A theoretical formula for the solubility of hydrogen in metals

Abstract

1— In certain metals such as Cu, hydrogen appears to be dissolved in the metal in the form of free protons, which do not affect the normal metal lattice, even when present at very considerable concentrations. In other metals such as Ti, definite metal hydrides are formed which have a different lattice structure from the pure metal. The metal Pd is intermediate since the hydrogen affects the lattice constant. It is the properties of the former group of metals which are first to be discussed here, since the fact that the normal metal lattice is (practically) unaffected seems to justify a very simple theoretical treatment of the solubility, and it is of some interest to examine how the theory compares with the facts. We shall find that we can bring the facts and the theory into satisfactory order together. The various types of solubility curve are shown in fig. 1. 2— From evidence such as the well-known p 1/2 law for the rate of diffusion of hydrogen through metals we may certainly assume that the hydrogen in the metal is atomic. For the present we shall neglect the difference between atoms of hydrogen and protons plus electrons, and merely assume that the atoms are present as such in the metal, without specific interaction with particular metallic atoms; the metal merely provides a region in which hydrogen atoms can exist and move in a definite field of potential energy. Specific contributions by the electrons of the hydrogen atoms will be considered later, when the hydrogen atoms in the metal will be considered as protons plus electrons.