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17 Previous studies of this model were either restricted to ^ = 0.5 (#=0), N = 2048 sites (Ref. 3) or to concentration c B = 0.25, iV = 500 sites lL. D. Fosdick, Phys.Rev. 1_16, 565 (1959)3 . This lattice size clearly is too small to study the phase transitions, however.18 This estimate is in good agreement with Ref. 3, indicating that the inaccuracy due to finite lattice size is small. 19A significant change of interaction parameters with lattice spacing has recently been revealed even for Principal planes of the 4 He solid-superfluid interface are expected to undergo roughening transitions at temperatures of about 1 K. An experiment is described in which two such transitions were observed in the hep-superfluid interface: first for the basal plane at 1.08 K and second for an orthogonal face at 0.85 K.

First-order phase transitions, such as solidliquid transitions, are commonly thought of and dealt with as purely bulk phenomena. It is appreciated that such transitions are probably usually nucleated in some fashion by impurities or walls, but details of this process have never before, to the authors' knowledge, been examined in careful detail. 1 What we report here are the first measurements of the continuous growth, on a microscopic scale, of a solid as the pressure approaches that of the solidification curve. The system studied is superfluid He 4 in contact with graphite in the form of Grafoil. 2 He 4 was chosen for convenience, but we must strongly emphasize that the basic phenomena studied are much more general in that they are qualitatively independent of both substrate and fluid. The data are analyzed in terms of a theory based on the van der Waals attraction between the fluid and the substrate, and good agreement between theory and experiment is obtained.One additional interesting effect is observed. Measurements of the pressure P in the system are along isopycnals, i.e., at constant He 4 number N and (essentially) constant He 4 volume V, the temperature T being varied. Along two such isopycnals, were the surface solid behaving like the bulk form, there would be a transition from the bcc phase to the hep phase. Comparison of the theory to experiment strongly indicates that 4 K. A. Reed and L, Wharton, to be published. the solid film being formed remains in a single phase, taken to be the bcc phase since this is the natural one over most of the temperature range. A definitive study, using neutron-scattering techniques, 3 would be most useful in examining this metastable behavior.The basic physical ideas involved in our work are relatively simple. The substrate provides an external potential in which the He 4 moves. In equilibrium the temperature T and He 4 chemical potential M are constant throughout the system, the local He 4 number density n(r) adjusting itself so that this is indeed the case. 4 Letting £/(r) be the external potential, the condition for equilibrium is M =M 0 {rc} + tf(r). Very generally, H 0 {n} must be regarded as afunctional of n(r) (and a function of T). Our analysis will be predicated on the assumption that the function is well-approximated by a local function of n(x) given by the bulk He 4 chemical potential V> Q (n(r),T) for the appropriate bulk phase of He 4 in the absence of any external effects. It is then convenient to regard M 0 as a function of the local pressure P(?) and T in place of the variable pair n(r) and T. The equilibrium condition then informs us that, on moving a small distance in the system, changes in U(r) are related to changes in P(r) via dU(r)=-(dii 0 /dP) T dP(r)=-[l/n(r)]dP(?).(1)Here the second equality follows from the local We report the continuous growth, on a microscopic scale, of solid He 4 from superfluid He 4 caused by its substrate interaction with Grafoil. The measurements indicate the presence of a surface solid layer whose thickness varies from 8...

The osmotic pressure of Hes-He4 mixtures has been measured at temperatures 0.027-0. 65 K, for concentrations up to 10-mole % He, and for hydrostatic pressures of 0.26, 10, and 20 atm.The osmotic pressure was measured directly with a sensitive specially designed diaphragm pressure gauge. The temperatureand concentrationdependenceof the osmotic pressure is in fair agreement with the effective, interactiontheoryproposed by Bardeen, Baym, and Pines (BBP).It also agrees with a simple empirical model whichavoids the complicated calculations involved in obtaining the thermodynamic properties at finite tempexatures from the BBP theory. The model fits the temperature dependence of other thermodynamic properties of solutions. The osmotic pressure at absolute zero at 10 and 20 atm is used to determine the Hes effective mass and somewhat speculative values of the BBP quasiparticle interaction V(k) underpressure. The interaction under pressure is found to have a minimum at a nonzero value of k, and it may give rise to a "supermobile" transition at comparatively high temperatures.

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The continuous nucleation of bcc solid 3 He from the liquid phase due to the presence of a MgO substrate is detected. For superfluid 4 He there is no evidence of continuous nucleation of either the hep or the bcc solid from the substrate. The experiment contrasts the influence of the square lattice of MgO with the triangular lattice of a basal-plane graphite substrate. The phenomenon of pore condensation for solid 3 He is discussed.PACS numbers: 67.80. Cx, 68.45.Da In this paper we present new results which compare the onset of solidification of 3 He and 4 He on a magnesium oxide substrate, which has cubic symmetry, with that already reported 1 * 2 for solidification on Grafoil, which has a hexagonal symmetry. The Grafoil experiments had shown that hep 4 He undergoes continuous solid nucleation whereas, surprisingly, bcc 3 He did not nucleate similarly. Since the van der Waals forces between the substrate and either isotope are identical, and this force is considered 1 to be responsible for the superpressurization of the first few helium layers on the substrate, we were led to suggest that the substrate symmetry (hexagonal graphite encouraging the hep 4 He) is the determining factor in the onset of solidification. To test this conclusion we repeated the experiments with a MgO substrate 3 * 4 which has a cubic symmetry. For this substrate we observed uniform nucjeation of the bcc 3 He whereas 4 He does not show any signs of surface solidification in either hep or bcc regions.We should emphasize that the experiment on Grafoil alone did not prove the relevance of substrate symmetry. During the condensation of the first layer of He on Grafoil, it is known from adsorption studies 5 that initially an ordered state is reached in which the helium atoms are registered with the graphite lattice. Subsequently, as the coverage is increased, a close-packed triangular two-dimensional lattice is formed, with a spacing incommensurate with the graphite lattice. It can then be argued that this layer, which is formed by either isotope, is the natural base for the continuing growth of hep 4 He, whereas it would not encourage the further growth of a bcc solid. The present experiments disprove the universality of this model, and demonstrate the importance of a matching substrate symmetry. Further experimental evidence from direct observation of the growth of aligned 4 He crystals on the Grafoil substrate will also be presented to support the conclusion.The experimental evidence for the onset of solidification is deduced from the measurement of equilibrium points along isopycnals 6 in the vicinity of the bulk melting curve. There appears a substantial difference between the isopycnal and the isochore for the bulk liquid when surface solidification occurs, in the presence of a substrate of sufficiently large surface area. The present experiments used a 2.9-g MgO sample prepared from compressed smoke at the University of Washington. 3 Its properties have been measured by Dash etal. 4 who showed that it produces krypton step like adsor...

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