STEP DEGENERACY AND STEP STEP INTERACTIONS

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 phi of the vicinal surface is smaller than a small angle phi(c). For phi > phi(c), the steps overlap and are degenerate. For phi < phi(c), the steps are far enough from each other to be non-degenerate. The critical angle phi(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 T << T(R), phi(c) is much smaller than previously thought (2.5-degrees 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/d2 interaction between steps has yet been obtained. The step degeneracy transition at phi(c) has not yet been observed either, although it should have drastic effects on the surface stiffness and growth rate of the crystal.