Lithium as an investment increased tendency for costlier components to be targeted for replacement by new technologies. Current projections of the global market for lithium-ion batteries range from $26 billion in 2023 ("Navigant Research") to a very optimistic $33 billion in 2019 ("Transparency Market Research"). Lithium metal is an extremely soft, highly reactive, and flammable element. It is most frequently found in deposits such as spodumene and pegmatite minerals, with larger resources in the U.S., Canada, Australia, China, Zimbabwe, and Russia. Lithium possesses a unique chemical profile making it the lightest metal in the periodic table and the least dense solid element. Its atomic
Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the