Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
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