9. Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, a sphere is constructed with vertex $A$ as the center and $\frac{2 \sqrt{3}}{3}$ as the radius. The length of the curve formed by the intersection of the sphere's surface with the cube's surface is $\qquad$.
Solve

As shown in the figure, $\overparen{F G}, \overparen{H I}, \overparen{J E}$ are arcs with $A$ as the center and $\frac{2 \sqrt{3}}{3}$ as the radius, with a central angle of $\frac{\pi}{6}$; $\overparen{E F}, \overparen{G H}, \overparen{I J}$ are arcs with $B, A_{1}, D$ as centers, $\frac{\sqrt{3}}{3}$ as the radius, and a central angle of $\frac{\pi}{2}$. Therefore, the total arc length is $3\left(\frac{2 \sqrt{3}}{3} \times \frac{\pi}{6}+\frac{\sqrt{3}}{3} \times \frac{\pi}{2}\right)=\frac{5 \sqrt{3} \pi}{6}$.