calcium carbonate

Hi Hector
First, if you are wishing to make a more transparent, yet properly bound paint by adding some form of calcium carbonate, you should really mull the calcium carbonate up into your chosen drying oil to a loose consistency and add this to your paint. Simply adding calcium carbonate to your paint will only make it leaner but would also make it slightly more opaque. Adding too much calcium carbonate in dry form to your paint would result in a film that is underbound, and may be prone to powdering, sensitivity to solvents, and even delamination.
As to the type of calcium carbonate, while they would all be chemically identical, and would in theory be capable of making a well bound paint that was more transparent, it is really the particle size and shape that contributes interesting handling properties. Only you can decide which are of interest to you. I know that ground calcite is popular but I am not sure about the particular grind commonly used and how that will influence paint handling. I have not personally performed a ton of experimentation using different CaC03 powders to influence handling but I know others have and hopefully they will chime in with suggestions.
A related question was rather fully discussed here on MITRA and that thread may be of interest to you.
https://www.artcons.udel.edu/mitra/forums/question?QID=111
The following thread is only peripherally on topic, but you may find the later portions of interest.
https://www.artcons.udel.edu/mitra/forums/question?QID=174
All the best

The intention is to mix the chalk with oils, correct? Mixing calcium carbonate (or any absorbent filler) with acrylics can significantly affect film strength.

Calcium carbonate derived from different mineral sources behave differently in paint. The material can be ground from limestone, a sedimentary rock formed in sea beads or alluvial deposits; or marble, which is limestone that has undergone heat and pressure below the earth’s crust; or chalk, a light, low structure material normally associated with the sedimentary deposition of the shells of such minute marine organisms as foraminifera, coccoliths and rhabdoliths. The particle structure and chemical behavior of these variations of calcite all differ slightly.
The particle size and shape of calcite in regards to the behavior and performance of paint are important for several reasons. One is the viscosity of the paint, which is related to the volume occupied by the dispersed solids within the paint vehicle.

Another consideration of the influence of particle size and shape on the behavior of paint is the surface area of the particle. The amount of paint binder required by a pigment to form a paste paint is called its oil absorption (OA) number. The greater the surface area of the particle, the more binder it demands to make into a paste or flowing paint. Synthetic (precipitated) calcium carbonate that consists of 0.05 micron needle-shaped particles has more surface area than the particles of ground limestone of the same size, which have simple structures resembling rhomboidal crystals. Because of the complex surface of the precipitated calcium carbonate, it will tend to scatter more light and consequently appear more opaque than the ground limestone particles. However, it is likely that this precipitated calcium carbonate will consume considerably more binder than the ground limestone.
Selecting the right type of calcite, taking into consideration particle size and shape, brightness, chemical constituents, and surface treatment are important factors when it comes to making paint or oil painting mediums.

​Thanks George.