Cu$_3$Au.[@vacancy] As $c^V \ll 1$, hopping rates of a tracer atom are simply proportional to $c^V$. This suggests to introduce a new Monte Carlo time unit 1 MCS$^*=c^V(T)\cdot 1$ MCS, where 1 MCS was defined above as one attempted vacancy exchange per lattice site. Regarding the simulated mean–square displacements as a function of the new time scale (with units MCS$^*$) allows us to extract diffusion constants $D_A$ and $D_B$ as shown in Fig. 1. Scales on the axes were obtained using the Cu$_3$Au transition temperature $T_0=663$K, the lattice parameter $a=3.74$Å and an additional parameter, which is determined by equating the calculated diffusion constant $D_B$ with the experimental $D_{Au}$ at $T/T_0=1.27$.[@diffusion1] The last parameter converts 1 MCS$^*$ directly into seconds. The favorable comparison between calculated and measured diffusion constants suggests that the above procedure, based on the atom–vacancy exchange algorithm and the knowledge of the experimental $c^V(T)$–function, provides a description of processes on the physical time scale. We shall come back to this issue in section \[THERMALACT\] in the context of nucleation processes.

Thermally activated versus continuous ordering \[THERMALACT\]
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At $T=T_0$ the model–system defined in the preceding section undergoes a first order phase transition [@Bind1; @SchwL; @Fron; @paper1] from the 