  A neutron star in binary orbit with a low-mass non-degenerate companion
becomes a source of x-rays with millisecond variability when mass accretion
spins it up. Centrifugally driven changes in density profile may initiate a
phase transition in a growing region of the core parallel to what may take
place in an isolated millisecond pulsar, but in reverse. Such a star will spend
a longer time in the spin frequency range over which the transition occurs than
elsewhere because the change of phase, paced by the spinup rate, is accompanied
by a growth in the moment of inertia. The population of accreters will exhibit
a clustering in the critical frequency range. A phase change triggered by
changing spin and the accompanying adjustment of moment of inertia has its
analogue in rotating nuclei.
