Helium: Solid-liquid interfaces (original) (raw)
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On the interface at the equilibrium crystallization
Journal of Statistical Physics, 1985
Properties of an interface, created at some experimental conditions in the course of the equilibrium crystallization process, are theoretically investigated. Influence of quantum and thermal fluctuations on smoothing-roughening phase transitions is considered. The phase diagram illustrating these properties is found.
The static and dynamic properties of vicinal surfaces on helium 4 crystals
Journal of Low Temperature Physics, 1995
We have studied melting-freezing waves propagating at low temperature (40c≈ 2.5 °, where the surface properties change from stepped and anisotropic to rough and Isotropic. This result confirms our previous prediction1 that such a crossover should occur at the small angle where the large step width is comparable to the average distance between steps. It also confirms the hypothesis that crystal surfaces are weakly coupled to the lattice in helium. In the ø→ 0 limit, we observed a clear stepped behaviour: the longitudinal component of the surface stiffness vanishes while the transverse component diverges. A quantitative analysis of these two components allowed us to measure the step energy and the interactions between steps. Good agreement is found with the prediction that step interactions result from the combination of elastic and entropic effects. We also found evidence that helium 3 impurities adsorb on the liquid-solid interface and lower the step energy when ordinary helium 4 (130 ppb of3He) is used instead of an ultrapure sample (0.4ppb). Furthermore, from the damping of the waves, we could study the dynamics of vicinal surfaces, i.e. their mobility as a function of temperature, angle and frequency. Here too, a crossover is observed from stepped to rough behavior. The dynamics is sensitive to the existence of steps up to higher angles than the stiffness. We show that a true stepped behavior is observed only if two conditions are fulfilled: the distance between steps must be much larger than the step width, and also larger than the mean wavelength of thermal phonons. By changing the frequency, we could finally confirm that the surface mobility increases when the phonon mean free path becomes smaller than the wavelength of the melting-freezing waves. We conclude with some suggestions for further theoretical and experimental studies.
Surface of a He3 Crystal: Crossover from Quantum to Classical Behavior
Physical Review Letters, 2004
3 He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To understand the reason for that, we have performed the first quantitative investigation on the growth dynamics of the basic (110) facet at 60 -110 mK. The obtained values of the step free energy suggest an extremely weak coupling of the solid-liquid interface to the crystal lattice which we show to be the result of quantum fluctuations of the interface. The renormalization group approach by Nozières and Gallet, modified to incorporate quantum fluctuations, explains well the temperature dependence of the step energy measured in this work and at ultralow temperatures by Tsepelin et al., where the coupling is known to be strong. We have thus shown that, paradoxically, the role of quantum fluctuations is at higher temperatures much larger than at low temperature.
Thermodynamics and roughening of solid-solid interfaces
Physical Review E, 2009
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the non-linear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of finger like structures aligned with the principal direction of the far field stress.
Theory of Phase Transitions at Internal Interfaces
Le Journal de Physique Colloques, 1988
A variety of phase transitions are possible at internal interfaces. I will systematically describe from a pedagogical point of view the various classes of phase transitions which are possible. Experiments which have been performed will be mentioned at the appropriate places. Theories which predict these phase transitions and which explain the behavior associated with the transitions are emphasized. Possibilities for phase diagrams are suggested. Wetting and melting of internal interfaces will also be discussed. I. Background. A decade ago the possibility of phase transitions occuring at internal interfaces would have been discounted by many researchers. For those who would have agreed with this possibility, many would not have been convinced that the evidence was strong enough to give conclusive evidence for such transitions. Today, the evidence is conclusive. Theorists and experimentalists alike are predicting and exploring a variety of transitions in grain boundaries. (The evidence for other solid-solid interfaces, such as interphase interfaces, antiphase boundaries, and stacking faults, is not yet as convincing.) People are beginning to consider how to take advantage of phase transitions which occur in internal interfaces by the appropriate processing of materials to produce the desired mfErostructura1 properies. In this article the many types of phase transitions which are possible in internal (i.e., solidsolid) interfaces are described. I hope to provide some general principles on how to decide whai is or is not a phase transition and on what the possible phase diagrams might be. A classification of most (if not all) of the work done on these transitions is provided. I intend to provide a fairly complete bibliography which will reference articles which have modeled such phase transitions and also observed them in both computer and "real" experiments. The thermodynamics of such phase transitions, which has been addressed in the past [1,2], will be discussed here where clarification is helpful. I am neglecting from consideration interface phase transitions associated with magnetism or other similar effects. For up-to-date collections of recent work in grain boundaries and other internal interfaces, I recommend one book [3], one review article [4], and two conference proceedings [5,6]. Other recent review articles which discuss grain-boundary phase transitions may also be found (71.
Vicinal surfaces of helium 4 crystals
Journal of Crystal Growth, 1996
The high mobility of the solid-superfluid interface of 4He crystals allows the propagation of melting-freezing waves. We used this technique for surfaces that are tilted by a small angle ~b with respect to the c-facets. We obtained the first experimental evidence for the existence of a crossover from stepped to rough behaviour as a function of the orientation q~. From the independent measurement of the two components of the surface stiffness, we obtained both the step energy and the step interaction. The temperature dependence of the interaction allows us to distinguish between the elastic and entropic contributions. We also understood how the crystal growth rate changes as a function of q~ from the low value of stepped surfaces to the high value of rough ones.
One of the most intriguing problems of heterogeneous crystal nucleation in droplets is its strong enhancement in the contact mode (when the foreign particle is presumably in some kind of contact with the droplet surface) compared to the immersion mode (particle immersed in the droplet). Heterogeneous centers can have different nucleation thresholds when they act in contact or immersion modes. The underlying physical reasons for this enhancement have remained largely unclear. In this paper we present a model for the thermodynamic enhancement of heterogeneous crystal nucleation in the contact mode compared to the immersion one. To determine if and how the surface of a liquid droplet can thermodynamically stimulate its heterogeneous crystallization, we examine crystal nucleation in the immersion and contact modes by deriving and comparing with each other the reversible works of formation of crystal nuclei in these cases. The line tension of a three-phase contact gives rise to additional terms in the formation free energy of a crystal cluster and affects its Wulff (equilibrium) shape. As an illustration, the proposed model is applied to the heterogeneous nucleation of hexagonal ice crystals on generic macroscopic foreign particles in water droplets at T) 253 K. Our results show that the droplet surface does thermodynamically favor the contact mode over the immersion one. Surprisingly, the numerical evaluations suggest that the line tension contribution (from the contact of three water phases (vapor-liquid-crystal)) to this enhancement may be of the same order of magnitude as or even larger than the surface tension contribution.