Systems and methods for providing in situ, controllably variable concentrations of one, two or more chemical components on a substrate to produce an integrated materials chip. The component concentrations can vary linearly, quadratically or according to any other reasonable power law with one or two location coordinates. In one embodiment, a source and a mask with fixed or varying aperture widths and fixed or varying aperture spacings are used to produce the desired concentration envelope. In another embodiment, a mask with one or more movable apertures or openings provides a chemical component flux that varies with location on the substrate, in one or two dimensions. In another embodiment, flow of the chemical components through nuzzle slits provides the desired concentrations. An ion beam source, a sputtering source, a laser ablation source, a molecular beam source, a chemical vapor deposition source and / or an evaporative source can provide the chemical component(s) to be deposited on the substrate. Carbides, nitrides, oxides, halides and other elements and compounds can be added to and reacted with the deposits on the substrate.