  We present an investigation of the phase diagram of cholesteric liquid
crystals within the framework of Landau - de Gennes theory. The free energy is
modified to incorporate all three Frank elastic constants and to allow for a
temperature dependent pitch in the cholesteric phase. It is found that the
region of stability of the cubic blue phases depends significantly on the value
of the elastic constants, being reduced when the bend elastic constant is
larger than splay and when twist is smaller than the other two. Most
dramatically we find a large increase in the region of stability of blue phase
I, and a qualitative change in the phase diagram, in a system where the
cholesteric phase displays helix inversion.
