an, = 3.32 A and in the a region the triangular structure is expanding continuously with decreasing p.1.0 1.1 1.2 1.3 l . L
6-
e
FIG. 13. - The position of the diffraction peak from adsorbed layers of 'He as function of the square root of the filling.
Figures 12 and 13 show our results. The phase diagram is drawn in the same way as above for D,, H, and 0,. The phase boundaries separate regions of particular diffraction groups. The same phases as for adsorbed D, are identified. In phase b we have a completed first layer and, in addition, some atoms in the second layer. The structure is even lateral triangular, not commensurate with the substrate, and ~ ( 1 0 ) = 2.185
k'.
This gives a nearest neighbour distance of a,, = 3.32A.
This ismeasured at the a to b phase line, just when the first layer is completed. At Brookhaven [9] a similar neutron diffraction measurement with 4He or Grafoil gave a,, = 3.19
h;
for a 14 per cent higher filling. The value of r and a,, varies so slowly in the b phase that the two values may be considered representative for the two isotopes.TABLE I11
The nearest neighbour distance a,, in Angstr@m
3He "He Dense monolayer 3.32 3.19 BuIk He, h.c.p.,
p = 160bar, T = 3.5k 3.50 3.42
In table I11 the a,, values are compared with the nearest neighbour distances in the h.c.p. phases of the bulk solids [lo].
In the region a in figure 12 we have a completed monolayer with a continuously varying lattice spacing depending on p
.
Examples of the neutron groups observed are shown in figure 14. The drawn curves are calculated by formula (1) above, and the coherence length is 150A.
I . . , . ;
1 . 6 1 7 1 . B 2.0 2 . 1 2 2 2 3
B ( R'I ) W R - ~ )
FIG. 14. - Diffraction groups for adsorbed 3He layers. The numbers in the figure give the filling ( p ) . The groups in the left figure are measured at 0.5 K and they are within the fi region of the phase diagram (Fig. 12). The groups to the right are measured at 1.5 K and they are within the a region of the phase diagram.
In the commensurate
4
regime we have confirmed that this structure exists in the region of pand T shown in figure 12, but the neutron scattering intensity is low and the uncertainty large. At
T = 0.5 K we see no group at p = 0.75. At p = 0.85 and O.% we see rather well resolved groups. At
p = 1.03 we see indication of a group but there is some extra scattering and the group is hardly visible. At p = 1.07 we see a flat background. The temperature dependence of the diffraction group at
p = 0.85 is shown in figure 15.
ADSORBED LAYERS OF DZ, Hz, O2 AND 3He ON GRAPHITE concluded on the basis of our data. The region
between the a and the
~
phase has been subject to considerable interest recently and in specific heat measurements an apparent new phase has been reported [ll]. To pursue the neutron diffraction measurements into this region will require a better graphite substrate.Acknowledgment. - This work received partial support from NATO Grant 1249. J. P. McTague's research was supported in part by U.S. NSF Grant CHE76-2 1293.
References
[I] NIELSEN, M. and ELLENSON, W. D., in Proceedings o f the Fourteenth International Conference on Low Tempera- ture Physics, Otaniemi, Finland, 1975, edited by M. Krusins and M. Vuorio (North-Holland, Amsterdam, 1975), p. 437.
[2] MCTAGUE, J. P. and NIELSEN, M., Phys. Rev. Lett. 37 (1976) 596.
NIELSEN, M. and MCTAGUE, J. P., Physica 86-88B (1977) 675.
[31 KJEMS, J. K., PASSELL, L., TAUB, H., DASH, J. G. and N o v ~ c o , A. D., Phys. Rev. B 13 (1976) 1446. [4] WARREN, B. E., Phys. Rev. 59 (1941) 693.
[51 THOREL, P. and CROSET, B., Proceeding o f the Conference on Neutron Scattering, Gatlinburg, USA (1976), edited by R. M. Moon (Oak Ridge National Laboratory, Oak Ridge, USA), Vol. 1, p. 85.
[61 ANDERSON, M. S. and SWENSON, C. A., Phys. Rev. B 10 (1974) 5184.
I71 TAUB, H., PASSELL, L., KJEMS, J. K., CARNEIRO, K., MCTAGUE, J. P. and DASH, J. G., Phys. Rev. Lett. 34 (1975) 654.
[81 BRETZ, M., DASH, J. G., HICKERNELL, D. C., MCLEAN, E. 0. and VILCHES, 0 . E., Phys. Rev. A 8 (1973) 1589. 191 CARNEIRO, K., ELLENSON, W. D., PASSELL, L., MCTAGUE,
J. P. and TAUB, H., Phys. Rev. Lett. 37 (1976) 1695.
FIG. 15. - Neutron diffraction groups for adsorbed 3He layers. The groups are measured at points along a horizontal line at
p = 0.85 in the phase diagram (Fig. 12) i.e. through the
6
and the 2-D phases.[lo] KELLER, W. E., Helium-3 and Helium-4, International Monograph Series, edited by K. Mendelsohn (Plenum Press N.Y., USA, 1969), p. 367.
[ 1 1 ] HEXING, S. V., VAN SCIVER, S. W. and VILCHES, 0. E., Jour. Low Temp. Phys. 25 (1976) 793.
DISCUSSION
M. BIENFAIT.
-
In your inelastic neutron magnetic and structural transitions occur at the same scattering experiments on hydrogen, you observe, temperature in which case the universality class is above the melting point, a broad spectrum at low that of the Heisenberg model with cubic anisotropy frequencies. Phonons do not exist in fluids. How do or the structural transition occurs first and is in the you interpret this broad spectrum ? three-state Botts class followed by a magnetic IsingM. NIELSEN.
-
Detailed balance has not been applied in the figure shown. I merely want to show how the phonon response changes when we melt the &-structure and at these energies the balance factor is-
1. Our groups at 20 K are not inconsistent with the scattering from a disordered 2-D lattice gas.transition. Your figure 11 indicates that the former situation occurs.
M. NIELSEN. - Yes ! However we cannot conclude that definitively on the basis of our present data. We are planning to measure the double structural peak (of the a-phase) with the ZYX
C4-18 M. NIELSEN, J. P. McTAGUE AND W. ELLENSON
observed groups (with grafoil) already gives an intrinsic natural line shape caused by other factors, such as fluctuations in the skewness.
J. G. DASH.
-
Current calorimetric measure- ments by 0. E. Vilches at the University of Washington show peaks in the heat capacity at coverages and temperatures corresponding to youra -6 phase boundary. These peaks are symmetric and constant in shape as the coverage is varied. I
believe that the peak strength varies linearly with coverage, as (N-N,), where N, is approximately equal to the amount for the completed first layer. This dependence, together with the temperature independence of the transition suggests that the phase change is occurring essentially in the quasi-2D solid islands of the second layer. Can your results be interpreted in this way ?
M. NIELSEN.
-
NO ! The intensity of the observed magnetic Bragg peak cannot be explained by the number of molecules in the second layer.J. A. VENABLES.
-
1) Can you tell us anything more about the 6-0, structure ? 2) A further comment on thea - p
0, transition : we showed a few years ago [I] that thea-p
transition in solid (3D) oxygen would not take place if it was not for the magnetic driving forces. The analogy with the case of a-F, is quite striking in this regard.[I] ENGLISH, C. A., SALAHUB, D. R. and VENABLES, J. A., Proc. Roy. Soc. A340 (1974) 81.
M. NIELSEN. - 1) Not much more. It is a
non-registered phase, the nearest neighbour distan- ces vary continuously with the filling between 3.35 and 3.43
