  We study some spectral properties of a simple two-dimensional model for small
angle defects in crystals and alloys. Starting from a periodic potential $V
\colon \R^2 \to \R$, we let $V_\theta(x,y) = V(x,y)$ in the right half-plane
$\{x \ge 0\}$ and $V_\theta = V \circ M_{-\theta}$ in the left half-plane $\{x
< 0\}$, where $M_\theta \in \R^{2 \times 2}$ is the usual matrix describing
rotation of the coordinates in $\R^2$ by an angle $\theta$. As a main result,
it is shown that spectral gaps of the periodic Schr\"odinger operator $H_0 =
-\Delta + V$ fill with spectrum of $R_\theta = -\Delta + V_\theta$ as $0 \ne
\theta \to 0$. Moreover, we obtain upper and lower bounds for a quantity
pertaining to an integrated density of states measure for the surface states.
