PART XI – November 1967 - Papers - The Limitation of Autoradiography as a Technique to Measure Grain Boundary Segregation

In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Because of this limited success, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. As a result of these calculations, it was concluded that autoradiograPhy is a rather insensitive technique to measure grain boundary segregation. The range (energies) of the emitted particles (ß and a) must be low, and the concentration of the radioactive speczes at the grain boundary must be (in general) two or three orders of magnitude greater than the concentration within the grain. Because of these very restricted conditions , the limited success of the technzque is not surprising. In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Sulfur segregation in iron1 and possibly polonium segregation in Pb-5 pct B1 2 alloys are the only autoradi-ography experiments that have demonstrated segregation to grain boundaries in metals without the formation of a second phase. Segregation to a boundary without the formation of a second phase is often called Gibbs' absorption and is discussed by McLean in Chapter 5 of Ref. 10. There are several394 experiments showing grain boundary diffusion of a radioisotope, but this type experiment is not representative of equilibrium between the concentration of an element at a grain boundary and that in bulk, so it will not be discussed in this paper. In an attempt to determine if temper embrittle ment of low-alloy steels was associated with segregation of antimony to grain boundaries, a program to use auto-radiography (using Sb-125) was initiated. Even though other measurements strongly suggest that segregation is occurring during embrittlement, no evidence of grain boundary segregation was observed in the auto-radiography experiments. An attempt was also made to detect segregation of carbon (using C-14) to grain boundaries in iron during slow cooling. There is again strong indirect evidence7 that segregation occurs during such a treatment, but the autoradiography experiment gave no evidence of such segregation. Because of the failure of these experiments and the general lack of success by our metallographic unit in measuring grain boundary segregation using autoradi-ography, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. MODEL SYSTEM The model system is illustrated in Figs. 1 and 2. It is a semi-infinite bicrystal with a single grain boundary perpendicular to the top face. The width of the grain boundary, W, is defined as the region to which segregation has occurred and it is assumed that this region is of constant composition. The assumption of an infinite dimension is for mathematical reasons but the results of such an analysis (as will be demonstrated later) are valid for even very small specimens. It also is assumed that the measurement is not limited by means of detecting the radiation (photographic emulsions, counters, and so forth) but that the means of detecting radiation is linearly sensitive to the radiation and has infinite resolving power. The distance y is the perpendicular distance from the center of the grain boundary to the point at which the background radiation is measured and x is the integration variable. CALCULATION FOR BETA PARTICLES Two values of the intensity of radiation will be calculated, the intensity at the center of the grain boundary and the intensity far from the grain boundary. The radiation at the center of the grain boundary can be calculated in the following way. Assume a grain boundary of width W having a uniform concentration equal to Cgb + Cb where CGb is the excess concentration of the element under consideration at the grain boundary and Cb is the bulk concentration. The intensity of radiation, IgB, at the center of the grain boundary, is a consequence of the amount of radioactive material, decay rate, absorption, and geometrical factors which can be represented mathematically by the following expression: