  The thermodynamic properties of the XXZ spin chain with integrable open
boundary conditions at the gaped region (i.e., the anisotropic parameter $\eta$
being a real number) are investigated.It is shown that the contribution of the
inhomogeneous term in the $T-Q$ relation of the ground state and elementary
excited state can be neglected when the size of the system $N$ tends to
infinity. The surface energy and elementary excitations induced by the
unparallel boundary magnetic fields are obtained.
