Radio morphology data have been collected for a sample of radio galaxies from the Revised Third Cambridge Catalog in the redshift range 0.15 < z < 0.65. Radio structure parameters including largest physical size, projected bending angle ( ), lobe length asymmetry (Q), and hot spot placement (Fanaroff-Riley ratio) have been measured from the highest-quality radio maps available. Combined with similar data for quasars in the same redshift range, these morphology data are used in conjunction with a quantification of the richness of the cluster environment around these objects (the amplitude of the galaxy-galaxy spatial covariance function, B gg ) to search for indirect evidence of a dense intracluster medium (ICM). This is accomplished by searching for confinement and distortions of the radio structure that are correlated with B gg . Correlations between physical size and hot spot placement with B gg show evidence for an ICM only at z 0.4, but there are no correlations at z ! 0.4, suggesting an epoch of z $ 0.4 for the formation of the ICM in these Abell richness class 0-1, FR2-selected clusters. X-ray-selected clusters at comparable redshifts, which contain FR1 type sources exclusively, are demonstrably richer than the FR2-selected clusters found in this study. The majority of the radio sources with high B gg values at z 0.4 can be described as '' fat doubles '' or intermediate FR2-FR1s. The lack of correlation between B gg and or B gg and Q suggests that these types of radio source distortion are caused by something other than interaction with a dense ICM. Therefore, a large cannot be used as an unambiguous indicator of a rich cluster around powerful radio sources. These results support the hypothesis made in our earlier paper that cluster quasars fade to become FR2s, then FR1s, on a timescale of 0.9 Gyr (for H 0 = 50 km s À1 Mpc À1 ).