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We have carried out parallel tempering Monte Carlo calculations on the binary six-atom mixed Lennard-Jones clusters, Ar(n)Xe(6-n) (n=0,1,2). We have looked at the classical configurational heat capacity C(V)(T) as a probe of phase behavior. All three clusters show a feature in the heat capacity in the region of 15-20 K. The Ar(2)Xe(4) cluster exhibits a further peak in the heat capacity near 7 K. We have also investigated dynamical properties of the Ar(2)Xe(4) cluster as a function of temperature using molecular dynamics. We report the interbasin isomerization rate and the bond fluctuation parameter obtained from these calculations. At 7 K, the isomerization rate is on the order of 0.01 ns(-1); at 20 K, the isomerization rate is greater than 10 ns(-1). Furthermore, at 7 K, the bond fluctuation parameter is less than 3%; at 20 K, it is in the range of 10-15% (depending on the sampling time used). Using this information, together with Monte Carlo quenching data, we assign the 15-20 K feature in the heat capacity to a solid-liquid phase change and the 7-K peak to a solid-solid phase change. We believe this is the smallest Lennard-Jones cluster system yet shown to exhibit solid-solid phase change behavior.