  To investigate the relationships between dynamical status and other important
characteristics of galaxy clusters, we conducted a study of X-ray cluster
morphology using a sample of 101 clusters at redshift z=0.05-1 taken from the
Chandra archive. The X-ray morphology is quantitatively characterized by a
series of objectively measured simple statistics of the X-ray surface
brightness distribution, which are designed to be robust against variations of
image quality caused by various exposure times and various cluster redshifts.
We found: (1) The distorted and non-distorted clusters occupy well-defined loci
in the L-T plane, demonstrating the measurements of the global luminosity and
temperature for distorted clusters should be interpreted with caution, or
alternatively, a rigorous morphological characterization is necessary when we
use a sample of clusters with heterogeneous morphological characteristics to
investigate the L-T or other related scaling relations. (2) Ellipticity and
Off-center show no evolutionary effects between high and low redshift cluster
subsets, while there may be a hint of weak evolutions for the Concentration and
Asymmetry, in such a way that high-z clusters show more distorted morphology.
(3) No correlation is found between X-ray morphology and X-ray luminosity or
X-ray morphology and X-ray temperature of clusters, implying that interaction
of clusters may not enhance or decrease the luminosity or temperature of
clusters for extended period of time.
