Yes, some smaller stars have no radiative zone, only convective.
Some larger stars have only radiative zone, no convective zone.
The radiative zone is characterized by the inability of atomic nuclei to hold onto any electrons, thus it is a transparent medium, easy for photons to move around.
At the tachocline it becomes cool enough for some atoms to form, larger nuclei taking on an electron or two. This renders the medium opaque. At the tachocline the opacity suddenly raises by a factor of 100.
Below the tachocline, in the radiative zone, heat flows by radiation, heat travels freely upwards heating the upper layers. The lower edge of the radiative zone, at .2R, is 7 million Kelvin, dropping to 2 million Kelvin at the top of the zone at .7R. The temperature gradient is less than the adiabatic lapse rate. Adiabatic lapse rate is how much a parcel cools off by expansion as it rises a certain distance (assuming no heat transfer into or out of [thus adiabatic]). Take a parcel, raise it up, let it cool and you find it is cooler than the medium around it, not warmer. Basically the same as a temperature inversion on Earth puts a lid on a cumulus cloud.
I'll keep reading up on it.