The dominating crystalline phase was delta–gamma alumina (δ-phase and γ-phase),

Thanks for your answer, you mean the natural clay contains both δ-phase and γ-phase Alumina?

How is it after clacination at around 800 C?

After heating the clay to 800°C, there is no pure Al2O3 in it, but chemical compounds in the system Al2O3-SiO2-Fe2O3, naturally with several other impurities.

Whether pure Al2O3 (in whatever form) exists within natural clay prior to heating is very questionable.

Thanks Vadim Verlotski for your answer, as I found, there is no free Alumina regarding clay to discuss its phase.

But if we deal with alumina itself, it will be alumina gamma phase after calcination at 800C.

800°C is not enough to convert gamma Al2O3 completely into alfa Al2O3, part of the gamma phase is retained. You need over 900°C to get 100% alpha phase.

I think this paper will help you:

H. Feng, H. Wang, z. Ma, S. Wang, P. Lin. Quantification of surface orientation on the stability of gamma-Al2O3 with different morphologies, Applied Surface Science, 594(2022)153509.

I think this paper will help you:

H. Feng, H. Wang, z. Ma, S. Wang, P. Li. Quantification of surface orientation effect on the thermal stability of gamma-Al2O3 with different morphologies//Applied Surface Science 594(2022)153509.