Institute of Metals Division - Solubility and Diffusion of Titanium in Iron

The investigation of solid-state diffusion phenomena may lead to much information concerning binary alloys. In particular, a study of the concentration gradients present in multiphase diffusion couples can lead to the determination of the solubility limits of the single-phase fields in the phase diagram. The specific concentration gradient which results from the heat treatment of a diffusion couple depends not only upon the time and temperature of diffusion, but also upon the number of phases existing in equilibrium at the diffusion temperature. Such concentration gradients possess sharp discontinuities whose terminal points correspond to the solubilities existing at the limits of the two-phase field in the phase diagram at the diffusion temperature. In general, there will be a discontinuity in the concentration curve for each two-phase field which exists in the phase diagram between the concentration limits of the couple. A number of investigators have analyzed the gradients present in multiphase diffusion couples. 1-8 The iron-titanium phase diagram exhibits a y loop in the temperature range from 900" to 1400°C, and the limit of the a + y field lies at some composition which is less than 1 wt pct Ti for any temperature. It was felt that a diffusion study could yield values not only for the diffusion coefficients involved, but also for the chemical solubilities in the phase diagram. The concentration gradients were analyzed by an X-ray absorption technique developed by Ogilvie.6 The absorption of a monochromatic X-ray beam is measured in steps parallel to the diffusion direction and the resulting intensity gradients are transformed into concentration gradients by applying the laws of X-ray absorption in a binary system. This technique has been applied by ogilvie6 to the systems Ni-Au, Cu-Au, Fe-Cr, and Ni-Cr; by Gelles7 to the systems Be-Fe, and Be-Ni and by Hilliarde to the system Al-Zn. Linear X-Ray Absorption Analysis—The use of X-ray absorption analysis as a tool for determining concentration gradients arises from the fact that the beam is absorbed according to the quantity and species of elements present in the sample and not according to their state of aggregation. This method is more advantageous than the chemical analysis of machined layers since it is less time consuming and less expensive and can analyze a very small area. IF a homogeneous binary alloy (A + B) is analyzed with two different monochromatic X-ray beams I0(2) and lo(2) the following relation between the transmitted intensities, the intrinsic absorption coefficients of A and B for the two different radiations and the weight fraction of each element may be derived.' In (I/Io) (a+b) xa(u/p)a(2) + xb(u/p)8(2) Eq. [1] is independent of specimen thickness and density, but requires that either element A or B possess an absorption edge between the wavelength limits of the two monochromatic beams. I, is evaluated for each radiation by measuring the transmitted intensity through a varying number of foils of a suitable absorber. A plot of the natural logarithm of the transmitted intensity as a function of the number of foils, when extrapolated to zero foils, yields the value of I,. If a plot of the ratio in Eq. [ I] is calculated as a function of xA, then a master curve results. From