These pretty lavender colored blue gemstone cabochons are called Blue Chalcedony from Turkey.
Chalcedony (kal SED' nee) is considered a semi precious gemstone and is any form of microcrystalline quartz , where the crystals are too small to be seen without high magnification.
However, in the rock world, only the translucent or transparent, single color types are usually named "chalcedony". Patterned stones are usually called agates or jaspers.
Chalcedony stone is mentioned in the bible as one of the twelve types of gemstones set in the foundation of the Jerusalem Wall.
The name probably comes from Chalcedon or Calchedon, an ancient port city on the Sea of Marmara in modern-day Turkey. Chalcedony cabochons usually have a waxy luster and a hardness of 7. They are tough cabochon stones, good for all jewelry and require no special care in wearing or cleaning.
Metaphysical Properties of Blue Chalcedony: Blue Chalcedony gemstones are said to restore calm and balance.