Calculations of the energy and migration characteristics of carbon and nitrogen in α-iron and vanadium

Abstract

Various properties of carbon and nitrogen in iron, and nitrogen in vanadium have been investigated with the aid of computer techniques. The metal-metal interaction, represented by a two-body central force which matches the elastic moduli, is sharply repulsive at close separation, and goes to zero midway between the second and third neighboring atoms. 531 atoms surrounding the defect were treated as individual particles, while the remainder of the crystal was treated as an elastic continuum with atoms imbedded in it. The iron-carbon interaction was represented by a cubic equation with the parameters chosen to yield the experimental value for the carbon migration energy, the activation volume (effectively zero), and the binding energy of a carbon atom to a vacancy. With this model the approximate experimental value of the energy of a carbon atom in solution in iron relative to Fe 3C was obtained. The model also gives the correct relaxation strength for internal friction, but does not reproduce closely the formation volume. The migration path for carbon, on the basis of this calculation, is a straight line from octahedral to octahedral position with the tetrahedral position as the saddle point. The behavior of nitrogen in iron is almost identical. The same method of calculation for nitrogen in vanadium reproduced closely the sizable experimental activation volume for this system. Some calculations of di-carbon formation and motion are also reported.