Nucleation of SolidHe4Interfaces between Grafoil and High-Pressure LiquidHe4

Abstract

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...

Hysteretic solidification of surfaceHe4measured by the modification of the specularity ofSm1, Jm2 1992Phys. Rev. Lett.351150View full textAdd to dashboardCite

“…The nucleus is stabilized by an excess pressure, proportional to the interfacial tension between liquid and solid. Although the mechanisms are different, both these models [19,20] predict that excess pressure will be required to solidify 4 He in a disordered medium and compete with the mechanism described by Landau and Saam [18].…”

“…The model used by Landau and Saam [18] to describe the nucleation of solid 4 He assumes a local 4 He number density which depends on position. The number density is increased inside the attractive well created by the van der Waals potential of the substrate, increasing the local pressure at the substrate compared to the bulk.…”

Role of Substrate Symmetry in Nucleating Solid Helium

“…The initial stage is identical to that analyzed by Landau and Saam, 1 and we show in Fig. 3 (broken curve) the calculated thickness Z s of the solid layer 1 …”

Entropy and magnetization measurements relating to the nature of the adsorbed phases of helium-3 under pressure

“…For example, Lawson 3~ detected preferentially oriented crystal growth of hcp solid 4He at a melting pressure of 85 atm on a specially prepared gold foil whose surface matched the solid, whereas previously no preferential orientation had been observed on copper. 31 Using a Grafoil substrate, Landau et al 32 found different results depending on whether the adsorbate is 3He or 4He. With 3He at temperatures between 30 and 320 mK they found no high-density phase if the melting curve was approached from an all-liquid state, but evidence for the existence of solid if the experiments started with solid present on the bulk melting curve.…”