Technical Notes - A Rationalization of the Oxygen Solid Solubility in Some Transition Metals

THE Hume-Rothery rule relating the relative sizes of the solvent and solute atoms in a substitutional solid solution for moderate to extensive solubility is, of course, well known and much used in the design of alloys. No such rule has been obtained for interstitial solid solutions, although a qualitatively similar relationship would be expected. Among the most common interstitial elements, oxygen, carbon, and nitrogen which can dissolve in important amounts in the transition metals, only in the case of oxygen is there enough solubility data available for an examination of the possibilities of a simple relationship between the extent of solubility and the properties of the metal solvents. Three properties were examined: 1—size of the octahedral space V into which oxygen atoms fit, 2— the elastic modulus E, and 3—the free energy ?F of formation of a low oxide, such as is known to be, or would be expected to be, in equilibrium with the terminal solid solution. The size factor or octahedral volume is so closely associated with the well known Hume-Rothery con- cept of size factor that additional development of this subject is hardly necessary. The octahedral volume used was not corrected to an elevated temperature, as this correction would have made no significant difference. The second factor, Young's modulus E, must be considered, since it is a measure of the strain energy required to force neighboring atoms apart so that an oxygen atom may enter the octahedral volume. The temperature dependence of the elastic modulus of many metals has been reported by Köster,1 but for a rather limited temperature range. Since the