9. In a right quadrilateral prism $A B C D-A_{1} B_{1} C_{1} D_{1}$ with all edges of length 2, $\angle B A D=60^{\circ}, M, N$ are the midpoints of edges $C C_{1}, A B$ respectively, then the volume of the tetrahedron $A_{1}-D_{1} M N$ is $\qquad$ .
Given, let the midpoint of $CD$ be $P$, then $V_{A_{1}-D_{1} M N}$ $=V_{M-A_{1} D_{1} N}=V_{M-P D_{1} N}=V_{N-P D_{1} M}$, $S_{\triangle P D_{1} M}=4-1-1-\frac{1}{2}=\frac{3}{2}$, connect $D N$, $D N \perp A B \Rightarrow D N \perp$ plane $P D_{1} M$, and $D N=\sqrt{3}$, so $V_{N-P D_{1} M}=\frac{\sqrt{3}}{2}$.