  The entanglement, purity and energy of two isolated two-level atoms which are
initially prepared in Bell state and each interacts with a thermal cavity field
are investigated by considering the atomic motion and the field-mode structure.
We achieve the analytical solutions of the atomic qubits by using the algebraic
dynamical approach and the influences of the field-mode structure parameter,
the strength of the thermal field and the detuning on the entanglement, purity
and energy are discussed. We also investigate the state evolution of the atomic
qubits based on the entanglement-purity-energy diagrams. Our results show that
the disentanglement process of the atomic qubits accompanies by excitations
transferring from atomic subsystem to cavity field modes and atomic state from
a pure state convert to the mixed states.
