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
Vapor–liquid–solid method the metal droplet). More specifically, Δµ is the difference between the chemical potential of the depositing species (Si in the above example) in the vapor and solid whisker phase. Δµ is the initial difference proceeding whisker growth (when formula_7), while formula_8 is the atomic volume of Si and formula_9 the specific free energy of the wire surface. Examination of the above equation, indeed reveals that small diameters (formula_10100 nm) exhibit small driving forces for whisker growth while large wire diameters exhibit large driving forces. Involves the removal of material from metal-containing solid targets by irradiating the surface with high-powered (~100