Diffusion bonding or diffusion welding is a solid-state welding technique used in metalworking, capable of joining similar and dissimilar metals. It operates on the principle of solid-state diffusion, wherein the atoms of two solid, metallic surfaces intersperse themselves over time. This is typically accomplished at an elevated temperature, approximately 50-70% of the absolute melting temperature of the materials. Diffusion bonding is usually implemented by applying high pressure, in conjunction with necessarily high temperature, to the materials to be welded; the technique is most commonly used to weld 'sandwiches' of alternating layers of thin metal foil, and metal wires or filaments. Currently, the diffusion bonding method is widely used in the joining of high-strength and refractory metals within the aerospace and nuclear industries. Diffusion bonding or diffusion welding is a solid-state welding technique used in metalworking, capable of joining similar and dissimilar metals. It operates on the principle of solid-state diffusion, wherein the atoms of two solid, metallic surfaces intersperse themselves over time. This is typically accomplished at an elevated temperature, approximately 50-70% of the absolute melting temperature of the materials. Diffusion bonding is usually implemented by applying high pressure, in conjunction with necessarily high temperature, to the materials to be welded; the technique is most commonly used to weld 'sandwiches' of alternating layers of thin metal foil, and metal wires or filaments. Currently, the diffusion bonding method is widely used in the joining of high-strength and refractory metals within the aerospace and nuclear industries. The act of diffusion welding is centuries old. This can be found in the form of 'filled gold,' a technique used to bond gold and copper for use in jewelry and other applications. In order to create filled gold, smiths would begin by hammering out an amount of solid gold into a thin sheet of gold foil. This film was then placed on top of a copper substrate and weighted down. Finally, using a process known as 'hot-pressure welding' or HPW, the weight/copper/gold-film assembly was placed inside an oven and heated until the gold film was sufficiently bonded to the copper substrate. Modern methods were described by the Soviet scientist N.F. Kazakov in 1953. Diffusion bonding involves no liquid fusion, and often no filler metal. No weight is added to the total, and the join tends to exhibit both the strength and temperature resistance of the base metal(s). The materials endure no, or very little, plastic deformation. Very little residual stress is introduced, and there is no contamination from the bonding process. It may be performed on a join surface of theoretically any size with no increase in processing time; practically speaking, the surface tends to be limited by the pressure required and physical limitations. It may be performed with similar and dissimilar metals, reactive and refractory metals, or pieces of varying thicknesses. Diffusion bonding is most often used for jobs either difficult or impossible to weld by other means, due to its relatively high cost. Examples include welding materials normally impossible to join via liquid fusion, such as zirconium and beryllium; materials with very high melting points such as tungsten; alternating layers of different metals which must retain strength at high temperatures; and very thin, honeycombed metal foil structures. Steady state diffusion is determined by the amount of diffusion flux that passes through the cross-sectional area of the mating surfaces. Fick's first law of diffusion states: where J is the diffusion flux, D is a diffusion coefficient, and dC/dx is the concentration gradient through the materials in question. The negative sign is a product of the gradient. Another form of Fick's law states: where M is defined as either the mass or amount of atoms being diffused, A is the cross-sectional area, and t is the time required. Equating the two equations and rearranging, we achieve the following result: