  We examined the morphology-density relations for galaxy samples selected by
luminosity and by mass in each of five massive X-ray clusters from z=0.023 to
0.83 for 674 spectroscopically-confirmed members. Rest-frame optical colors and
visual morphologies were obtained primarily from Hubble Space Telescope images.
Morphology-density relations (MDR) are derived in each cluster from a complete,
luminosity-selected sample of 452 galaxies with a magnitude limit M_V <
M^{*}_{V} + 1. The change in the early-type fraction with redshift matches
previous work for massive clusters of galaxies. We performed a similar
analysis, deriving MDRs for complete, mass-selected samples of 441 galaxies
with a mass-limit of 10^{10.6} M_{\sun}. Our mass limit includes faint objects,
the equivalent of =~1 mag below L^{*} for the red cluster galaxies, and
encompasses =~70% of the stellar mass in cluster galaxies. The MDRs in the
mass-selected sample at densities of Sigma > 50 galaxies Mpc^{-2} are similar
to those in the luminosity-selected sample but show larger early-type
fractions. However, the trend with redshift in the fraction of elliptical and
S0 galaxies with masses > 10^{10.6} M_{\sun} differs significantly between the
mass- and luminosity-selected samples. The clear trend seen in the early-type
fraction from z=0 to z=~ 0.8 is not found in mass-selected samples. The
early-type galaxy fraction changes much less, and is consistent with being
constant at 92% +/- 4% at \Sigma> 500 galaxies Mpc^{-2} and 83 +/- 3% at 50 <
\Sigma < 500 galaxies Mpc^{-2}. This suggests that galaxies of mass lower than
> 10^{10.6} M_{\sun} play a significant role in the evolution of the early-type
fraction in luminosity-selected samples. (Abstract abridged)
