I recently published a review paper about the effect of sulfates on cement hydration and properties (setting time, rheology, phase assemblage, and compressive strength). Take a look, it may help:
Article Effects of sulfates on the hydration of Portland cement -A review
Unfortunately, I did not talk specifically about barium sulfate.
Dear Hamdy A. Abdel-Gawwad thank you for asking this interesting technical question. We work in the field of organometllic chemistry, so I would not call myself a proven expert in this area. However, I came across a potentially useful reference which might help you in your analysis:
The influence of barium sulphate and barium carbonate on the Portland cement
(see attached pdf file)
Also please take a look at the following closely related article:
Hydration of clinkers doped with baryte with and without addition of gypsum
Article Hydration of clinkers doped with baryte with and without add...
Unfortunately this paper has not been posted as public full text on RG. However, it has been published just two years ago. So you could try to request the full text directly from the authors.