Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
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