Surface Conduction Theory and the Farnell-Chanter Counts

Abstract

This quantitative theory of the emulsion and the mechanisms of exposure and development is based on Tamm's quantum-mechanical theory of surface conduction. Photo-electrons fall from the conduction band into one or other of two conducting surfaces—that of the silver halide crystal and that of an adsorbed layer of silver iodide—giving rise respectively to the internal and external images. Directly two electrons are present in a surface a “sub-centre” is produced which can be augmented by further electrons acting singly. In the case of the external image one electron suffices to“build-up” the sub-centre to a readily developed “centre”: but access to the sub-centre is not immediate. Several sub-centres, slow to develop, may be formed before a centre appears, causing high intensity reciprocity failure. Low intensity reciprocity failure is attributed to the presence in the colloid of sub-microscopic crystals, the surface of each acting as a single electron trap. The loss in this manner of a final electron has no influence on reciprocity failure.The mechanism of external development resembles that of exposure, the electrons being derived from and lost to the developer ions. The effective concentration of the developer is proportional to the area of the grain, hence uniform development con be achieved only when the size range of the grains is small. Equations are derived which predict the behaviour of an emulsion in terms of the grain form and size distribution and of three emulsion parameters. The equations are too numerous for numerical solution except by computer. Using approximations the theory is found to be in good agreement with the Farnell-Chanter counts though one emulsion raises unsolved problems.