The standard primary ingredient included in most powders that are referred to as "mineral makeup." The claim for bismuth oxychloride (which is also known as synthetic pearl) is that it is all-natural and better for skin than talc. In fact, in many ways talc is a purer ingredient than bismuth oxychloride. Bismuth oxychloride, which seldom occurs in nature, is manufactured by combining bismuth, a by-product of lead and copper metal refining, with chloride (chlorine compound) and water. It's used in cosmetics because it has a distinct shimmery, pearlescent appearance and a fine white powder texture that adheres well to skin. Bismuth oxychloride is heavier than talc. Pure bismuth is a naturally occurring, grayish-white powder. It and its derivatives are used as skin protectives, thickeners, and absorbent agents. Bismuth oxychloride was permanently listed by the FDA as a coloring agent in 1977 and as a synthetic ingredient.
Some people react to bismuth oxychloride due to its unique crystalline structure. What happens is that the crystals can "poke" at skin and get stuck in the pores, where the sharper "spokes" can cause sensitivity. This is more of a problem when bismuth oxychloride is the main ingredient in powder makeup.
References for this information:
The International Cosmetic Ingredient Dictionary and Handbook, Eleventh Edition, 2006