angle, conventionally called $\theta$ and measured from the close-packed direction. In contrast to $\theta=0$ steps, even for temperatures much below $\varepsilon_k$, there are always a non-vanishing number of kinks, the density of which are fixed by geometry (and so are proportional to $\tan \theta$). In a bond-counting model, the energetic portion of the step free energy per length (or, equivalently, the line tension, since the surface is maintained at constant \[zero\] charge[@IS]) $\beta(\theta)$ is cancelled by its second derivative with respect to $\theta$, so that the stiffness is due to the entropy contribution alone. Away from close-packed directions, this entropy can be determined by simple combinatoric factors at low temperature $T$.[@rottman; @avron; @Cahn]

Interest in this whole issue has been piqued by the recent finding by Dieluweit [*et al.*]{} [@dieluweit02] that the stiffness as predicted in the above fashion, assuming that only nearest-neighbor (NN) interactions $\epsilon_1$ are important, underestimates the values for Cu(001) derived from two independent types of experiments: direct measurement of the diffusivity on vicinal Cu surfaces with various tilts and examination of the shape of (single-layer) islands. The agreement of the two types of measurements assures that the underestimate is not an anomaly due to step-step interactions. 