  We model the synthesis of molecules and dust in the inner wind of the
oxygen-rich Mira-type star IK Tau, by considering the effects of periodic
shocks induced by the stellar pulsation on the gas, and by following the
non-equilibrium chemistry in the shocked gas layers between 1 and 10 Rstar. We
consider a complete set of molecules and dust clusters, and combine the
nucleation phase of dust formation with the condensation of these clusters into
dust grains. Our derived molecular abundances and dust properties are compared
to the most recent observational data. The chemistry is described by using a
chemical kinetic network of reactions and the condensation mechanism is
described by a Brownian formalism. The shocks drive an active non-equilibrium
chemistry in the dust formation zone of IK Tau where the collision destruction
of CO in the post-shock gas triggers the formation of C-bearing species such as
HCN and CS. Most of the modelled molecular abundances agree well with the
latest values derived from Herschel data. Clusters of alumina are produced
within 2 Rstar and lead to a population of alumina grains close to the stellar
surface. Clusters of silicates form at larger radii (r > 3 Rstar), where their
nucleation is triggered by the formation of HSiO and H2SiO. They efficiently
condense and reach their final grain size distribution between ~ 6 and 8 Rstar,
with a major population of medium size grains peaking at~ 0.02 microns. This
two dust-shell configuration agrees with recent interferometric observations.
The derived dust-to-gas mass ratio for IK Tau is in the range 1-6x10^-3 and
agrees with values derived from observations of O-rich Mira-type stars. Our
results confirm the importance of periodic shocks in chemically shaping the
inner wind of AGB stars and providing gas conditions conducive to the efficient
synthesis of molecules and dust by non-equilibrium processes.
