You will find below a helpful article about the in stone casting process as well as which stones are suitable for stone casting or not and why?

Introduction 

Not all types of stones are suited for an in stone place casting method- Diamonds excepted , stone minerals are not good conductors of heat, they can suffer shock during rapid heat or cooling.

Up to 2mm diameter cooling and quenching of the flask after casting,it is the most critical stage for thermal shock to stones, the larger the stone the more care is needed. In order for the stone to remain set in the casting and not be placed under excess stress ,its dimensions should match as closely as possible those of the jewelry piece that has been designed. There will always be slight variations in the size of the stone but by using calibrated stones this variation should be minimized. 

As said before not  all stones can be used for example Amethysts and citrine change colour when they are exposed to temperatures over 350 degree Celsius ( 662F), even certain widely available  stones ( topaz) may lose their color. Peridot  does not change colours but it is very sensitive to acids or pickling solutions and these operations will dull its polish.