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In a 1-D diatomic lattice, the dispersion relation for lattice vibration is given by:
$\omega =\surd( \beta (1/M + 1/m)+\beta(\surd(1/M + 1/m)^2 -4sin^2ka/Mm))$
$v = \omega/k$
gives the phase velocity.
At $ka = 0$(zone center), the phase velocity comes out to be infinity.
is this correct?
the group velocity is zero as there is a local maxima in the zone center.
It is a standing wave ($v_{\rm group}=0$) of infinite wavelength with a finite frequency. So yes, the phase velocity is also infinite.
