  In this paper we propose a time discretization of a system of two parabolic
equations describing diffusion-driven atom rearrangement in crystalline matter.
The equations express the balances of microforces and microenergy; the two
phase fields are the order parameter and the chemical potential. The initial
and boundary-value problem for the evolutionary system is known to be well
posed. Convergence of the discrete scheme to the solution of the continuous
problem is proved by a careful development of uniform estimates, by weak
compactness and a suitable treatment of nonlinearities. Moreover, for the
difference of discrete and continuous solutions we prove an error estimate of
order one with respect to the time step.
