  In this paper, we take into account black hole solutions of
Brans-Dicke-Maxwell theory and investigate their stability and phase transition
points. We apply the concept of geometry in thermodynamics to obtain phase
transition points and compare its results with those, calculated in canonical
ensemble through heat capacity. We show that these black holes enjoy second
order phase transitions. We also show that there is a lower bound for the
horizon radius of physical charged black holes in Brans-Dicke theory which is
originated from restrictions of positivity of temperature. In addition, we find
that employing specific thermodynamical metric in the context of geometrical
thermodynamics, yields divergencies for thermodynamical Ricci scalar in places
of the phase transitions. It will be pointed out that due to characteristics
behavior of thermodynamical Ricci scalar around its divergence points, one is
able to distinguish the physical limitation point from the phase transitions.
In addition, the free energy of these black holes will be obtained and its
behavior will be investigated. It will be shown that the behavior of the free
energy in the place where the heat capacity diverges, demonstrates second order
phase transition characteristics.
