S. Balibar

The Surface Tension of B.c.c. 3He Crystals

We have measured the surface tension γ of b.c.c. solid helium-3 from the visual observation of large single crystals, in equilibrium with their liquid phase, between 0.1 and 0.4 K. This first direct measurement gives a much larger result (γ = (0.060 ± 0.011) erg/cm2) than previously estimated from the maximum temperature at which facets were observed on growing crystals (0.10 K). We propose that quantum fluctuations reduce the step energy and broaden the roughening transition, so that dynamic roughening may occur far below the static roughening temperature.

The growth rate of3He crystals

We have measured the relaxation of the shape of3He crystals under the effect of gravity and surface tension, close to the minimum in their melting curve atTmin=0.32 K. A growth rate is deduced, which is found to be at a maximum atTmin when the latent heat is zero. We interpret this maximum value (k=0.18±0.04 sec/m) as the intrinsic mobility of the liquid-solid interface and compare it with existing theories. We also consider on which side the latent heat is released during growth, and how it may cross the liquid-solid interface.

Adsorption of 3He on 4He crystal surfaces

We have compared the surface properties of crystals respectively grown from normal 4He containing 130 ppb of 3He and from ultrapure 4He (0.4 ppb). Below 0.4 K, 3He impurities are found to decrease both the surface tension and the step energy. Our results are consistent with the existence of two-dimensional bound states for 3He atoms at the solid-liquid interface. Quantitative agreement with the data is found with a binding energy es ≈ 4.3 K and a 3He density saturating around 0.4 monolayer. The presence of steps is found to increase the binding energy by about 10 mK.

Step degeneracy and step-step interactions

Abstract When slightly misoriented with respect to a high symmetry direction, crystal surfaces are usually called vicinal. However, they should be called so only if they can be described as a set of terraces limited by well separated, weakly interacting, steps. Such a situation occurs if the step width w is much smaller than the average step-step distance d , i.e. if the tilt angle φ of the vicinal surface is smaller than a small angle φ c . For φ > φ c , the steps overlap and are degenerate. For φ φ c , t from each other to be non-degenerate. The critical angle φ c tends to zero at the roughening temperature T R where the width w diverges. As shown by recent work on helium crystals, even if TLtT R , φ c is much smaller than previously thought (2.5° in this particular case). The two surface stiffness components of truly vicinal surfaces are predicted to be very different from each other (the vicinal surface is highly anisotropic); they are also directly related to the magnitude of step-step interactions. We present a review on crystal shapes, crystallization waves and step fluctuations, and explain why, in our opinion, no clear evidence of a 1 d 2 interaction between steps has yet been obtained. The step degeneracy transition at φ c has not yet been observed either, although it should have drastic effects on the surface stiffness and growth rate of the crystal.

Optical Measurement of Wetting by 3He-4He Mixtures Near Their Tri-Critical Point

We have measured the contact angle of the interface of phase-separated 3He-4He mixtures against a sapphire window using an interferometric method in an optical cryostat. Our measurement has been performed at saturated vapor pressure, along the phase separation line and near Tt, the temperature of the tri-critical point. We have found that the contact angle is finite, contrary to what was generally accepted up to now, i.e., complete wetting by the 4He-rich phase. Furthermore, this angle does not tend to zero when the temperature approaches Tt. This is a remarkable exception to “critical point wetting,” a phenomenon which is usually observed near ordinary critical points.

Accurate rotation and displacement in the millikelvin range: A new positioner design

dc micromotors have been used to rotate helium 4 crystals in a pressurized cell (25 bars) at very low temperature (down to 30 mK). After slight modifications of the motors and optimization of bearings and transmission design, rotations of ±6° were obtained with an accuracy of ±0.01° and a dissipation of 20 μW.

Stress driven instability at the crystal-melt interface of helium4

Abstract We have studied the effect of nonhydrostatic stresses on the equilibrium shape of pure helium-4 crystals[1]. First, by applying small stresses, a macroscopic melting of the crystal is produced which is quadratic in the strain and can be quantitatively understood using simple thermodynamics and elasticity theory[2]. Secondly, above a certain threshold in strain, easily visible grooves appear on the crystal surface[1][3]. This is the first quantitative evidence for the general instability which was first predicted by Grinfeld[4].

Vicinal surfaces of helium 4 crystals

Abstract The high mobility of the solid-superfluid interface of 4 He crystalls allows the propagation of melting-freezing waves. We used this technique for surfaces that are tilted by a small angle o 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 o. 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 o from the low value of stepped surfaces to the high value of rough ones.

Crystalline surfaces in helium

Abstract The particular properties of helium at low temperature recently allowed important progress in the general understanding of the structure and dynamics of crystal surfaces. Excellent agreement has been found between experimental results in helium 4 and the renormalization group theories of the roughening transition, which predict that it is an infinite order (Kosterlitz-Thouless) phase transition. The dynamic roughening of a crystal surface, i.e. the influence of a finite growth rate, has been particularly clarified. The dominant growth process of smooth faces close to their roughening transition has been shown to be the two-dimensional nucleation of terraces. In both helium 3 and helium 4, it also appeared possible to measure and analyze the three interface coefficients which describe the dissipation at rough crystal surfaces is non-equilibrium situations. The latter studies provide interesting information on the elementary processes (heat and mass flow) which occur in quantum liquids during their crystallization. A general review of all these phenomena is given.

The roughening transition and the growth of helium crystals

Abstract We present a review on the roughening transition and the surface of helium crystals, whose behaviour is well described by the modern or “critical” theory of roughening and whose study brings important information on the microscopic details of crystal growth processes.